M 


SMITHSONIAN   MISCELLANEOUS  COLLECTIONS 

VOLUME  63,   NUMBER  6 


SMITHSONIAN 

PHYSICAL  TABLES 


SIXTH  REVISED  EDITION 


PREPARED  BY 

FREDERICK   E.    FOWLE 

AID,  SMITHSONIAN   ASTROPHYSICAL  OBSERVATORY 


(PUBLICATION    2269) 


CITY  OF  WASHINGTON 

PUBLISHED  BY  THE  SMITHSONIAN  INSTITUTION 
1914 


Engineering 
Library 


ADVERTISEMENT. 

In  connection  with  the  system  of  meteorological  observations  established  by 
the  Smithsonian  Institution  about  1850,  a  series  of  meteorological  tables  was 
compiled  by  Dr.  Arnold  Guyot,  at  the  request  of  Secretary  Henry,  and  the  first 
edition  was  published  in  1852.  Though  primarily  designed  for  meteorological 
observers  reporting  to  the  Smithsonian  Institution,  the  tables  were  so  widely  used 
by  physicists  that  it  seemed  desirable  to  recast  the  work  entirely.  It  was  decided 
to  publish  three  sets  of  tables,  each  representative  of  the  latest  knowledge  in  its 
field,  and  independent  of  one  another,  but  forming  a  homogeneous  series.  The 
first  of  the  new  series,  Meteorological  Tables,  was  published  in  1893,  tne  second, 
Geographical  Tables,  in  1894,  and  the  third,  Physical  Tables,  in  1896.  In  1909 
yet  another  volume  was  added,  so  that  the  series  now  comprises  :  Smithsonian 
Meteorological  Tables,  Smithsonian  Geographical  Tables,  Smithsonian  Physical 
Tables,  and  Smithsonian  Mathematical  Tables. 

The  fourteen  years  which  had  elapsed  in  1910  since  the  publication  of  the  first 
edition  of  the  Physical  Tables,  prepared  by  Professor  Thomas  Gray,  had  brought 
such  changes  in  the  material  upon  which  the  tables  must  be  based  that  it  became 
necessary  to  make  a  radical  revision  for  the  5th  revised  edition  issued  in  1910. 
That  revision  has  been  still  further  continued  for  the  present  sixth  edition. 

CHARLES  D.  WALCOTT, 
Secretary  of  the  Smithsonian  Institution. 
June,  1914. 


PREFACE   TO   THE   STH    REVISED   EDITION. 

The  present  Smithsonian  Physical  Tables  are  the  outcome  of  a  radical  revision 
of  the  set  of  tables  compiled  by  Professor  Thomas  Gray  in  1896.  Recent  data 
and  many  new  tables  have  been  added  for  which  the  references  to  the  sources 
have  been  made  more  complete;  and  several  mathematical  tables  have  been 
added,  — some  of  them  especially  computed  for  this  work.  The  inclusion  of  these 
mathematical  tables  seems  warranted  by  the  demand  for  them.  In  order  to  pre- 
serve a  uniform  change  of  argument  and  to  facilitate  comparison,  many  of  the 
numbers  given  in  some  tables  have  been  obtained  by  interpolation  in  the  data 
actually  given  in  the  papers  quoted. 

Our  gratitude  is  expressed  for  many  suggestions  and  for  help  in  the  improve- 
ment of  the  present  edition  :  to  the  U.  S.  Bureau  of  Standards  for  the  revision  of 
the  electrical,  magnetic,  and  metrological  tables  and  other  suggestions  ;  to  the 
U.  S.  Coast  and  Geodetic  Survey  for  the  revision  of  the  magnetic  and  geodetic 
tables ;  to  the  U.  S.  Geological  Survey  for  various  data ;  to  Mr.  Van  Orstrand  for 
several  of  the  mathematical  tables ;  to  Mr.  Wead  for  the  data  on  the  musical 
scales ;  to  Mr.  Sosman  for  the  new  physical-chemistry  data  ;  to  Messrs.  Abbot, 
Becker,  Lanza,  Rosa,  and  Wood ;  to  the  U.  S.  Bureau  of  Forestry  and  to  others. 
We  are  also  under  obligation  to  the  authors  and  publishers  of  Landolt-Bornstein- 
Meyerhoffer's  Physikalisch-chemische  Tabellen  (1905)  and  B.  O.  Peirce's  Mathe- 
matical Tables  for  the  use  of  certain  tables. 

It  is  hardly  possible  that  any  series  of  tables  involving  so  much  transcribing, 
interpolation,  and  calculation  should  be  entirely  free  from  errors,  and  the  Smith- 
sonian Institution  will  be  grateful,  not  only  for  notice  of  whatever  errors  may  be 
found,  but  also  for  suggestions  as  to  other  changes  which  may  seem  advisable  for 
later  editions. 

F.  E.  FOWLE. 

ASTROPHYSICAL  OBSERVATORY 

OF  THE  SMITHSONIAN  INSTITUTION, 

June,  1910 

PREFACE   TO   THE   6xn   REVISED   EDITION. 

The  revision  commenced  for  the  fifth  edition  has  been  continued ;  a  large  pro- 
portion of  the  tables  have  been  rechecked,  typographical  errors  corrected,  later 
data  inserted  and  many  new  tables  are  added,  including  among  others  a  new  set  of 
wire  tables  from  advance  sheets  courteously  given  by  the  Bureau  of  Standards, 
new  mathematical  tables  computed  by  Mr.  Van  Orstrand  and  those  on  Rontgen 
rays  and  radioactivity.  The  number  of  tables  has  been  increased  from  335  to 
over  400.  We  express  our  gratitude  to  the  Bureau  of  Standards,  to  the  Geophysical 
Laboratory,  the  Geological  Survey,  and  to  those  who  have  helped  through  sug- 
gested improvements,  new  data,  or  by  calling  our  attention  to  errors  in  the  earlier 
editions. 

F.  E.  FOWLE. 
ASTROPHYSICAL  OBSERVATORY 
OF  THE  SMITHSONIAN  INSTITUTION, 
October,  1913. 


TABLE  OF  CONTENTS. 


PAGE 

Introduction  on  units  of  measurement  and  conversion  factors        .         .  xvii 

Units  of  measurement :  general  discussion xvii 

Dimension  formulae  for  dynamic  units xix 

"                 "         "    heat  units xxv 

"          of  electric  and  magnetic  units  :  general  discussion        .        .  xxvii 

"          formulas  in  electrostatic  system xxviii 

"                "         "  electromagnetic  system xxxi 

Practical  units  of  electricity,  legalization  of  .        .        .         .                 .  xxxv 

TABLE 

1.  Formulae  for  conversion  factors  :  (a)  Fundamental  units      ...      2 

(b)  Derived  units  ...       2 

I.  Geometric  and  dynamic  units      2 

II.  Heat  units  ....       3 

III.  Magnetic  and  electric  units      3 

2.  Tables  for  converting  17.  S.  weights  and  measures  : 

(1)  Customary  to  metric 5 

(2)  Metric  to  customary 6 

3.  Equivalents  of  metric  and  British  imperial  weights  and  measures  : 

(1)  Metric  to  imperial 7 

(2)  Multiples,  metric  to  imperial 8 

(3)  Imperial  to  metric         ........      9 

(4)  Multiples,  imperial  to  metric        .         .         .         .         .         .10 

4.  Volume  of  a  glass  vessel  from  weight  of  its  volume  of  water  or  mercury     1 1 

5.  Derivatives  and  integrals 12 

6.  Series 13 

7.  Mathematical  constants 14 

8.  Reciprocals,  squares,  cubes  and  square  roots  of  natural  numbers        .  15 

9.  Logarithms,  1000-2000 24 

10.  Logarithms 26 

11.  Antilogarithms 28 

12.  Antilogarithms,  .9000-1.0000      ........    30 

13.  Circular  (trigonometric)  functions,  argument  (°,  '.)  .        .        .32 

14.  argument  (radians)       .        .        .    37 

15.  Logarithmic  factorials,  n!,  n==  i  to  100 40 

16.  Hyperbolic  functions 41 

17.  Factorials,  1-20 47 


CONTENTS. 


18.  Exponential  functions    .         .  .         .                           .     48 

19.  Values  of  e^  and  e~x  and  their  logarithms  .                  .                           .54 

H  —  n 

20.  "       "  e?  and  *"*"*  "       "             "  ......     55 


21.  "       "  e~*ande4    '  "             ......     55 

22.  "       u  ^  and  e~x  and        "  "           for  fractional  values  of  x     .     56 

23.  Probability  of  errors  of  observations  :  probability  integral      .         .         .56 

24.  "  "           "           "                     "                                  "                         "                                                          's? 

25.  Values  of  0.6745  */-™  •     57 


27.  "          "   0.8453        -T--v     .........      58 


29.  Least-squares  formulae  .........     59 

30.  Inverse  of  probability  integral.     Diffusion     .  .  .60 

31.  Logarithms  of  the  gamma  function  T(«)  for  values  of  n  between  i  and  2     62 

32.  Values  for  the  first  seven  zonal  harmonics  from  6  =  0°  to  0=90°          .     64 

/»- 

33.  Value  for  /  2(i  —  sin20sin2</>)=Bd<l>  for  different  values  of  0 ;  also  the  cor- 

•J     o 

responding  logarithms     .........     66 

34.  Moments  of  inertia,  radii  of  gyration,  corresponding  weights          .         '67 

35.  Strength  of  materials :  (a)  metals          ...  .  .68 

(b)  stones •     .  68 

(c)  brick  ....  ...  68 

(</)  concretes     .......  68 

36.  "         "          "  timber  tests 69 

•37  "          u'         it  n          it  ....  70 

38.  Moduli  of  rigidity          .                           .         .  •     7 1 

39.  Variation  of  the  moduli  of  rigidity  with  the  temperature        .  .     7 1 

40.  Young's  modulus  ......  ....     72 

41.  Compressibility  of  the  more  important  solid  elements  .  .     73 

42.  Hardness •  -73 

43.  Relative  hardness  of  the  elements         ...  -73 

44.  Poisson's  ratio '73 

45.  Elastic  moduli  of  crystals,  formulae        .  ....     74 

46.  "  "       "        "         numerical  results  .         •     75 

47.  Compressibility  of  O,  air,  N,  H  at  different  pressures  and  temperatures     76 

48.  "  "  ethylene          "        "  "  "  "  •     76 

.Q  ((  ((  U  ((  ((  U  «  «  t         H^ 

50.  "  "  carbon  dioxide  at  "  "  "  "  .     77 

51.  "  "  gases,  values  of  a 77 


CONTENTS.  Vll 

52.  Compressibility  of  air  and  oxygen  between  18°  and  22°C      .         .         -77 

53.  Relation  between  pressure,  temperature  and  volume  of  sulphur  dioxide     78 

54.  "  "               "                  "              "          "        "  ammonia           .     78 

55.  Compressibility  of  liquids      .........     79 

56.  "  "  solids .         .80 

57.  Specific  gravities  corresponding  to  the  Baume  scale       .         .         .         .81 

58.  Reduction  of  weighings  in  air  to  vacuo 82 

59.  "          "  densities     "    "    "       "  82 

60.  Densities  of  the  solid  and  liquid  elements      .  .                  -83 

61.  "         "  various  woods    .........     85 

62.  "         "        "        solids 86 

63.  "         "        "        alloys     .  .     87 

64.  "         "        "        natural  and  artificial  minerals         .         .         .         .88 

65.  "         "  molten  tin  and  tin-lead  eutectic 88 

66.  Weight  in  grams  per  square  meter  of  sheet  metal  .         .     89 

67.  "       "  various  common  units  of  sheet  metal     .  ...     89 

68.  Densities  of  various  liquids  .........     90 

69.  "          "        "       gases     ....  ...                  .     91 

70.  "         "        "       aqueous  solutions  of  salts,  bases  and  acids    .         .     92 

71.  Density  of  water  free  from  air  between  o°  and  36°  C    .         .         .         -94 

72.  Volume  of  water  at  temperatures  between  o°  and  36°  C  in  terms  of  its 


volume  at  the  temperature  of  maximum  density 

•     95 

73- 

Density  and  volume  of  water  at  different  temperatures  from-io  to  250° 

C     96 

74- 

"    '     "         "       "  mercury  at  "                   "               "    -10  "  360° 

C     97 

75- 

Densities  aqueous  ethyl  alcohol.     Temp,  variation 

.     98 

76. 

"              "        mixtures  methyl  alcohol,  cane-sugar  or  sulphuric  acid  100 

77- 

Velocity  of  sound  in  solids    ........ 

.    IOI 

78. 

"       "      "  liquids  and  gases  . 

.    102 

79- 

Musical  scales       

•    103 

80. 

«           « 

.    103 

81. 

Acceleration  of  gravity  at  sea  level  and  different  latitudes     . 

.    IO4 

82. 

Results  of  some  of  the  more  recent  gravity  determinations    . 

•    105 

83- 

Value  of  gravity  at  some  of  the  U.  S.  C.  and  G.  Survey  stations   . 

.  106 

84. 

Length  of  seconds  pendulum  for  sea  level  and  different  latitudes 

.  107 

85- 

Determinations  of  the  length  of  the  seconds  pendulum 

.  107 

86. 

Miscellaneous  geodetic  data           ....                  .         . 

.  108 

87. 

Lengths  of  degrees  on  earth's  surface    

.  108 

88. 

Miscellaneous  astronomical  data  - 

.  109 

89. 

Planetary  data       .......... 

.    IIO 

90. 

Equation  of  time  .......... 

.     IIO 

91. 

Miscellaneous  astronomical  data  ....... 

.    IIO 

92. 

Terrestrial  magnetism  :  secular  change  of  decimation  . 

.   in 

93- 

"                 "              dip  or  inclination     ... 

•  JI3 

94. 

"                "              secular  change  of  dip       .... 

•  "3 

95- 

"                 "              horizontal  intensity          .... 

.  114 

96. 

"                "              secular  change  of  horizontal  intensity 

.  114 

Vlii  CONTENTS. 

I 

97.  Terrestrial  magnetism:  total  intensity 115 

98.  "  secular  change  of  total  intensity     .         .         .  115 

99.  agonic  line     .         .         .         .         .         .         .116 

100.  Magnetic  elements  at  magnetic  observatories       .         .         .         .         -117 

101.  Pressure  of  mercury  and  water  columns 118 

102.  Reduction  of  barometer  to  standard  temperature         .        .         .        .119 

103.  "  "         gravity,  inch  and  metric  scales    .  120 

104.  "  "           "         "  latitude  45° :  inch  scale     .        .        .        .121 

105.  "  "          "         "        "        "      metric  scale          .        .        .122 

106.  Correction  of  barometer  for  capillarity :  inch  and  metric  scale     .        .  123 

107.  Volume  of  mercury  meniscus  in  cu.  mm.      .         .         .         .         .         .123 

108.  Aerodynamics:  data  for  wind  pressures      .         .         .         .  .124 

109.  "     "    the  soaring  of  planes     .....  125 

no.     Coefficients  of  friction 126 

in.     Lubricants 126 

112.  "          for  cutting  tools 126 

113.  a  Viscosity  of  water  at  different  temperatures     .....  127 
b  Specific  viscosity  of  water  at  different  temperatures          .        .        .127 

114.  Coefficients  of  viscosity  for  solutions  of  alcohol  in  water     .         .         .  128 

115.  Specific  viscosity  of  mineral  oils 128 

116.  "  various  oils  .         .  .         .        .         .        .  128 

117.  Viscosity  of  various  liquids 129 

118.  "         "        "  "        temperature  variation        ....  130 

119.  Specific  viscosity  of  solutions  :  variation  with  density  and  temperature  131 

120.  "  "         "         "           atomic  concentrations           .         .         .  135 

121.  Viscosity  of  gases  and  vapors 136 

122.  "         "  air  20? 2  C 136 

123.  "  gases  and  vapors,  temperature  variation  .         .         .         -137 

124.  Diffusion  of  an  aqueous  solution  into  pure  water        ....  138 

125.  "  vapors      .  .  139 

126.  "         "  gases  and  vapors      ........  140 

127.  "         "  metals  into  metals .  140 

128.  Solubility  of  inorganic  salts  in  water :  temperature  variation        .         .  141 

129.  "  a  few  organic  salts  in  water :  temperature  variation         .  142 

130.  "  gases  in  water          .         .         .         ,         .         .         .         .  142 

131.  "        ,  change  produced  by  uniform  pressure        ....  143 

132.  Absorption  of  gases  by  liquids 144 

133.  Capillarity  and  surface  tension :  water  and  alcohol  in  air    .        .        .  145 

134.  miscellaneous  liquids  in  air       .         -145 

135.  aqueous  solutions  of  salts  .         .         .  145 

136.  Capillarity  and  surface  tension  :  liquids  in  contact  with  air,  water  or 

mercury .         .        .         .         .         .        .        .         .        .         .         .  1 46 

137.  Capillarity  and  surface  tension  :  liquids  at  solidifying  point  .  146 

138.  "  "          "           "          thickness  of  soap  films      .         .         .146 

139.  Vapor  pressures  .        . 147 

140.  "  "        of  ethyl  alcohol           .        .        .        .        .        .        -149 


CONTENTS.  IX 

141.  Vapor  pressures  of  methyl  alcohol       .  149 

142.  "  "        and  temperatures:  (a)  carbon  disulphide .        .         .  150 

(£)  chlorobenzine        .        .        .  150 
(*r)  bromobenzine        .         .         .  150 

(d)  aniline 150 

(e)  methyl  salicylate  .        .        .  151 
(/)  bromonaphthaline          .         .  151 
(£•)  mercury         .        .        .        .151 

143.  Vapor  pressure  of  solutions  of  salts  in  water 152 

144.  Pressure  of  saturated  aqueous  vapor  at  low  temperature  over  ice        .  154 

145.  "        "        "  "  "     "     "  "  "    water    .  154 

146.  "        "        "  "  "    o°to5o°C          .        .        .        .154 
147-           "        "        "               "  "    50°  to  374°  C       .  .155 

148.  Weight  in  grains  of  aqueous  vapor  in  a  cubic  foot  of  saturated  air       .156 

149.  "       "  grams  "         "  "     "  "      "      meter  of     "          "        .  156 

150.  Hygrometry,  vapor  pressure  in  the  atmosphere 157 

151.  dew-points      .        .        .        .        .         .        .        .        .  158 

152.  Relative  humidity        ..........  160 

153.  Values  of  0.378*?  in  the  atmospheric  pressure  equation  /*  =  .Z?  — 0.378*?  161 

154.  Table  for  facilitating  the  calculation  of  ^760 162 

155.  Logarithms  of  6/760  for  values  of  h  between  80  and  800     .        .        .  162 

156.  Values  of  i+  0.00367  /: 

(a)  for  values  of  t  between  o°  and  10°  C,  by  tenths  .        .        .164 

(b)  "        "       "  "        "  -  90°  "  +  1990°  C,  by  tens       .        .  165 

(c)  Logarithms  for  t    "—49°  "  +399°  C,  by  units       .        .  166 
(/)  "  "   "    "    400°  «    1990°  C,  by  tens  .        .        .168 

157.  Determination  of  heights  by  the  barometer 169 

158.  Barometric  pressures  corresponding  to  different  temperatures  of  the 

boiling-point  of  water : 

(a)  Common  measure        .        .        .        .        .        .  .  .170 

(b)  Metric  measure  .        .        .        .        .        .        .  .  -171 

159.  International  Primary  wave-length  standard,  Red  Cd.  line  .  .  .  172 

1 60.  Secondary       "          standards  Fe.  arc  lines   .        .         .172 

161.  Additional  standard  Fe.  lines 172 

162.  Stronger  lines  of  some  of  the  elements 172 

163.  Rowland's  standard  solar  wave-lengths  (also  corrections)    .        .        .173 

164.  Tertiary  standard  wave-lengths  Fe.  arc  lines 176 

165.  Wave-lengths  of  the  Fraunhofer  lines 177 

1 66.  Photometric  standards 178 

167.  Intrinsic  brightness  of  various  lights 178 

1 68.  Visibility  of  white  lights 178 

169.  Efficiency  of  various  electric  lights      .        .        .        .        .        .        .  179 

170.  Sensitiveness  of  the  eye  to  radiation  of  different  wave-lengths:   low 

(threshold)  intensities     .         .         .         .         .         .         .         .         .  180 

171.  Sensitiveness  of  the  eye  :  greater  intensities 180 

172.  Sensibility  of  the  eye  to  small  differences  of  intensity  (Fechner)          .  180 


CONTENTS. 


173- 

The  solar  constant  and  temperature    . 

.  181 

174- 

Solar  spectrum  energy  ;  atmospheric  transparency 

.  181 

175. 

Distribution  of  solar  energy  in  spectrum      ..... 

.  181 

i76. 

Distribution  of  intensity  of  radiation  over  solar  disk    . 

.   181 

177. 

Transmissibiiity  of  radiation  by  dry  and  moist  air        ... 

.  182 

178. 

Brightness  of  sky          ......... 

.  182 

179. 

Relative  intensities  of  sun-  and  sky-light      

.  182 

180. 

182 

181. 

Relative  intensities  of  solar  radiation  —  monthly  change     . 

.  183 

182. 

Mean  monthly  and  yearly  temperatures        ..... 

.  183 

183- 

Indices  of  refraction  of  Jena  glasses     ...... 

.  184 

184. 

«        «          «          u     «          c 

.  184 

o 

185. 

"        "          "          "     "                    temperature  coefficients 

.  184 

186. 

"         "          "           for  rock  salt        

.  185 

187. 

"        "          "            "      "      "     temperature  coefficients  . 

.  185 

188. 

"        "          "             "   sylvine  

.  185 

189. 

"        "          "            "  fluorite  .         

•  185 

190. 

"        "         "            "       "       temperature  coefficients 

.  186 

191. 

"        "          "            "   Iceland  spar           

.  186 

192. 

"        "          "             "  nitroso-dimethyl-aniline 

.  186 

Q._ 

«        «          "             "   quartz  

187 

194. 

"        "         "            "  various  alums        

.  187 

195- 

"         "          "             "         "       monorefringents 

.  1  88 

196. 

"        "          "            "        "       uniaxial  crystals 

.  189 

197. 

"        "          "             "         "       biaxial  crystals 

.  190 

198. 

"        "          "            "  solutions  of  salts  and  acids  : 

(a)  solutions  in  water 

.  191 

(b)         «          "  alcohol      . 

.  191 

(c)         "          "  potassium  permanganate 

.  191 

199. 

"        "          "            "  various  liquids       ..... 

.  192 

200. 

"        "          "            "  gases  and  vapors  .                  ... 

•  193 

202. 

"               "              "         n  —  1.68  to  210         .... 

.  194 

203. 

"              "              "         n  —  i  546  to  i  68^    .... 

.  194 

204. 

•  195 

2OC 

((                            «                       U              « 

206 

«                          U                      l(              it 

207. 

.  196 

208. 

Reflection  of  light,  perpendicular  incidence  :  various  values  of  n 

.  197 

209. 

"          "      "      incidence  varying  :  n  near  unity     .         .         • 

.  197 

2IO. 

"         "      "             "              "           n  =  1.55  .... 

.  197 

211. 

,    iq8 

iq8 

213. 

Transmissibiiity  of  radiation  by  Jena  glasses       .... 

.    199 

214. 

"              "         ««:«:««            .... 

.   199 

215- 

"              "         "         "      "    ultra-violet  glasses      . 

.   I99 

CONTENTS.  XI 

216.  Transmissibility  of  radiation  by  alum,  rock  salt,  sylvine,  fluorite,  Ice- 

land spar,  quartz .  200 

217.  Color  screens  (Landolt) 201 

218.  "          "        (Wood) 201 

219.  "          "        (Jena  glasses)        ........  202 

2i9a.  Transmissibility  of  radiation  by  water 202 

220.  Rotation  of  the  plane  of  polarized  light  by  solutions    ....  203 

221.  "          "    "       "       **  "       "  sodium  chlorate  and  quartz  203 

222.  Colors  of  thin  films,  Newton's  rings 204 

223.  Thermal  conductivity  of  metals  and  alloys 205 

224.  Thermal  conductivity  at  high  temperature 206 

225.  "  "             of  various  substances 207 

226.  "  "  "  water  and  salt  solutions          ....  207 

227.  "  "             "  organic  liquids 207 

228.  "  "             "  gases 207 

229.  Diffusivities          ...........  208 

230.  Heat  of  combustion     ..........  209 

231.  Heat  values  and  analyses  of  various  fuels  :  (a)  coals   ....  210 

(b)  peats  .         .         .         .210 

(c)  liquid  fuels          .         .210 

232.  Chemical  and  physical  properties  of  explosives 211 

233.  Heat  of  combination    .         .         .         .         .         .         .         .         .         .212 

234.  Latent  heat  of  vaporization .214 

235.  "         "     "  fusion 216 

236.  Melting-points  of  the  chemical  elements       .         .         .         .         .         .217 

237.  Boiling-points    "    "  "  "  ....  218 

238.  Densities,  melting  and  boiling  points,  inorganic  compounds          .         .219 

239.  Effect  of  pressure  on  melting  points    .  220 

240.  "       "         "         "  freezing  point  of  water 221 

241.  Melting  points  of  various  mixtures  of  metals 222 

242.  "  «».<«•'"  «  "          "  222 

243.  Low-melting-point  alloys      .         .        .         .         .         .         .         .         .222 

244.  Densities,  melting-points,  boiling-points  of  organic  compounds : 

(a)  Paraffin  series 223 

(b)  Olefine  series 223 

(c)  Acetylene  series 224 

(if)  Monatomic  alcohols 224 

(e)   Alcoholic  ethers 224 

(/)  Ethyl  ethers 224 

(g)  Miscellaneous     .........  225 

245.  Transformation  and  melting-points,  minerals  and  eutectics  .         .         .  226 

246.  Lowering  of  freezing-points  by  salts  in  solution    .....  227 

247.  Raising  of  boiling-points  by  salts  in  solution        .....  229 

248.  Freezing  mixtures ...  230 

249.  Critical  temperatures,  pressure,  volumes  and  densities  of  gases   .         .231 

250.  Coefficients  of  linear  expansion  of  the  chemical  elements     .         .         .  232 


"  "       " 


Xll  CONTENTS. 

251.  Coefficients  of  linear  expansion  of  miscellaneous  substances        .        .  233 

252.  "  "  cubical       "           "  crystalline  and  other  solids     .         .  234 

"  liquids    ......  235 

"  thermal  expansion  of  gases 236 

255.  Mechanical  equivalent  of  heat :  various  data         .....  237 

256.  "  "          "     "       adopted  values  (Ames)       .        .         .237 

257.  "     "      conversion  values       .         .        .         -237 

258.  Specific  heats  of  the  chemical  elements        ......  238 

259.  "  "     "  water  and  mercury 239 

260.  Additional  specific  heats  of  the  elements 240 

261.  Mean  specific  heats  of  quartz,  silica  glass  and  platinum       .        .         .  240 

262.  Specific  heats  of  various  solids    ........  241 

263.  "  "      "        "       liquids 241 

264.  "  "      "        "       minerals  and  rocks 242 

265.  "  "      "        "       gases  and  vapors 243 

266.  Gas  and  mercury  thermometers  :  formulae 244 

267.  Comparison  of  hydrogen  and  i6m  thermometers  :  o°  to  100°  C.  .  244 

268.  "  "          "          "     59"'            "               o°  to  100°  C.           .  244 

269.  "  "          "           "     I61"  and  591" thermometers: -5°  to-35°C.  244 

270.  Comparison  of  air  and  i6m  glass  thermometers  :  o°  to  300°  C.     .         .  245 

271.  "  "   "      "     591"     "               "               100°  to  200°  C.         .  245 

272.  "  "  hydrogen  and  various  mercury  thermometers        .         .  246 

273.  "  "  air  and  high  temperature  (59m)  mercury  thermometer  .  246 

274.  "  "  H.,  toluol,  alcohol,  petrol  ether,  pentane  thermometers  246 

275.  Platinum  resistance  thermometry 247 

276.  Thermodynamic  scale ;  temperature  of  ice-point  ....  247 

277.  Standard  points  for  calibration  of  thermometers  ....  247 

278.  Stem  correction  for  thermometers        .......  248 

279-         "  "  "  249 

280.  "  "          "  249 

281.  Calibration  of  thermo-element  Pt.-Pt.  Rh 250 

282.  "  "         "           "         Cu-Constantan     .                 ...  250 

283.  Radiation  formulae  and  constants  for  perfect  radiator  .         .        .         .251 

284.  "         in  calories  for  perfect  radiators  at  various  temperatures      .  251 

285.  "         distribution  in  spectrum  at  various  temperatures          .         .251 

286.  Cooling  by  radiation  and  convection  :  ordinary  pressures     .         .         .  252 

287.  "        "          "          "  "            different  pressures    .         .         .  252 

288.  "         "           "          "  "             very  small  pressures          .         .  253 

289.  "         "  "          "             "           temperature  and  pressure  effects  253 

290.  Properties  and  constants  of  saturated  steam :  metric  measure      .        .  254 

291.  "  "           "          "         "            "        common  measure  .        .  255 

292.  Ratio  of  the  electrostatic  to  the  electromagnetic  unit  of  electricity       .  260 

293.  Electromotive  force  of  standard  cells  :  absolute  current  measures         .  261 

294.  Data  for  voltaic  cells  :  (a)  double  fluid  cells 262 

(£)  single  fluid  cells 263 

(f)    standard  cells 263 


CONTENTS.  Xlii 

294.  Data  for  voltaic  cells :  (d)  secondary  (storage)  cells    ....  263 

295.  Contact  differences  of  potential,  solids  with  liquids  and  liquids  with 

liquids  in  air    .         .         .         .         .         .         .         .         .         .  264 

296.  Contact  differences  of  potential,  solids  with  solids  in  air  .        .  266 

297.  Potential  difference  between  metals  in  various  salt  solutions         .         .  267 

298.  Thermoelectric  powers         .         ."        .         .         .         .         .         .         .  268 

299.  "  "       with  alloys       .         .         .         .         .         .         .  269 

300.  "  "     platinum          .         .         .         .         .         .270 

301.  "  "       of  Pt.  with  Pt.  Rh.  alloys        .        .        .        .270 

302.  Peltier  effect        .        .        .        .        .        .        .        .        .        .        .271 

303.  "  "     Fe-constantan,  Cu-constantan .         .         .         .         .         .271 

304.  "          "     E.  M.  F.  in  volts 271 

305.  Various  determinations  of  the  ohm       .......  272 

306.  Specific  resistance  of  metallic  wires 273 

307.  Specific  resistance  of  metals 274 

308.  Temperature  resistance  coefficient 276 

309.  Conductivities  of  three-metal  and  other  alloys 277 

310.  "  "    alloys 278 

311.  Allowable  carrying  capacity  rubber-covered  copper  wires    .        .        .  279 

312.  Resistance  of  metals  and  alloys  at  low  temperatures    ....  280 

313.  Temperature  variation  of  electrical  resistance  of  glass,  porcelain  .         .  282 

314.  Temperature  resistance  coefficients  of  glass,  porcelain,  quartz       .         .282 

315.  Tabular  comparison  of  wire  gages 283 

316.  Wire  tables.     Mass  and  volume  resistivities  of  Cu.  and  Al.          .         .  284 

317.  "         "  Temperature  coefficients  of  copper        ....  285 

318.  "         "  Reduction  to  standard  temperatures      ....  285 

319.  Standard  annealed  copper  wire,  English  units        .         .  286 

320.  "         "  "               "              "          "     metric  units          .         .  289 

321.  Hand-drawn  aluminum  wire,  English  units    .         .         .  292 

322.  "         "  "        "              "            "           metric  units        .        .  293 

323.  Dielectric  strength ;  steady  potential  for  spark  in  air  ....  294 

324.  "  "           alternating  potential  for  spark  in  air     .     '    .         .  294 

325.  "  "          potentials  for  longer  sparks  in  air         ...  295 

326.  "  "          effect  of  (air)  pressure 295 

327.  "  "          of  various  materials 296 

328.  "  "  "  kerosene 296 

329.  Electric  resistance  with  alternating  currents  (straight  wires)         .         .  297 

330.  "  "          for  high  frequencies 297 

331.  Wireless  telegraphy  ;  wave-lengths,  frequencies,  oscillation  constant    .  298 

332.  "  "             radiation  resistance  for  various  wave-lengths        .  300 

333.  International  atomic  weights  and  electrochemical  equivalents      .         ..  301 

334.  Conductivity  of  a  few  dilute  solutions 302 

335.  Electrochemical  equivalents  and  densities  of  nearly  normal  solutions  .  302 

336.  Specific  molecular  conductivity  of  solutions         .....  303 

337.  "  "                   "            "         "          limiting  values          .         .  304 

338.  "  "                 "           "        "         temperature  coefficients  .  304 


XIV  CONTENTS. 

339.  Equivalent  conductivity  of  salts,  acids,  bases  in  solution      .         .         .  305 

340.  "  some  additional  salts  in  solution         .         .  307 

341.  conductance  of  the  separate  ions        .....  308 

342.  Hydrolisis  of  ammonium  acetate  :  ionization  of  water          .         .         .  308 

343.  Dielectric  constants  (specific  inductive  capacity)  of  gases     .         .         .  309 
344-  "                 "               "             "                 "          "      "       temperature 

coefficient        ...........  309 

345.  Dielectric  constants  (specific  inductive  capacity)  of  gases  :  pressure  co- 

efficient   310 

346.  Dielectric  constants  of  liquids     .         .         .         .         .         .         .         .310 

347.  "  "       "       temperature  coefficient  .         .         .         .312 

348.  "  "  "  liquefied  gases 312 

349.  "  "            "  standard  solutions  for  calibrations  .         .         .313 

350.  "  "  «  solids 313 

351-  "  crystals 314 

352.  Permeability  of  iron  rings  and  wire,  various  inductions        .         .         .315 

353.  Permeability  of  transformer  iron  : 

(a)  specimen  of  Westinghouse  No.  8  transformer         .         .         .  315 

(b)  "          "  "  "    6  ...  316 

(c)  "          "  "  "    4  ...  316 

(d)  "  Thomson-Houston  i5oo-watt  transformer  .         .  316 

354.  Magnetic  properties  of  iron  and  steel  .         .         .         .         .         .         -317 

355-  "            "  cast  iron  in  intense  fields          .         .         .         -317 

356.  corrections  for  ring  specimens 317 

357.  Composition  and  magnetic  properties  of  iron  and  steel        .         .         -318 

358.  Permeability  of  some  of  the  specimens  in  Table  303    ....  320 

359.  Magnetic  properties  of  soft  iron  at  o°  and  100°  C 320 

360.  "  "  "  steel  at  o°  and  100°  C 320 

361.  "  «  "  cobalt  at  100°  C 321 

362.  "  «  «  nickel  "     "      " 321 

363.  "  "  "  magnetite 321 

364.  "  "  Lowmoor  wrought  iron 321 

365.  "  "  "  Vicker's  tool  steel 321 

366.  "  "           "  Hadfield's  manganese  steel     .         .         .         .321 

367.  Saturation  values  for  different  steels 321 

368.  Magnetic  properties  of  iron  in  very  weak  fields   .         .         .         .         .322 

369.  Dissipation  of  energy  in  cyclic  magnetization  of  magnetic  substances  .  322 
37°-  "            "      "        "       "                "               "  cable  transformers     .  322 

371.     Demagnetizing  factors  for  rods 323 

372'  "        Shuddemagen's  values      .....  323 

373.  Dissipation  of  energy  in  cyclic  magnetization  of  various  substances     .  324 

374-  "            "       "        "      "                  "              "  transformer  steels      .  325 

375.  Magneto-optic  rotation,  formulae  :  Verdet's  constant    .         .         .         .326 

376-  "          "  "         in  solids 327 

377-  "          "  "         "  liquids 328 

3/8«  "          "  solutions  of  salts  and  acids  in  water   .         .  329 


CONTENTS.  XV 


379- 

•  330 

380. 

Verdet's  and  Kundt's  constants  ...         0         ... 

•  330 

381- 

Values  of  Kerr's  constant    ........ 

•  331 

382. 

Dispersion  of  Kerr's  effect.     Ingersoll's  values   .... 

•  33i 

383- 

"       "          "          Foote's         "          .... 

•  331 

384- 

Magnetic  susceptibility         ........ 

•  332 

3S5- 

Variation  of  the  resistance  of  bismuth  in  magnetic  field 

•  333 

386. 

"    "          "           "  nickel      "         "            " 

•  333 

387- 

"  various  metals  in  a  magnetic  field  . 

•  333 

388. 

Transverse  galvanomagnetic  and  thermomagnetic  effects     . 

•  334 

389- 

Variation  of  the  Hall  constant  with  the  temperature    . 

•  334 

390. 

Rontgen  rays  (x-rays)  ionization  due  to        

•  335 

391- 

"           "     Secondary  Rontgen  rays         

•  335 

392. 

Cathodic  rays        

•  335 

393- 

absorption  coefficients  .... 

•  336 

394- 

X-R  spectra  and  atomic  numbers        ...... 

•  336 

395- 

Radioactivity  :  production  of  phosphorescence    .... 

•  337 

396- 

"                        "          "  a  particles      

•  337 

397- 

"               heating  effects      

•  337 

398. 

various  constants           ...... 

•  338 

399- 

•  340 

400. 

«                            it                 n             u    o      u 

•  340 

401. 

«                                         «                          U                    «                 « 

•  340 

402. 

"               ions  produced  by  the  a,  /5,  and  y  rays  . 

•  34i 

403- 

radium  emanation  ;  units      ..... 

•  34i 

404. 

vapor  pressure  of  Ra  emanation  .... 

•  34i 

4°5- 

spectra          ........ 

•  34i 

406. 

Miscellaneous  constants,  molecular,  atomic,  etc. 

•342 

407. 

Periodic  system  of  the  elements  

•  343 

Definitions  of  units      

•  345 

Index  ........•••• 

•  349 

INTRODUCTION. 


UNITS   OF  MEASUREMENT  AND   CONVERSION  FORMULAE. 

Units.  —  The  quantitative  measure  of  anything  is  a  number  which  expresses  the 
ratio  of  the  magnitude  of  the  thing  to  the  magnitude  of  some  other  thing  of  the 
same  kind.  In  order  that  the  number  expressing  the  measure  may  be  intelligi- 
ble, the  magnitude  of  the  thing  used  for  comparison  must  be  known.  This  leads 
to  the  conventional  choice  of  certain  magnitudes  as  units  of  measurement,  and 
any  other  magnitude  is  then  simply  expressed  by  a  number  which  tells  how  many 
magnitudes  equal  to  the  unit  of  the  same  kind  of  magnitude  it  contains.  For 
example,  the  distance  between  two  places  may  be  stated  as  a  certain  number  of 
miles  or  of  yards  or  of  feet.  In  the  first  case,  the  mile  is  assumed  as  a  known 
distance  ;  in  the  second,  the  yard,  and  in  the  third,  the  foot.  What  is  sought  for 
in  the  statement  is  to  convey  an  idea  of  the  distance  by  describing  it  in  terms  of 
distances  which  are  either  familiar  or  easily  referred  to  for  comparison.  Similarly 
quantities  of  matter  are  referred  to  as  so  many  tons  or  pounds  or  grains  and  so 
forth,  and  intervals  of  time  as  a  number  of  hours  or  minutes  or  seconds.  Gen- 
erally in  ordinary  affairs  such  statements  appeal  to  experience ;  but,  whether  this 
be  so  or  not,  the  statement  must  involve  some  magnitude  as  a  fundamental  quan- 
tity, and  this  must  be  of  such  a  character  that,  if  it  is  not  known,  it  can  be  readily 
referred  to.  We  become  familiar  with  the  length  of  a  mile  by  walking  over  dis- 
tances expressed  in  miles,  with  the  length  of  a  yard  or  a  foot  by  examining  a  yard 
or  a  foot  measure  and  comparing  it  with  something  easily  referred  to,  —  say  our 
own  height,  the  length  of  our  foot  or  step,  —  and  similarly  for  quantities  of  other 
kinds.  This  leads  us  to  be  able  to  form  a  mental  picture  of  such  magnitudes 
when  the  numbers  expressing  them  are  stated,  and  hence  to  follow  intelligently 
descriptions  of  the  results  of  scientific  work.  The  possession  of  copies  of  the 
units  enables  us  by  proper  comparisons  to  find  the  magnitude-numbers  express- 
ing physical  quantities  for  ourselves.  The  numbers  descriptive  of  any  quan- 
tity must  depend  on  the  intrinsic  magnitude  of  the  unit  in  terms  of  which  it  is 
described.  Thus  a  mile  is  1760  yards,  or  5280  feet,  and  hence  when  a  mile  is 
taken  as  the  unit  the  magnitude-number  for  the  distance  is  i,  when  a  yard  is  taken 
as  the  unit  the  magnitude-number  is  1760,  and  when  afoot  is  taken  it  is  5280. 
Thus,  to  obtain  the  magnitude-number  for  a  quantity  in  terms  of  a  new  unit  when 
it  is  already  known  in  terms  of  another  we  have  to  multiply  the  old  magnitude- 
number  by  the  ratio  of  the  intrinsic  values  of  the  old  and  new  units ;  that  is,  by 
the  number  of  the  new  units  required  to  make  one  of  the  old. 


XV111  INTRODUCTION. 

Fundamental  Units  of  Length  and  Mass.  —  It  is  desirable  that  as  few 
different  kinds  of  unit  quantities  as  possible  should  be  introduced  into  our  measure- 
ments, and  since  it  has  been  found  possible  and  convenient  to  express  a  large 
number  of  physical  quantities  in  terms  of  length  or  mass  or  time  units  and  com- 
binations of  these,  they  have  been  very  generally  adopted  as  fundamental  units. 
Two  systems  of  such  units  are  used  in  this  country  for  scientific  measurements, 
namely,  the  customary,  and  the  French  or  metric,  systems.  Tables  of  conversion 
factors  are  given  in  the  book  for  facilitating  comparisons  between  quantities  ex- 
pressed in  terms  of  one  system  with  similar  quantities  expressed  in  the  other.  In 
the  customary  system  the  standard  unit  of  length  is  the  yard  and  is  now  defined 
as  3600/3937  meter.  The  unit  of  mass  is  the  avoirdupois  pound  and  is  defined 
as  1/2.20462  kilogram. 

The  British  yard  is  defined  as  the  "  straight  line  or  distance  (at  62°  F.)  between 
the  transverse  lines  in  the  two  gold  plugs  in  the  bronze  bar  deposited  in  the  office 
of  the  exchequer."  The  British  standard  of  mass  is  the  pound  avoirdupois  and 
is  the  mass  of  a  piece  of  platinum  marked  "  P.  S.  1844,  i  lb.,"  preserved  in  the 
exchequer  office. 

In  the  metric  system  the  standard  of  length  is  the  meter  and  is  defined  as  the 
distance  between  two  lines  at  o°  Centrigrade  on  a  platinum  iridium  bar  deposited 
at  the  International  Bureau  of  Weights  and  Measures.  This  bar  is  known  as  the 
International  Prototype  Meter,  and  its  length  was  derived  from  the  "  metre  des 
Archives,"  which  was  made  by  Borda.  Copies  of  the  International  Prototype 
Meter  are  possessed  by  the  various  governments,  and  are  called  "  National 
Prototypes." 

Borda,  Delambre,  Laplace,  and  others,  acting  as  a  committee  of  the  French 
Academy,  recommended  that  the  standard  unit  of  length  should  be  the  ten  mil- 
lionth part  of  the  length,  from  the  equator  to  the  pole,  of  the  meridian  passing 
through  Paris.  In  1795  the  French  Republic  passed  a  decree  making  this  the 
legal  standard  of  length,  and  an  arc  of  the  meridian  extending  from  Dunkirk  to 
Barcelona  was  measured  by  Delambre  and  Mechain  for  the  purpose  of  realizing 
the  standard.  From  the  results  of  that  measurement  the  meter  bar  was  made 
by  Borda.  The  meter  is  not  now  defined  in  terms  of  the  meridian  length,  and 
hence  subsequent  measurements  of  the  length  of  the  meridian  have  not  affected 
the  length  of  the  meter. 

The  metric  standard  of  mass  is  the  kilogram  and  is  defined  as  the  mass  of  a 
piece  of  platinum-indium  deposited  at  the  International  Bureau  of  Weights  and 
Measures.  This  standard  is  known  as  the  International  Prototype  Kilogram. 
Its  mass  is  equal  to  that  of  the  older  standard,  the  "kilogramme  des  Archives," 
made  by  Borda  and  intended  to  have  the  same  mass  as  a  cubic  decimeter  of  dis- 
tilled water  at  the  temperature  of  4°  C.  Copies  of  the  International  Prototype 
Kilogram  are  possessed  by  the  various  governments,  and  as  in  the  case  of  the 
meter  standards  are  called  National  Prototypes. 


INTRODUCTION.  XIX 

Comparisons  of  the  French  and  customary  standards  are  given  in  tabular  form 
in  Table  2  ;  and  similarly  Table  3,  differing  slightly,  compares  the  British  and 
French  systems.  In  the  metric  system  the  decimal  subdivision  is  used,  and  thus 
we  have  the  decimeter,  the  centimeter,  and  the  millimeter  as  subdivisions,  and 
the  dekameter,  hektometer.  and  kilometer  as  multiples.  The  centimeter  is  most 
commonly  used  in  scientific  work. 


Time.  —  The  unit  of  time  in  both  the  systems  here  referred  to  is  the  mean 
solar  second,  or  the  86,4ooth  part  of  the  mean  solar  day.  The  unit  of  time  is 
thus  founded  on  the  average  time  required  for  the  earth  to  make  one  revolution 
on  its  axis  relatively  to  the  sun  as  a  fixed  point  of  reference. 


Derived  Units.  — Units  of  quantities  depending  on  powers  greater  than  unity 
of  the  fundamental  length,  mass,  and  time  units,  or  on  combinations  of  different 
powers  of  these  units,  are  called  "  derived  units."  Thus,  the  unit  of  area  and  of 
volume  are  respectively  the  area  of  a  square  whose  side  is  the  unit  of  length  and 
the  volume  of  a  cube  whose  edge  is  the  unit  of  length.  Suppose  that  the  area  of 
a  surface  is  expressed  in  terms  of  the  foot  as  fundamental  unit,  and  we  wish  to 
find  the  area-number  when  the  yard  is  taken  as  fundamental  unit.  The  yard  is 
3  times  as  long  as  the  foot,  and  therefore  the  area  of  a  square  whose  side  is  a 
yard  is  3  X  3  times  as  great  as  that  whose  side  is  a  foot.  Thus,  the  surface  will 
only  make  one  ninth  as  many  units  of  area  when  the  yard  is  the  unit  of  length  as 
it  will  make  when  the  foot  is  that  unit.  To  transform,  then,  from  the  foot  as  old 
unit  to  the  yard  as  new  unit,  we  have  to  multiply  the  old  area-number  by  1/9,  or  by 
the  ratio  of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  area.  This  is  the 
same  rule  as  that  given  above,  but  it  is  usually  more  convenient  to  express  the 
transformations  in  terms  of  the  fundamental  units  directly.  In  the  above  case, 
since  on  the  method  of  measurement  here  adopted  an  area-number  is  the  product 
of  a  length-number  by  a  length-number  the  ratio  of  two  units  is  the  square  of  the 
ratio  of  the  intrinsic  values  of  the  two  units  of  length.  Hence,  if  /  be  the  ratio 
of  the  magnitude  of  the  old  to  that  of  the  new  unit  of  length,  the  ratio  of  the  cor- 
responding units  of  area  is  /2.  Similarly  the  ratio  of  two  units  of  volume  will  be 
T8,  and  so  on  for  other  quantities. 


Dimensional  Formulae.  —  It  is  convenient  to  adopt  symbols  for  the  ratios 
of  length  units,  mass  units,  and  time  units,  and  adhere  to  their  use  throughout ; 
and  in  what  follows,  the  small  letters,  /,  #z,  /,  will  be  used  for  these  ratios.  These 
letters  will  always  represent  simple  numbers,  but  the  magnitude  of  the  number 
will  depend  on  the  relative  magnitudes  of  the  units  the  ratios  of  which  they  repre- 
sent. When  the  values  of  the  numbers  represented  by  /,  m,  t  are  known,  and  the 
powers  of  /,  m,  and  /  involved  in  any  particular  unit  are  also  known,  the  factor  for 
transformation  is  at  once  obtained.  Thus,  in  the  above  example,  the  value  of  / 
was  1/3  and  the  power  of  /involved  in  the  expression  for  area  is  /2;  hence,  the 
factor  for  transforming  from  square  feet  to  square  yards  is  1/9.  These  factors 


XX  INTRODUCTION. 

have  been  called  by  Prof.  James  Thomson  "change  ratios,"  which  seems  an 
appropriate  term.  The  term  "  conversion  factor  "  is  perhaps  more  generally 
known,  and  has  been  used  throughout  this  book. 

Conversion  Factor.  —  In  order  to  determine  the  symbolic  expression  for  the 
conversion  factor  for  any  physical  quantity,  it  is  sufficient  to  determine  the  degree 
to  which  the  quantities  length,  mass,  and  time  are  involved  in  the  quantity.  Thus, 
a  velocity  is  expressed  by  the  ratio  of  the  number  representing  a  length  to  that 
representing  an  interval  of  time,  or  L/T,  an  acceleration  by  a  velocity-number 
divided  by  an  interval  of  time-number,  or  L/T2,  and  so  on,  and  the  correspond- 
ing ratios  of  units  must  therefore  enter  to  precisely  the  same  degree.  The  fac- 
tors would  thus  be  for  the  above  cases,  ljt  and  ///2.  Equations  of  the  form  above 
given  for  velocity  and  acceleration  which  show  the  dimensions  of  the  quantity  in 
terms  of  the  fundamental  units  are  called  "  dimensional  equations."  Thus 

E  =  ML2T-2 

is  the  dimensional  equation  for  energy,  and  ML2T~2  is  the  dimensional  formula 
for  energy. 

In  general,  if  we  have  an  equation  for  a  physical  quantity 


where  C  is  a  constant  and  LMT  represents  length,  mass,  and  time  in  terms  of  one 
set  of  units,  and  we  wish  to  transform  to  another  set  of  units  in  terms  of  which 

T      A/T    T1 

the  length,  mass,  and  time  are  LyM/T,,  we  have  to  find  the  value  of  —',—  ',—  ',  which 

JL  M.    1 

in  accordance  with  the  convention  adopted  above  will  be  /  m  /,  or  the  ratios  of 
the  magnitudes  of  the  old  to  those  of  the  new  units. 

Thus  L,  =  L/,  M;  =  Mw,  Ty  =  T/,  and  if  Qy  be  the  new  quantity-number 


=  CL°/aM<WTc/c  = 


or  the  conversion  factor  is  Pm*?,  a  quantity  of  precisely  the  same  form  as  the 
dimension  formula  I^MT0. 

We  now  proceed  to  form  the  dimensional  and  conversion  factor  formulas  for 
the  more  commonly  occurring  derived  units. 

1.  Area.  —  The  unit  of  area  is  the  square  the  side  of  which  is  measured  by 
the  unit  of  length.     The  area  of  a  surface  is  therefore  expressed  as 

S  =  CLa, 

where  C  is  a  constant  depending  on  the  shape  of  the  boundary  of  the  surface 
and  L  a  linear  dimension.  For  example,  if  the  surface  be  square  and  L  be  the 
length  of  a  side  C  is  unity.  If  the  boundary  be  a  circle  and  L  be  a  diameter 
C  =  7T/4,  and  so  on.  The  dimensional  formula  is  thus  L2,  and  the  conversion 
factor  P. 

2.  Volume.  —  The  unit  of  volume  is  the  volume  of  a  cube  the  edge  of  which 
is  measured  by  the  unit  of  length.    The  volume  of  a  body  is  therefore  expressed  as 


INTRODUCTION.  XXI 

V  =  CL8, 

where  as  before  C  is  a  constant  depending  on  the  shape  of  the  boundary.     The 
dimensional  formula  is  L3  and  the  conversion  factor  /3. 

3.  Density.  —  The  density  of  a  substance  is  the  quantity  of  matter  in  the  unit 
of  volume.     The  dimension  formula  is  therefore  M/V  or  MLr3,  and  conversion 
factor  ml~&. 

Example.  —  The  density  of  a  body  is  150  in  pounds  per  cubic  foot:  required 
the  density  in  grains  per  cubic  inch. 

Here  m  is  the  number  of  grains  in  a  pound  =  7000,  and  /  is  the  number  of 
inches  in  a  foot=  12  ;  .\  ml~*=  7000/1 2*  =  4.051.  Hence  the  density  is  150  X 
4.051  =607.6  in  grains  per  cubic  inch. 

NOTE.  —  The  specific  gravity  of  a  body  is  the  ratio  of  its  density  to  the  density  of  a  standard 
substance.  The  dimension  formula  and  conversion  factor  are  therefore  both  unity. 

4.  Velocity.  —  The  velocity  of  a  body  at  any  instant  is  given  by  the  equation 
v  =  -^^  or  velocity  is  the  ratio  of  a  length-number  to  a  time-number.     The  di- 
mension formula  is  LT"1,  and  the  conversion  factor  lt~\ 

Example.  —  A  train  has  a  velocity  of  60  miles  an  hour :  what  is  its  velocity  in 
feet  per  second  ? 

Here  /=  ^280  and  / 1=3600  ;  .*.  lt~l  =  ^5°  =  44  _  1>4g7.     Hence  the  velo- 

3600      30 

city  =  60  X  1-467  =  88. o  in  feet  per  second. 

5.  Angle.  — An  angle  is  measured  by  the  ratio  of  the  length  of  an  arc  to  the 
length  of  the  radius  of  the  arc.     The  dimension  formula  and  the  conversion 
factor  are  therefore  both  unity. 

6.  Angular  Velocity.  —  Angular  velocity  is  the  ratio  of  the  magnitude  of  the 
angle  described  in  an  interval  of  time  to  the  length  of  the  interval.     The  dimen- 
sion formula  is  therefore  T"1,  and  the  conversion  factor  is  t~\ 

7.  Linear  Acceleration. — Acceleration  is  the  rate  of  change  of  velocity  or 

a=.~-     The  dimension  formula  is  therefore  VT"1  or  LT~2,  and  the  conversion 
dt 

factor  is  //~2. 

Example.  —  A  body  acquires  velocity  at  a  uniform  rate,  and  at  the  end  of  one 
minute  is  moving  at  the  rate  of  20  kilometers  per  hour:  what  is  the  acceleration 
in  centimeters  per  second  per  second  ? 

Since  the  velocity  gained  was  20  kilometers  per  hour  in  one  minute,  the  accel- 
eration was  1200  kilometers  per  hour  per  hour. 

Here /=ioo  ooo  and /=36oo  ;  .•.  //~2  =  ioo  ooo/36oo2=. 00771,  and  there- 
fore acceleration  —  .00771  X  1200  =  9.26  centimeters  per  second. 

8.  Angular  Acceleration.  —  Angular  acceleration  is  rate  of  change  of  angu- 


XX11  INTRODUCTION. 

lar  velocity.     The  dimensional  formula  is  thus  angular  velocity  Qr  ^  and  thg 
conversion  factor  t~<2>. 

9.  Solid  Angle.  —  A  solid  angle  is  measured  by  the  ratio  of  the  surface  of 
the  portion  of  a  sphere  enclosed  by  the  conical  surface  forming  the  angle  to  the 
square  of  radius  of  the  spherical  surface,  the  centre  of  the  sphere  being  at  the 

vertex  of  the  cone.     The  dimensional  formula  is  therefore  -^^  or  i,  and  hence 

J_/ 

the  conversion  factor  is  also  i. 

10.  Curvature.  —  Curvature  is  measured  by  the  rate  of  change  of  direction  of 
the  curve  with  reference  to  distance  measured  along  the  curve  as  independent 

variable.     The  dimension  formula  is  therefore  ,an^  e  or  L"1.  and  the  conversion 

length 

factor  is  l~l. 

11.  Tortuosity.  —  Tortuosity  is  measured  by  the  rate  of  rotation  of  the  tan- 
gent plane  round  the  tangent  to  the  curve  of  reference  when  length  along  the 

curve  is  independent  variable.     The  dimension  formula  is  therefore    ar>^  e  or 

length 

L"1,  and  the  conversion  factor  is  l~l. 

12.  Specific  Curvature  of  a  Surface.  —  This  was  defined  by  Gauss  to  be. 
at  any  point  o£  the  surface,  the  ratio  of  the  solid  angle  enclosed  by  a  surface 
formed  by  moving  a  normal  to  the  surface  round  the  periphery  of  a  small  area 
containing  the  point,  to  the  magnitude  of  the  area.     The  dimensional  formula  is 

therefore  solld  angle  Or  L~2,  and  the  conversion  factor  is  thus  /~2. 
surface 

13.  Momentum.  —  Tkis  is  quantity  of  motion  in  the  Newtonian  sense,  and  is, 
at  any  instant,  measured  by  the  product  of  the  mass-number  and  the  velocity- 
number  for  the  body. 

Thus  the  dimension  formula  is  MV  or  MLT"1,  and  the  conversion  factor  mlt~l. 

Example.  —  A  mass  of  10  pounds  is  moving  with  a  velocity  of  30  feet  per  sec- 
ond: what  is  its  momentum  when  the  centimeter,  the  gram,  and  the  second  are 
fundamental  units  ? 

Here  #2  =  453.59,  7=30.48,  and  /=  i ;  /.  mirl  =  453-59  X  30-48=  13825. 
The  momentum  is  thus  13825  X  10  X  30  =  4  147  500. 

14.  Moment  of  Momentum.  —  The  moment  of  momentum  of  a  body  with 
reference  to  a  point  is  the  product  of  its  momentum-number  and  the  number 
expressing  the  distance  of  its  line  of  motion  from  the  point.     The  dimensional 
formula  is  thus  ML*!**"1,  and  hence  the  conversion  factor  is  w/2/"1. 

15.  Moment  of  Inertia.  — The  moment  of  inertia  of  a  body  round  any  axis 
is  expressed  by  the  formula  2,tnr2,  where  m  is  the  mass  of  any  particle  of  the  body 


INTRODUCTION.  XX  Hi 

and  r  its  distance  from  the  axis.  The  dimension  formula  for  the  sum  is  clearly 
the  same  as  for  each  element,  and  hence  is  ML2.  The  conversion  factor  is  there- 
fore w/2. 

16.  Angular  Momentum.  —  The  angular  momentum  of  a  body  round  any 
axis  is  the  product  of  the  numbers  expressing  the  moment  of  inertia  and  the 
angular  velocity  of  the  body.     The  dimensional  formula  and  the  conversion  fac- 
tor are  therefore  the  same  as  for  moment  of  momentum  given  above. 

17.  Force.  —  A  force  is  measured  by  the  rate  of  change  of  momentum  it  is 
capable  of  producing.      The  dimension  formulae  for  force   and   "  time  rate  of 
change  of  momentum  "  are  therefore  the  same,  and  are  expressed  by  the  ratio 
of  momentum-number  to  time-number  or  MLT~2.     The  conversion  factor  is  thus 


NOTE.  —  When  mass  is  expressed  in  pounds,  length  in  feet,  and  time  in  seconds,  the  unit  force 
is  called  the  poundal.  When  grams,  centimeters,  and  seconds  are  the  corresponding  units  the  unit 
of  force  is  called  the  dyne. 

Example.     Find  the  number  of  dynes  in  25  poundals. 

Here  m  =  453-59>  l  =  3°-4-8,  and  /=  i  ;  /.  mlf~*=.  453-59  X  30.48  —  13825 
nearly.  The  number  of  dynes  is  thus  13825  X  25  =  345625  approximately. 

18.  Moment  of  a  Couple,  Torque,  or  Twisting  Motive.  —  These  are  dif- 
ferent names  for  a  quantity  which  can  be  expressed  as  the  product  of  two  numbers 
representing  a  force  and  a  length.     The  dimension  formula  is  therefore  FL  or 
ML2T~2,  and  the  conversion  factor  is  w/2/~2. 

19.  Intensity  of  a  Stress.  —  The  intensity  of  a  stress  is  the  ratio  of  the  num- 
ber expressing  the  total  stress  to  the  number  expressing  the  area  over  which  the 
stress  is  distributed.     The  dimensional  formula  is  thus  FL~2  or  ML~~1T~2,  and  the 
conversion  factor  is  «/~V~a. 

20.  Intensity  of  Attraction,  or  "  Force  at  a  Point."  —  This  is  the  force  of 
attraction  per  unit  mass  on  a  body  placed  at  the  point,  and  the  dimensional  for- 
mula is  therefore  FM"1  or  LT~2,  the  same  as  acceleration.     The  conversion  fac- 
tors for  acceleration  therefore  apply. 

21.  Absolute  Force  of  a  Centre  of  Attraction,  or  "  Strength  of  a  Cen- 
tre." —  This  is  the  intensity  of  force  at  unit  distance  from  the  centre,  and  is  there- 
fore the  force  per  unit  mass  at  any  point  multiplied  by  the  square  of  the  distance 
from  the  centre.    The  dimensional  formula  thus  becomes  FL2M-1  or  L8T~2.    The 
conversion  factor  is  therefore  /8/~2. 

22.  Modulus  of  Elasticity.  —  A  modulus  of  elasticity  is  the  ratio  of  stress 
intensity  to  percentage  strain.     The  dimension  of  percentage  strain  is  a  length 
divided  by  a  length,  and  is  therefore  unity.    Hence,  the  dimensional  formula  of  a 
modulus  of  elasticity  is  the  same  as  that  of  stress  intensity,  or  MLr^T"2,  and  the 
conversion  factor  is  thus  also  ml~lt~*. 


XXIV  INTRODUCTION. 

23.  Work  and  Energy.  —  When  the  point  of  application  of  a  force,  acting  on 
a  body,  moves  in  the  direction  of  the  force,  work  is  done  by  the  force,  and  the 
amount  is  measured  by  the  product  of  the  force  and  displacement  numbers.  The 
dimensional  formula  is  therefore  FL  or  ML2T~2. 

The  work  done  by  the  force  either  produces  a  change  in  the  velocity  of  the  body 
or  a  change  of  shape  or  configuration  of  the  body,  or  both.  In  the  first  case  it 
produces  a  change  of  kinetic  energy,  in  the  second  a  change  of  potential  energy. 
The  dimension  formulae  of  energy  and  work,  representing  quantities  of  the  same 
kind,  are  identical,  and  the  conversion  factor  for  both  is 


24.  Resilience.  —  This  is  the  work  done  per  unit  volume  of  a  body  in  distort- 
ing it  to  the  elastic  limit  or  in  producing  rupture.    The  dimension  formula  is  there- 
fore ML2T~2L-8  or  ML-'T-2,  and  the  conversion  factor  mt~lr2. 

25.  Power,  or  Activity.  —  Power  —  or,  as  it  is  now  very  commonly  called,  ac- 
tivity —  is  defined  as  the  time  rate  of  doing  work,  or  if  W  represent  work  and  P  power 

p  __  dw^     The  dimensionai  formula  is  therefore  WT"1  or  ML*T-8,  and  the  con- 
dt 

version  factor  w/2/"8,  or  for  problems  in  gravitation  units  more  conveniently  fit'*, 
where  /stands  for  the  force  factor. 

Examples,    (a)  Find  the  number  of  gram  centimeters  in  one  foot  pound. 

Here  the  units  of  force  are  the  attraction  of  the  earth  on  the  pound  *  and 
the  gram  of  matter,  and  the  conversion  factor  is  fl,  where  /  is  453.59  and  /is 
30.48. 

Hence  the  number  is  453.59  X  30.48  =  13825. 

(£)  Find  the  number  of  foot  poundals  in  i  ooo  ooo  centimeter  dynes. 
Here  m  =  1/453.59,  /=  1/30.48,  and  t  =  i  ;  /.  mI2rz  =  1/453-59  X  3°-482, 
and  io«mPr*=  107453.59  X  3Q-482=  2.373. 


(c)  If  gravity  produces  an  acceleration  of  32.2  feet  per  second  per  second,  how 
many  watts  are  required  to  make  one  horse-power  ? 

One  horse-power  is  550  foot  pounds  per  second,  or  550  X  32.2  =  17710  foot 
poundals  per  second.  One  watt  is  io7  ergs  per  second,  that  is,  io7  dyne  centi- 
meters per  second.  The  conversion  factor  is  ^z/2/'8,  where  *«  =  453-59,  /  =  30.48, 
and  /=  i,  and  the  result  has  to  be  divided  by  io7,  the  number  of  dyne  centime' 
ters  per  second  in  the  watt. 

Hence,  177  iomftt*/iol=  17710  X  453-59  X  3o.482/io7=r  746.3. 

(d)  How  many  gram  centimeters  per  second  correspond  to  33000  foot  pounds 
per  minute  ? 

The  conversion  factor  suitable  for  this  case  isflf\  where/is  453.59,  /is  30.48, 
and  /  is  60. 

Hence,  33000  //~1  =  33000  X  453-59  X  30.48/60  =  7  604  ooo  nearly. 

*  It  is  important  to  remember  that  in  problems  like  that  here  given  the  term  "  pound  "  or 
"  gram  "  refers  to  force  and  not  to  mass. 


INTRODUCTION.  XXV 


HEAT  UNITS. 

I.  If  heat  be  measured  in  dynamical  units  its  dimensions  are  the  same  as  those 
of  energy,  namely  ML2T~2.  The  most  common  measurements,  however,  are 
made  in  thermal  units,  that  is,  in  terms  of  the  amount  of  heat  required  to  raise 
the  temperature  of  unit  mass  of  water  one  degree  of  temperature  at  some  stated 
temperature.  This  method  of  measurement  involves  the  unit  of  mass  and  some 
unit  of  temperature  ;  and  hence,  if  we  denote  temperature-numbers  by  ©  and  their 
conversion  factors  by  0,  the  dimensional  formula  and  conversion  factor  for  quan- 
tity of  heat  will  be  M®  and  mO  respectively.  The  relative  amount  of  heat  com- 
pared with  water  as  standard  substance  required  to  raise  unit  mass  of  different 
substances  one  degree  in  temperature  is  called  their  specific  heat,  and  is  a  simple 
number. 

Unit  volume  is  sometimes  used  instead  of  unit  mass  in  the  measurement  of 
heat,  the  units  being  then  called  thermometric  units.  The  dimensional  formula 
is  in  that  case  changed  by  the  substitution  of  volume  for  mass,  and  becomes  L8®, 
and  hence  the  conversion  factor  is  to  be  calculated  from  the  formula  1*9. 


For  other  physical  quantities  involving  heat  we  have :  — 


2.  Coefficient  of  Expansion.  —  The  coefficient  of  expansion  of  a  substance 
is  equal  to  the  ratio  of  the  change  of  length  per  unit  length  (linear),  or  change 
of  volume  per  unit  volume  (voluminal)  to  the  change  of  temperature.  These 
ratios  are  simple  numbers,  and  the  change  of  temperature  is  inversely  as  the  mag- 
nitude of  the  unit  of  temperature.  Hence  the  dimensional  and  conversion-factor 
formulae  are  0"1  and  0~l. 


3.  Conductivity,  or  Specific  Conductance.  —  This  is  the  quantity  of  heat 
transmitted  per  unit  of  time  per  unit  of  surface  per  unit  of  temperature  gradient. 
The  equation  for  conductivity  is  therefore,  with  H  as  quantity  of  heat, 


and  the  dimensional  formula  -^7=,  =  —  „  which  gives  mt~lt~l  for  conversion  factor. 

(yJLl       JL  1 


In  thermometric  units  the  formula  becomes  L^T"1,  which  properly  represents 
diffusivity.  In  dynamical  units  H  becomes  ML2T~2,  and  the  formula  changes  to 
MLT"3®-1.  The  conversion  factors  obtained  from  these  are  Pt~l  and 
respectively. 


XXVI  INTRODUCTION. 

4.  Thermal  Capacity.  —  This  is  the  product  of  the  number  for  mass  and 
the  specific  heat,  and  hence  the  dimensional  formula  and  conversion  factor  are 
simply  M  and  m. 

5.  Latent  Heat.  —  Latent  heat  is  the  ratio  of  the  number  representing  the 
quantity  of  heat  required  to  change  the  state  of  a  body  to  the  number  represent- 
ing the  quantity  of  matter  in  the  body.     The  dimensional  formula  is  therefore 
M0/M  or  ®,  and  hence  the  conversion  factor  is  simply  the  ratio  of  the  tejnpera- 
ture  units  or  6.     In  dynamical  units  the  factor  is  /2/~2.* 

6.  Joule's  Equivalent.  —  Joule's  dynamical  equivalent  is  connected  with 
quantity  of  heat  by  the  equation 

ML2T~2^JH  or  JM®. 

This  gives  for  the  dimensional  formula  of  J  the  expression  L2T~?©~1.  The  conver- 
sion factor  is  thus  represented  by  /2/~20~l.  When  heat  is  measured  in  dynamical 
units  J  is  a  simple  number. 


7.  Entropy.  —  The  entropy  of  a  body  is  directly  proportional  to  the  quantity 
of  heat  it  contains  and  inversely  proportional  to  its  temperature.  The  dimen- 
sional formula  is  thus  M®/®  or  M,  and  the  conversion  factor  is  m.  When  heat  is 
measured  in  dynamical  units  the  factor  is  mlzt~z9~l. 

Examples,  (a)  Find  the  relation  between  the  British  thermal  unit,  the  calorie, 
and  the  therm. 

Neglecting  the  variation  of  the  specific  heat  of  water  with  temperature,  or  de- 
fining all  the  units  for  the  same  temperature  of  the  standard  substance,  we  have 
the  following  definitions.  The  British  thermal  unit  is  the  quantity  of  heat  required 
to  raise  the  temperature  of  one  pound  of  water  i°  F.  The  calorie  is  the  quan- 
tity of  heat  required  to  raise  the  temperature  of  one  kilogramme  of  water  i°  C. 
The  therm  is  the  quantity  of  heat  required  to  raise  the  temperature  of  one  gramme 
of  water  i°  C.  Hence  :  — 

(1)  To  find  the  number  of  calories  in  one  British  thermal  unit,  we    have 

**  =  -45359  and  0  =  f  5  •'•  w#—  45359  X  S/9  =  -25I99- 

(2)  To   find   the    number   of   therms   in    one    calorie,   m=iooo  and  6=1; 
.:  mO=.  1000. 

It  follows  at  once  that  the  number  of  therms  in  one  British  thermal  unit  is 
1000  X  .25199  =  251.99. 

(V)  What  is  the  relation  between  the  foot  grain  second  Fahrenheit-degree  and 
the  centimetre  gramme  second  Centigrade-degree  units  of  conductivity  ? 

The  number  of  the  latter  units  in  one  of  the  former  is  given  by  the  for- 

*  It  will  be  noticed  that  when  0  is  given  the  dimension  formula  L2T~2  the  formulae  in  thermal 
and  dynamical  units  are  always  identical.  The  thermometric  units  practically  suppress  mass. 


INTRODUCTION.  XXVli 

mula  ml~lt~l&°,  where  #z  =  . 064799,  7=30.48,  and  t=  i,  and  is  therefore  = 
.064799/30.48  =  2.126  X  io~3- 

(c)  Find  the  relation  between  the  units  stated  in  (ft)  for  emissivity; 

In  this  case  the  conversion  formula  is  ml~*t~l,  where  ml  and  /  have  the 
same  value  as  before.  Hence  the  number  of  the  latter  units  in  the  former  is 
0.064  799/30.48- =  6.975  X  io~5. 

(d)  Find  the  number  of  centimeter  gram    second   units   in    the    inch  grain 
hour  unit  of  emissivity. 

Here  the  formula  is -aw/"2/"1,  where  ^  =  0.064799,  7=2.54,  and  ^  =  3600. 
Therefore  the  required  number  is  o.o64799/2-54'2  X  3600  =  2.790  X  io~6. 

(<?)  If  Joule's  equivalent  be  776  foot  pounds  per  pound  of  water  per  degree 
Fahrenheit,  what  will  be  its  value  in  gravitation  units  when  the  metre,  the 
kilogramme,  and  the  degree  Centigrade  are  units  1 

The  conversion  factor  in  this  case  is  ,^_,  or  /0~l,  where  /  =  .3048  and 
0-l=i.8;  .'.  776  X  .3048  X  1.8=425.7. 

(/)  If  Joule's  equivalent  be  24832  foot  poundals  when  the  degree  Fahren- 
heit is  unit  of  temperature,  what  will  be  its  value  when  kilogram  meter  second 
and  degree-Centigrade  units  are  used  1 

The  conversion  factor  is  ^r~0~\  where  /=  .3048,  t  =  i,  and  0~l  =  1.8  ; 
.-.  24832  X  l-r'20~l  =  24832  X  .3048'  X  1.8  =  4152.5. 

In  gravitation  units  this  would  give  4152.5/9.81  =  423.3. 

ELECTRIC   AND   MAGNETIC   UNITS. 

There  are  two  systems  of  these  units,  the  electrostatic  and  the  electromagnetic 
systems,  which  differ  from  each  other  because  of  the  different  fundamental  suppo- 
sitions on  which  they  are  based.  In  the  electrostatic  system  the  repulsive  force 
between  two  quantities  of  static  electricity  is  made  the  basis.  This  connects  force, 

quantity  of  electricity,  and  length  by  the  equation  f=a  |p,where  /  is  force,  a  a 

quantity  depending  on  the  units  employed  and  on  the  nature  of  the  medium,  q  and 
qt  quantities  of  electricity,  and  /  the  distance  between  q  and  qt.  The  magnitude  of 
the  force  /  for  any  particular  values  of  q,  qt  and  /  depends  on  a  property  of  the 
medium  across  which  the  force 'takes  place  called  its  inductive  capacity.  The  in- 
ductive capacity  of  air  has  generally  been  assumed  as  unity,  and  the  inductive 
capacity  of  other  media  expressed  as  a  number  representing  the  ratio  of  the  induc- 
tive capacity  of  the  medium  to  that  of  air.  These  numbers  are  known  as  the  spe- 
cific inductive  capacities  of  the  media.  According  to  the  ordinary  assumption, 
then,  of  air  as  the  standard  medium,  we  obtain  unit  quantity  of  electricity  when 
in  the  above  equation  q  =  qt,  and/",  a,  and  /  are  each  unity.  A  formal  definition 
is  given  below. 

In  the  electromagnetic  system  the  repulsion  between  two  magnetic  poles  or 


XXV111  INTRODUCTION. 

quantities  of  magnetism  is  taken  as  the  basis.  In  this  system  the  quantities  force, 
quantity  of  magnetism,  and  length  are  connected  by  an  equation  of  the  form 

/.         mm, 

f~*-jr*, 

where  m  and  mt  are  in  this  case  quantities  of  magnetism,  and  the  other  symbols 
have  the  same  meaning  as  before.  In  this  case  it  has  been  usual  to  assume  the 
magnetic  inductive  capacity  of  air  to  be  unity,  and  to  express  the  magnetic  induc- 
tive capacity  of  other  media  as  a  simple  number  representing  the  ratio  of  the  in- 
ductive capacity  of  the  medium  to  that  of  air.  These  numbers,  by  analogy  with 
specific  inductive  capacity  for  electricity,  might  be  called  specific  inductive  capac- 
ities for  magnetism.  They  are  usually  called  permeabilities.  ( Vide  Thomson, 
"  Papers  on  Electrostatics  and  Magnetism,"  p.  484.)  In  this  case,  also,  like  that 
for  electricity,  the  unit  quantity  of  magnetism  is  obtained  by  making  m  =  mt,  and 
/,  0,  and  /  each  unity. 

In  both  these  cases  the  intrinsic  inductive  capacity  of  the  standard  medium  is 
suppressed,  and  hence  also  that  of  all  other  media.  Whether  this  be  done  or  not, 
direct  experiment  has  to  be  resorted  to  for  the  determination  of  the  absolute  val- 
ues of  the  units  and  the  relations  of  the  units  in  the  one  system  to  those  in  the 
other.  The  character  of  this  relation  can  be  directly  inferred  from  the  dimen- 
sional formulae  of  the  different  quantities,  but  these  can  give  no  information  as  to 
the  relative  absolute  values  of  the  units  in  the  two  systems.  Prof.  Riicker  has 
suggested  (Phil.  Mag.  vol.  27)  the  advisability  of  at  least  indicating  the  exist- 
ence of  the  suppressed  properties  by  putting  symbols  for  them  in  the  dimensional 
formulae.  This  has  the  advantage  of  showing  how  the  magnitudes  of  the  different 
units  would  be  affected  by  a  change  in  the  standard  medium,  or  by  making  the 
standard  medium  different  for  the  two  systems.  In  accordance  with  this  idea,  the 
symbols  K  and  P  have  been  introduced  into  the  formulae  given  below  to  represent 
inductive  capacity  in  the  electrostatic  and  the  electromagnetic  systems  respectively. 
In  the  conversion  formulae  k  and/  are  the  ordinary  specific  inductive  capacities 
and  permeabilities  of  the  media  when  air  is  taken  as  the  standard,  or  generally 
those  with  reference  to  the  first  medium  taken  as  standard.  The  ordinary  for- 
mulae may  be  obtained  by  putting  K  and  P  equal  to  unity. 


ELECTROSTATIC   UNITS. 

i.  Quantity  of  Electricity.  —  The  unit  quantity  of  electricity  is  defined  as 
that  quantity  which  if  concentrated  at  a  point  and  placed  at  unit  distance  from  an 
equal  and  similarly  concentrated  quantity  repels  it,  or  is  repelled  by  it,  with  unit 
force.  The  medium  or  dielectric  is  usually  taken  as  air,  and  the  other  units  in  ac- 
cordance with  the  centimeter  gram  second  system. 

In  this  case  we  have  the  force  of  repulsion  proportional  directly  to  the  square 
of  the  quantity  of  electricity  and  inversely  to  the  square  of  the  distance  between 
the  quantities  and  to  the  inductive  capacity.  The  dimensional  formula  is  there- 
fore the  same  as  that  for  [force  X  length2  X  inductive  capacity]*  or 
and  the  conversion  factor  is 


INTRODUCTION.  XXIX 

2.  Electric  Surface  Density  and  Electric  Displacement.  —  The  density 
of  an  electric  distribution  at  any  point  on  a  surface  is  measured  by  the  quantity 
per  unit  of  area,  and  the  electric  displacement  at  any  point  in  a  dielectric  is  mea- 
sured by  the  quantity  displaced  per  unit  of  area.    These  quantities  have  therefore 
the  same  dimensional  formula,  namely,  the  ratio  of  the  formulae  for  quantity  of 
electricity  and  for  area  or  M^Lr^T^K*,  and  the  conversion  factor  m*l~*t~l&. 

3.  Electric  Force  at  a  Point,  or  Intensity  of  Electric  Field.  —  This  is 
measured  by  the  ratio  of  the  magnitude  of  the  force  on  a  quantity  of  electricity  at 
a  point  to  the  magnitude  of  the  quantity  of  electricity.     The  dimensional  formula 
is  therefore  the  ratio  of  the  formulae  for  force  and  electric  quantity,  or 


which  gives  the  conversion  factor 

4.  Electric  Potential  and  Electromotive  Force.  —  Change  of  potential 
is  proportional  to  the  work  done  per  unit  of  electricity  in  producing  the  change. 
The  dimensional  formula  is  therefore  the  ratio  of  the  formulae  for  work  and  elec- 

tric quantity,  or 

ML2T-< 


which  gives  the  conversion  factor 

5.  Capacity  of  a  Conductor.  —  The  capacity  of  an  insulated  conductor  is 
proportional  to  the  ratio  of  the  numbers  representing  the  quantity  of  electricity  in 
a  charge  and  the  potential  of  the  charge.     The  dimensional  formula  is  thus  the 
ratio  of  the  two  formulae  for  electric  quantity  and  potential,  or 

*  __  T  v 

r*" 

which  gives  Ik  for  conversion  factor.    When  K  is  taken  as  unity,  as  in  the  ordinary 
units,  the  capacity  of  an  insulated  conductor  is  simply  a  length. 

6.  Specific  Inductive  Capacity.  —  This  is  the  ratio  of  the  inductive  capac- 
ity of  the  substance  to  that  of  a  standard  substance,  and  hence  the  dimensional 
formula  is  K/K  or  i.* 

7.  Electric  Current.  —  Current  is  quantity  flowing  past  a  point  per  unit  of 
time.     The  dimensional  formula  is  thus  the  ratio  of  the  formulae  for  electric  quan- 
tity and  for  time,  or 


and  the  conversion  factor 


*  According  to  the  ordinary  definition  referred  to  air  as  standard  medium,  the  specific  inductive 
capacity  of  a  substance  is  K,  or  is  identical  in  dimensions  with  what  is  here  taken  as  inductive  ca- 
pacity. Hence  in  that  case  the  conversion  factor  must  be  taken  as  i  on  the  electrostatic  and  as 
the  electromagnetic  system. 


XXX  INTRODUCTION. 

8.  Conductivity,  or  Specific  *  Conductance.  —  This,  like  the  corresponding 
term  for  heat,  is  quantity  per  unit  area  per  unit  potential  gradient  per  unit  of  time. 
The  dimensional  formula  is  therefore 


K*     _  T-1K  or  _  electric  quantity  _  t 
-L^T-1K~^rp~  area  X  potential  gradient  X  time 


The  conversion  factor  is  t~lk. 

9.  Specific  *  Resistance.  —  This  is  the  reciprocal  of  conductivity  as  above 
defined,  and  hence  the  dimensional  formula  and  conversion  factor  are  respec- 
tively TK-1  and  tk~\ 

10.  Conductance.  —  The  conductance  of  any  part  of  an  electric  circuit,  not 
containing  a  source  of  electromotive  force,  is  the  ratio  of  the  numbers  represent- 
ing the  current  flowing  through  it  and  the  difference  of  potential  between  its  ends. 
The  dimensional  formula  is  thus  the  ratio  of  the  formulae  for  current  and  poten- 
tial, or 


from  which  we  get  the  conversion  factor  lt~^k, 

1  1  .   Resistance.  —  This  is  the  reciprocal  of  conductance,  and  therefore  the 
dimensional  formula  and  the  conversion  factor  are  respectively  L^TKT1  and 

rltk~\ 


EXAMPLES   OF   CONVERSION    IN    ELECTROSTATIC   UNITS. 

(a)  lind  the  factor  for  converting  quantity  of  electricity  expressed  in  foot  grain 
second  units  to  the  same  expressed  in  c.  g.  s.  units. 

By  (i)  the  formula  is  mlfit~l&,  in  which  in  this  case  m  =  0.0648,  1=  30.48,  t  = 
i,  and  k  =  i  ;  /.  the  factor  is  0.0648^  X  30.48^  =  4.2836. 

(£)  Find  the  factor  required  to  convert  electric  potential  from  millimeter  milli- 
gram second  units  to  c.  g.  s.  units. 

By  (4)  the  formula  is  m*Pt~lk~^,  and  in  this  case  m  =  o.ooi,  t=  o.i,  t=  i,  and 
&=i'}  .-.  the  factor  =  o.ooi*  X  o.i-  —  o.oi. 

(c)  Find  the  factor  required  to  convert  from  foot  grain  second  and  specific  in- 
ductive capacity  6  units  to  c.  g.  s.  units. 

By  (5)  the  formula  is  Ik,  and  in  this  case  /=30.48  and  &  =  6;  .*.  the  factor 
=  30.48  X  6  =  182.88. 

*  The  term  "  specific,/'  as  used  here  and  in  9,  refers  conductance  and  resistance  to  that  between 
the  ends  of  a  bar  of  unit  section  and  unit  length,  and  hence  is  different  from  the  same  term  in 
specific  heat,  specific  inductivity,  capacity,  etc.,  which  refer  to  a  standard  substance. 


INTRODUCTION.  XXXI 


ELECTROMAGNETIC   UNITS. 

As  stated  above,  these  units  bear  the  same  relation  to  unit  quantity  of  magne- 
tism that  the  electric  units  do  to  quantity  of  electricity.  Thus,  when  inductive 
capacity  is  suppressed,  the  dimensional  formula  for  magnetic  quantity  on  this  sys- 
tem is  the  same  as  that  for  electric  quantity  on  the  electrostatic  system.  All  quan- 
tities in  this  system  which  only  differ  from  corresponding  quantities  defined  above 
by  the  substitution  of  magnetic  for  electric  quantity  may  have  their  dimensional 
formulae  derived  from  those  of  the  corresponding  quantity  by  substituting  P 
for  K. 

i.  Magnetic  Pole,  or  Quantity  of  Magnetism.  —  Two  unit  quantities  of 
magnetism  concentrated  at  points  unit  distance  apart  repel  each  other  with  unit 
force.  The  dimensional  formula  is  thus  the  same  as  for  [force  X  length2  X  in- 
ductive capacity]-  or  M^UT"1?1,  and  the  conversion  factor  is 


2.  Density  of  Surface  Distribution  of  Magnetism.  —  This  is  measured 
by  quantity  of  magnetism  per  unit  area,  and  the  dimension  formula  is  therefore 
the  ratio  of  the  expressions  for  magnetic  quantity  and  for  area,  or  MiL~iT~1P*l 
which  gives  the  conversion  factor 


3-  Magnetic  Force  at  a  Point,  or  Intensity  of  Magnetic  Field.  —  The 
number  for  this  is  the  ratio  of  the  numbers  representing  the  magnitudes  of  the 
force  on  a  magnetic  pole  placed  at  the  point  and  the  magnitude  of  the  magnetic 
pole. 

The  dimensional  formula  is  therefore  the  ratio  of  the  expressions  for  force  and 
magnetic  quantity,  or 

TV/FT  T— 2 

]\/riT  ~$'T~i~p~$ 

M-L^T~1P^  ' 

and  the  conversion  factor  ^/~-/~1/~i. 

4.  Magnetic  Potential.  —  The  magnetic  potential  at  a  point  is  measured  by 
the  work  which  is  required  to  bring  unit  quantity  of  positive  magnetism  from  zero 
potential  to  the  point.     The  dimensional  formula  is  thus  the  ratio  of  the  formula 
for  work  and  magnetic  quantity,  or 

ML2T~2 
M^UT-1? 
which  gives  the  conversion  factor  mlllt~lp~^. 

5.  Magnetic    Moment.  —  This   is   the   product   of  the   numbers  for  pole 
strength  and  length  of  a  magnet.     The  dimensional  formula  is  therefore  the  pro- 
duct of  the  formulae  for  magnetic  quantity  and  length,  or  M^L4T~1P-,  and  the  con- 
version factor  ; 


6.  Intensity  of  Magnetization.  —  The  intensity  of  magnetization  of  any  por- 
tion of  a  magnetized  body  is  the  ratio  of  the  numbers  representing  the  magni- 


XXXli  INTRODUCTION. 


tude  of  the  magnetic  moment  of  that  portion  and  its  volume.     The  dimensional 
formula  is  therefore  the  ratio  of  the  formulae  for  magnetic  moment  and  volume,  or 


The  conversion  factor  is  therefore 

7.  Magnetic  Permeability,*  or  Specific  Magnetic  Inductive  Capacity. 
—  This  is  the  analogue  in  magnetism  to  specific  inductive  capacity  in  electricity. 
It  is  the  ratio  of  the  magnetic  induction  in  the  substance  to  the  magnetic  induc- 
tion in  the  field  which  produces  the  magnetization,  and  therefore  its  dimensional 
formula  and  conversion  factor  are  unity. 

8.  Magnetic  Susceptibility.  —  This  is  the  ratio  of  the  numbers  which  repre- 
sent the  values  of  the  intensity  of  magnetization  produced  and  the  intensity  of  the 
magnetic  field  producing  it.     The  dimensional  formula  is  therefore  the  ratio  of 
the  formulae  for  intensity  of  magnetization  and  magnetic  field  or 

or  P. 

The  conversion  factor  is  therefore/,  and  both  the  dimensional  formula  and  con- 
version factor  are  unity  in  the  ordinary  system. 

9.  Current  Strength.  —  A  current  of  strength  c  flowing  round  a  circle  of 
radius  r  produces  a  magnetic  field  at  the  centre  of  intensity  2-ircjr.     The  dimen- 
sional formula  is  therefore  the  product  of  the  formulae  for  magnetic  field  intensity 
and  length,  or  M^I/T"1?"*,  which  gives  the  conversion  factor 


10.  Current  Density,  or  Strength  of  Current  at  a  Point.  —  This  is  the 
ratio  of  the  numbers  for  current  strength  and  area.  The  dimensional  formula 
and  the  conversion  factor  are  therefore  MiL-fT~1P-i  and 


ii.  Quantity  of  Electricity.  —  This  is  the  product  of  the  numbers  for  cur- 
rent and  time.   The  dimensional  formula  is  therefore  M^T-1?-*  X  T= 
and  the  conversion  factor 


12.  Electric  Potential,  or  Electromotive  Force.  —  As  in  the  electrostatic 
system,  this  is  the  ratio  of  the  numbers  for  work  and  quantity  of  electricity.  The 
dimensional  formula  is  therefore 


and  the  conversion  factor 

*  Permeability,  as  ordinarily  taken  with  the  standard  medium  as  unity,  has  the  same  dimension 
formula  and  conversion  factor  as  that  which  is  here  taken  as  magnetic  inductive  capacity.  Hence 
for  ordinary  transformations  the  conversion  factor  should  be  taken  as  i  in  the  electromagnetic  and 
J"2/2  in  the  electrostatic  systems. 


INTRODUCTION.  xxxiii 

13.  Electrostatic  Capacity.  —  This  is  the  ratio  of  the  numbers  for  quantity 
of  electricity  and  difference  of  potential.     The  dimensional  formula  is  therefore 


and  the  conversion  factor  /~1/^>~1. 

14.  Resistance  of  a  Conductor.  —  The  resistance  of  a  conductor  or  elec- 
trode is  the  ratio  of  the  numbers  for  difference  of  potential  between  its  ends  and 
the  constant  current  it  is  capable  of  producing.  The  dimensional  formula  is 
therefore  the  ratio  of  those  for  potential  and  current  or 


The  conversion  factor  thus  becomes  //-1/,  and  in  the  ordinary  system  resistance 
has  the  same  conversion  factor  as  velocity. 

15.  Conductance.  —  This  is  the  reciprocal  of  resistance,  and  hence  the  dimen- 
sional formula  and  conversion  factor  are  respectively  L^TP"1  and  l~ltp~l. 

16.  Conductivity,  or  Specific  Conductance.  —  This  is  quantity  of  electric- 
ity transmitted  per  unit  of  area  per  unit  of  potential  gradient  per  unit  of  time. 
The  dimensional  formula  is  therefore  derived  from  those  of  the  quantities  men- 
tioned as  follows  :  — 

M'L>P-> 


The  conversion  factor  is  therefore  l~*tp~\ 

17.  Specific  Resistance.  —  This  is  the  reciprocal  of  conductivity  as  defined 
in  1  6,  and  hence  the  dimensional  formula  and  conversion  factor  are  respectively 
and 


18.  Coefficient  of  Self-induction,  or  Inductance,  or  Electro-kinetic  In- 
ertia. —  These  are  for  any  circuit  the  electromotive  force  produced  in  it  by  unit 
rate  of  variation  of  the  current  through  it.  The  dimensional  formula  is  therefore 
the  product  of  the  formulae  for  electromotive  force  and  time  divided  by  that  for 
current  or 


The  conversion  factor  is  therefore  lp,  and  in  the  ordinary  system  is  the  same  as 
that  for  length. 

19.  Coefficient  of  Mutual  Induction.  —  The  mutual  induction  of  two  cir- 
cuits is  the  electromotive  force  produced  in  one  per  unit  rate  of  variation  of  the 
current  in  the  other.  The  dimensional  formula  and  the  conversion  factor  are 
therefore  the  same  as  those  for  self-induction. 


XXXIV  INTRODUCTION. 

20.  Electro-kinetic  Momentum.  —  The  number  for  this  is  the  product  of 
the  numbers  for  current  and  for  electro-kinetic  inertia.  The  dimensional  formula 
is  therefore  the  product  of  the  formulae  for  these  quantities,  or  M*!^"1?"*  X  LP 
*  and  the  conversion  factor  is 


21.  Electromotive  Force  at  a  Point.  —  The  number  for  this  quantity  is 
the  ratio  of  the  numbers  for  electric  potential  or  electromotive  force  as  given  in 
12,  and  for  length.  The  dimensional  formula  is  therefore  M*L*T~~2P*,  and  the 
conversion  factor 


22.  Vector  Potential.  —  This  is  time  integral  of  electromotive  force  at  a 
point,  or  the  electro-kinetic  momentum  at  a  point.  The  dimensional  formula 
may  therefore  be  derived  from  21  by  multiplying  by  T,  or  from  20  by  dividing 
by  L.  It  is  therefore  M^T"1?*,  and  the  conversion  factor 


23.  Thermoelectric  Height.  —  This  is  measured  by  the  ratio  of  the  num- 
bers for  electromotive  force  and  for  temperature.  The  dimensional  formula  is 
therefore  the  ratio  of  the  formulae  for  these  two  quantities,  or  M^lJT"2?*®"1,  and 
the  conversion  factor 


24.  Specific  Heat  of  Electricity.  —  This  quantity  is  measured  in  the  same 
way  as  23,  and  hence  has  the  same  formulas. 

25.  Coefficient  of  Peltier  Effect.  —  This  is  measured  by  the  ratio  of  the 
numbers  for  quantity  of  heat  and  for  quantity  of  electricity.     The  dimensional 
formula  is  therefore 


and  the  conversion  factor 


EXAMPLES    OF    CONVERSION    IN    ELECTROMAGNETIC    UNITS. 

(a)  Find  the  factor  required  to  convert  intensity  of  magnetic  field  from  foot 
grain  minute  units  to  c.  g.  s.  units. 

By  (3)  the  formula  is  w*/"*/-1/"*,  and  in  this  case  m  =  0.0648,  /=  30.48,  t '  = 
60,  and/  =  i  ;  /.  the  factors  =  0.0648*  X  30.48"*  X  6o-1=  0.00076847. 

Similarly  to  convert  from  foot  grain  second  units  to  c.  g.  s.  units  the  factor  is 
0.0648*  X  30.48"*=  0.046  1 08. 

(£)  How  many  c.  g.  s.  units  of  magnetic  moment  make  one  foot  grain  second 
unit  of  the  same  quantity  ? 

By  (5)  the  formula  is  0iW~y,  and  the  values  for  this  problem  are  m  —  0.0648, 
/=  30.48,  /  =  i,  and/  =  i  ;  /.  the  number  =  0.0648*  X  30.48*=  1305.6. 

(c)  If  the  intensity  of  magnetization  of  a  steel  bar  be  700  in  c.  g.  s.  units,  what 
will  it  be  in  millimeter  milligram  second  units  ? 


INTRODUCTION.  XXXV 


By  (6)  the  formula  is  wV*/-1/*,  and  in  this  case  m  =  1000,  /=  10,  t  =  i,  and 
/  =  i  ;  /.  the  intensity  =  700  X  1000*  X  10*  =  70000. 

(</)  Find  the  factor  required  to  convert  current  strength  from  c.  g.  s.  units  to 
earth  quadrant  io~n  gram  and  second  units. 

By  (9)  the  formula  is  m*fit~lp-*,  and  the  values  of  these  quantities  are  here  m  = 
lo11,  /=  io~9,  /=  i,  and/  =  i  ;  /.  the  factor  =  lo1*  X  io~$=  10. 


(e)  Find  the  .factor  required  to  convert  resistance  expressed  in  c.  g.  s.  units  into 
the  same  expressed  in  earth-quadrant  io~u  gram  and  second  units. 

By  (14)  the  formula  is  lt~lp,  and  for  this  case  /=  io~9,  /=  i,  and  p  =  i  ; 
/.  the  factor  =  io~9. 

(/)  Find  the  factor  required  to  convert  electromotive  force  from  earth-quadrant 
io~n  gram  and  second  units  to  c.  g.  s.  units. 

By  (12)  the  formula  is  w*/1/-^*,  and  for  this  case  m  =  io~u,  /=  io9,  /=  i, 
and/  =  i  ;  .*.  the  factor  =  io8. 


PRACTICAL   UNITS. 

In  practical  electrical  measurements  the  units  adopted  are  either  multiples  or 
submultiples  of  the  units  founded  on  the  centimeter,  the  gram,  and  the  second 
as  fundamental  units,  and  air  is  taken  as  the  standard  medium,  for  which  K  and  P 
are  assumed  unity.  The  following,  quoted  from  the  report  to  the  Honorable  the 
Secretary  of  State,  under  date  of  November  6th,  1893,  by  the  delegates  repre- 
senting the  United  States,  gives  the  ordinary  units  with  their  names  and  values 
as  defined  by  the  International  Congress  at  Chicago  in  1893  :  — 

"  Resolved,  That  the  several  governments  represented  by  the  delegates  of  this 
International  Congress  of  Electricians  be,  and  they  are  hereby,  recommended  to 
formally  adopt  as  legal  units  of  electrical  measure  the  following :  As  a  unit  of  re- 
sistance, the  international  ohm,  which  is  based  upon  the  ohm  equal  to  io9  units  of 
resistance  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  is  represented 
by  the  resistance  offered  to  an  unvarying  electric  current  by  a  column  of  mercury 
at  the  temperature  of  melting  ice  14.4521  grams  in  mass,  of  a  constant  cross- 
sectional  area  and  of  the  length  of  106.3  centimeters. 

"  As  a  unit  of  current,  the  international  ampere,  which  is  one  tenth  of  the  unit  of 
current  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  which  is  represented 
sufficiently  well  for  practical  use  by  the  unvarying  current  which,  when  passed 
through  a  solution  of  nitrate  of  silver  in  water,  and  in  accordance  with  accom- 
panying specifications,*  deposits  silver  at  the  rate  of  0.001118  of  a  gram  per 
second. 

*  "  In  the  following  specification  the  term  '  silver  voltameter '  means  the  arrangement  of  appara- 
tus by  means  of  which  an  electric  current  is  passed  through  a  solution  of  nitrate  of  silver  in  water. 
The  silver  voltameter  measures  the  total  electrical  quantity  which  has  passed  during  the  time  of 
the  experiment,  and  by  noting  this  time  the  time  average  of  the  current,  or,  if  the  current  has  been 
kept  constant,  the  current  itself  can  be  deduced. 

"  In  employing  the  silver  voltameter  to  measure  currents  of  about  one  ampere,  the  following 
arrangements  should  be  adopted  :  — 


XXXVI  INTRODUCTION. 

"  As  a  unit  of  electromotive  force,  the  international  volt,  which  is  the  electro- 
motive force  that,  steadily  applied  to  a  conductor  whose  resistance  is  one  interna- 
tional ohm,  will  produce  a  current  of  one  international  ampere,  and  which  is  rep- 
resented sufficiently  well  for  practical  use  by  T^§£  of  the  electromotive  force 
between  the  poles  or  electrodes  of  the  voltaic  cell  known  as  Clark's  cell,  at  a  tem- 
perature of  15°  C.,  and  prepared  in  the  manner  described  in  the  accompanying 
specification.* 

"  As  a  unit  of  quantity,  the  international  coulomb,  which  is  the  quantity  of  elec- 
tricity transferred  by  a  current  of  one  international  ampere  in  one  second. 

"As  a  unit  of  capacity,  the  international  farad,  which  is  the  capacity  of  a  con- 
denser charged  to  a  potential  of  one  international  volt  by  one  international  cou- 
lomb of  electricity.f 

"  As  a  unit  of  work,  the  joule,  which  is  equal  to  io7  units  of  work  in  the  c.  g.  s. 
system,  and  which  is  represented  sufficiently  well  for  practical  use  by  the  energy 
expended  in  one  second  by  an  international  ampere  in  an  international  ohm. 

"As  a  unit  of  power,  the  watt,  which  is  equal  to  io7  units  of  power  in  the  c.  g.  s. 
system,  and  which  is  represented  sufficiently  well  for  practical  use  by  the  work 
done  at  the  rate  of  one  joule  per  second. 

"  As  the  unit  of  induction,  the  henry,  which  is  the  induction  in  a  circuit  when 
the  electromotive  force  induced  in  this  circuit  is  one  international  volt,  while  the 
inducing  current  varies  at  the  rate  of  one  ampere  per  second. 

"  The  Chamber  also  voted  that  it  was  not  wise  to  adopt  or  recommend  a  stand- 
ard of  light  at  the  present  time." 

By  an  Act  of  Congress  approved  July  i2th,  1894,  the  units  recommended  by 
the  Chicago  Congress  were  adopted  in  this  country  with  only  some  unimportant 
verbal  changes  in  the  definitions. 

By  an  Order  in  Council  of  date  August  23d,  1894,  the  British  Board  of  Trade 
adopted  the  ohm,  the  ampere,  and  the  volt,  substantially  as  recommended  by 
the  Chicago  Congress.  The  other  units  were  not  legalized  in  Great  Britain. 
They  are,  however,  in  general  use  in  that  country  and  all  over  the  world. 

"  The  kathode  on  which  the  silver  is  to  be  deposited  should  take  the  form  of  a  platinum  bowl 
not  less  than  io  centimeters  in  diameter  and  from  4  to  5  centimeters  in  depth. 

"  The  anode  should  be  a  plate  of  pure  silver  some  30  square  centimeters  in  area  and  2  or  3 
millimeters  in  thickness. 

"  This  is  supported  horizontally  in  the  liquid  near  the  top  of  the  solution  by  a  platinum  wire 
passed  through  holes  in  the  plate  at  opposite  corners.  To  prevent  the  disintegrated  silver  which 
is  formed  on  the  anode  from  falling  on  to  the  kathode,  the  anode  should  be  wrapped  round  with 
pure  filter  paper,  secured  at  the  back  with  sealing  wax. 

"  The  liquid  should  consist  of  a  neutral  solution  of  pure  silver  nitrate,  containing  about  1 5  parts 
by  weight  of  the  nitrate  to  85  parts  of  water. 

"  The  resistance  of  the  voltameter  changes  somewhat  as  the  current  passes.  To  prevent  these 
changes  having  too  great  an  effect  on  the  current,  some  resistance  besides  that  of  the  voltameter 
should  be  inserted  in  the  circuit.  The  total  metallic  resistance  of  the  circuit  should  not  be  less 
than  io  ohms." 

*  A  committee,  consisting  of  Messrs.  Helmholtz,  Ayrton,  and  Carhart,  was  appointed  to  pre- 
pare specifications  for  the  Clark's  cell,  but  no  report  was  made,  on  account  of  Helmholtz's  death. 

t  The  one  millionth  part  of  the  farad  is  more  commonly  used  in  practical  measurements,  and  is 
called  the  microfarad. 


PHYSICAL   TABLES 


TABLE  1 . 
FUNDAMENTAL  AND  DERIVED  UNITS, 


To  change  a  quantity  from  one  system  of  units  to  another  :  substitute  in  the  correspond- 
ing conversion  factor  from  the  following  table  the  ratio  of  the  magnitudes  of  the  old  units 
to  the  new  and  multiply  the  old  quantity  by  the  resulting  number.  For  example  :  to  reduce 
velocity  in  miles  per  hour  to  feet  per  second,  the  conversion  factor  is  //-*;  /=528o/i, 
^=3600/1,  therefore  the  factor=528o/36oo=i.467. 


(a)  FUNDAMENTAL  UNITS. 


Name  of  Unit. 


Symbol. 


Conversion  Factor. 


Length. 

Mass. 

Time. 

Temperature. 

Electric  Inductive  Capacity. 

Magnetic  Inductive  Capacity. 


L 

M 
T 
© 
K 
P 


(&)  DERIVED  UNITS. 
/.    Geometric  and  Dynamic  Units. 


Name  of  Unit. 


Conversion  Factor. 


Area. 
Volume. 
Angle. 
Solid  Angle. 
Curvature. 
Tortuosity. 

Specific  curvature  of  a  surface. 
Angular  velocity. 
Angular  acceleration. 
Linear  velocity. 
Linear  acceleration. 
Density. 

Moment  of  inertia. 

Intensity  of  attraction,  or  "force  at  a  point." 
Absolute  force  of  a  centre  of  attraction,  or  "  strength ") 
of  a  centre."  j" 

Momentum. 

Moment  of  momentum,  or  angular  momentum. 
Force. 

Moment  of  a  couple,  or  torque. 
Intensity  of  stress. 
Modulus  of  elasticity. 
Work  and  energy. 
Resilience. 
Power  or  activity. 


ml* 
IT2 

/8/~2 
mlt~l 


m  /-1  /~a 


SMITHSONIAN  TABLES. 


TABLE  1 . 
FUNDAMENTAL  AND  DERIVED  UNITS. 


//.    Heat  Units. 

Name  of  Unit. 

Conversion  Factor. 

Quantity  of  heat  (thermal  units). 

m  0 

"                "     (thermometric  units). 

1*0 

"                "     (dynamical  units). 

m  /2  /~2 

Coefficient  of  thermal  expansion. 

^H 

Conductivity  (thermal  units). 

m  /-1  /-1 

(thermometric  units),  or  diffusivity. 

/a/~~1 

(dynamical  units). 

m  1  1~*  &~l 

Thermal  capacity. 

m 

Latent  heat  (thermal  units). 

0 

"     (dynamical  units). 

/2/"~2 

Joule's  equivalent. 

/2  /~2  0 

Entropy  (heat  measured  in  thermal  units). 

m 

"         (   "            "         "  dynamical  units). 

m  /2  /~2  0 

///.   Magnetic  and  Electric  Units. 

Conversion  factor 

Conversion  factor 

Name  of  Unit. 

for  electrostatic 

for  electromag- 

system. 

netic  system. 

Magnetic  pole,  or  quantity  of  mag-  ) 

1    i    -» 

*  i 

netism.                                              ) 

P 

Density  of  surface  distribution  of) 

m\  /-'  £~i 

|    x_j    ,_!    .  j 

magnetism.                                      j" 

lip 

Intensity  of  magnetic  field. 

m*  /*  r2  & 

m\  l~k  /-1^-J 

Magnetic  potential. 

m*  1*  t~*  $ 

m*  ft  t~l  p~* 

Magnetic  moment. 

m*  fi  k~* 

m*  fi  f~lfl 

Intensity  of  magnetisation. 

nfi  l~%  k~l 

m*  l~*  t~l  p^ 

Magnetic  permeability. 
Magnetic   susceptibility   and    mag-) 
netic  inductive  capacity.                 ) 

i 

i 

P 

Quantity  of  electricity. 
Electric  surface  density  and  electric  ) 

m*  I1  r1  & 

rtfljpr* 

displacement.                                   ) 

m       p 

Intensity  of  electric  field. 

m*  f~}  r1  k-* 

m*  fi  t~*  p* 

Electric  potential  and  e.  m.  f. 

m*  fi  t~l  k~* 

m*  /3  /~2/* 

Capacity  of  a  condenser. 
Inductive  capacity. 

Ik 
k 

£££* 

Specific  inductive  capacity. 
Electric  current. 

i 
m*  I  t     K? 

i 

SMITHSONIAN  TABLES. 


TABLE  1. 
FUNDAMENTAL  AND  DERIVED  UNITS, 


///.   Magnetic  and  Electric  Units. 

Conversion  factor 

Conversion  factor 

Name  of  Unit. 

for  electrostatic 

for  electromag- 

system. 

netic  system. 

Conductivity. 

t*k 

t^tr* 

Specific  resistance. 

t  k~l 

/2  t~l  p 

Conductance. 

I  t~l  k 

/~1  tp~l 

Resistance. 

/-1  /  k~l 

/  t~l  p 

Coefficient  of   self    induction    and) 
coefficient  of  mutual  induction.      ) 

***** 

IP 

Electrokinetic  momentum. 

m*  /»  XT* 

m*  I*  r1/* 

Electromotive  force  at  a  point. 

ml  /-*  /-I  k~\ 

m*  /*  t~*  p* 

Vector  potential. 

m*  /-*  k~* 

m*  fi  r~l  p^ 

Thermoelectric  height  and  specific") 
heat  of  electricity.                           j 

w»  /I  /-»*-**-' 

m*  I*  /-2/i  0~l 

Coefficient  of  Peltier  effect. 

m*  F*  t  k~*  6 

j  7~i  ysi  /) 

SMITHSONIAN  TABLES. 


TABLE  2. 
TABLES  FOR  CONVERTING  U.   S.  WEIGHTS  AND  MEASURES.4 

(1)  CUSTOMARY   TO   METRIC. 


LINEAR. 

CAPACITY. 

Inches 
to 
millimeters. 

Feet  to 
meters. 

Yards  to 
meters. 

Miles 
to 
kilometers 

Fluid 
drams  to 
milliliters 
or  cubic 
centimeters. 

Fluid 
ounces 
to 
milliliters. 

Liquid 
quarts  to 
liters. 

Gallons  to 

liters. 

25.4001 

0.304801 

0.914402 

1.60935 

i 

3-70 

29.57 

0.94633 

3-78533 

50.8001 

0.609601 

1.828804 

3.21869 

2 

7-39 

59.15 

1.89267 

7.57066 

76.2002 

0.914402 

2.743205 

4.82804 

3 

11.09 

88.72 

2.83900 

11.35600 

IOI.6oO2 
127.0003 

1.219202 
1.524003 

3.657607 
4.572009 

6-43739 
8.04674 

4 

5 

14.79 
18.48 

118.29 
147.87 

3-78533 

4-73  i  67 

I5-I4i33 
18.92666 

152.4003 
177.8004 
203.2004 

1.828804 
2.133604 
2.438405 

5.486411 
6.400813 

7-3I52I5 

9.65608 

11.2654' 
12.87478 

6 

1 

22.18 

25.88 
29.57 

177-44 
207.01 
236.58 

5.67800 
6.62433 
7.57066 

22.71199 
30.28266 

228.6005 

2.743205 

8.229616 

14.48412 

9 

33-27 

266.16 

8.51700 

34.06799 

SQUARE. 

WEIGHT. 

Square 
inches  to 
square  cen- 
timeters. 

Square  feet 
to  square 
decimeters. 

Square 
yards  to 
square 
meters. 

Acres  to 
hectares. 

Grains  to 
milligrams. 

Avoirdu- 
pois ounces 
to  grams. 

Avoirdu- 
pois pounds 
to  kilo- 
grams. 

Troy 
ounces  to 
grams. 

6.452 

9.290 

0.836 

0.4047 

i 

64.7989 

28.3495 

0-45359 

31.10348 

12.903 

18.581 

1.672 

0.8094 

2 

129.5978 

56.6991 

0.90718 

62.20696 

19-355 

27.871 

2.508 

1.2141 

3 

194.3968 

85.0486 

1.36078 

93-3  l  °44 

25.807 
32.258 

37.161 
46.452 

3-345 
4.181 

1.6187 
2-0234 

4 
5 

259.1957 
323.9946 

113.3981 
141.7476 

1.81437 
2.26796 

124.41392 

I55-5I74Q 

38.710 

55-742 

5-017 

2.4281 

6 

388.7935 

170.0972 

2.72155 

186.62088 

45.161 

5T-6l3 
58.065 

65.032 
74.323 
83-613 

5.853 
6.689 

7.525 

2.8328 

3-2375 
3.6422 

n 
J 
9 

453.5924 
518.3913 
583-  *  903 

198.4467 
226.7962 
255.H57 

3-I75I5 
3.62874 
4.08233 

2I7-72437 
248.82785 

279-93I33 

CUBIC. 

Cubic 
inches  to 
cubic  cen- 
timeters. 

Cubic  feet 
to  cubic 
meters. 

Cubic 
yards  to 
cubic 
meters. 

Bushels  to 
hectoliters. 

i  Gunter's  chain    =      20.1168      meters. 
i  sq.  statute  mile  =    259.000     hectares. 

i  fathom                =       1.829        meters. 

16.387 

0.02832 

0.765 

0.35239 

i  nautical  mile       =  1853.25          meters. 

32-774 

0.05663 

1.529 

0.70479 

i  foot                     =       0.304801    meter. 

A 

J5 

49.161 

65.549 
81.936 

0.08495 
0.11327 
0.14159 

2.294 
3.058 
3-823 

1.05718 
1.40957 
1.76196 

i  avoir,  pound       =    453.5924277  grams. 
1  5432.35639  grains  =       i.ooo    kilogram. 

I 

98.323 
II47IO 

0.16990 
0.19822 

4.587 
5-352 

2.11436 
2.46675 

8 

131.097 

0.22654 

6.II6 

2.81914 

9 

147.484 

0.25485 

6.881 

3-I7I54 

According  to  an  executive  order  dated  April  15,  1893,  the  United  States  yard  is  defined  as  3600/3937  meter,  and 
the  avoirdupois  pound  as  1/2.20462  kilogram. 

i  meter  (international  prototype)  =  1553164.13  times  the  wave-length  of  the  red  Cd.  line.  Benoit,  Fabry  and 
Perot.  C.  R.  144,  1907  differs  only  in  the  decimal  portion  from  the  measure  of  Michelson  and  Benoit  14  years  earlier. 

The  length  of  the  nautical  mile  given  above  and  adopted  by  the  U.  S.  Coast  and  Geodetic  Survey  many  years  ago, 
is  defined  as  that  of  a  minute  of  arc  of  a  great  circle  of  a  sphere  whose  surface  equals  that  of  the  earth  (Clarke's  Sphe- 
roid of  1866). 

*  Quoted  from  sheets  issued  by  the  United  States  Bureau  of  Standards. 

SMITHSONIAN  TABLES. 


TABLE  2  (continued). 
TABLES  FOR  CONVERTING  U.  S.  WEIGHTS  AND  MEASURES. 

(2)  METRIC   TO    CUSTOMARY. 


LINEAR. 

CAPACITY. 

Millili- 

ters  or 

C 

-enti- 

] 

)eca- 

Hecto- 

Meters to 

Meters  to 

Meters  to 

Kilometers 

cubic  cen- 

liters to 

liters 

liters 

inches. 

feet. 

yards. 

to  miles. 

timeters 

luid 

to 

to 

to  fluid 
drams. 

ounces. 

gallons. 

bushels. 

i 

39-3700 

3.28083 

1.093611 

0.62137 

i 

0.27 

0.338 

1.0567 

2 

.6418 

2.8378 

2 

78.7400 

6.56167 

2.187222 

1.24274 

2 

0.54 

0.676 

2.1134 

5-2836 

5.6756 

!  3 

I  iS.IIOO 

9.84250 

3.280833 

1.86411 

3 

0.8  1 

I 

.014 

3.1701 

7 

•92  S3 

8.5135 

4 

157.4800 

i3'I2333 

4-374444 

248548 

4 

1.  08 

I 

•3  S3 

4.2268 

10.5671 

j  1.3513 

5 

196.8500 

16.40417 

5.468056 

3-I0685 

5 

1-35 

I 

.691 

5.2836 

13.2089 

14.1891 

6 

236.2200 

19.68500 

6.561667 

3.72822 

6 

1.62 

2.029 

6.3403 

15 

•8S07 

17.0269 

7 

275.5900 

22.96583 

7-655278 

4-34959 

7 

1.89 

2.367 

7-3970 

18 

-4924 

19.8647 

8 

314.9600 

26.24667 

8.748889 

4.97096 

8 

2.16 

2 

•70S 

8-4537 

21 

.1342 

22.7026 

9 

354-3300 

29.52750 

9.842500 

5-59233 

9 

2.43 

3-043 

9.5104 

23.7760 

25.5404| 

SQUARE. 

WEIGHT. 

Square 

Square 

Square 

Milli- 

Kilo- 

Hecto- 

Kilo- 

centimeters 
to  square 
inches. 

meters  to 
square 
feet. 

meters  to 
square 
yards. 

Hectares 
to  acres. 

grams  to 
grains. 

grams  to 
grains. 

grams  to 
ounces 
avoirdupois. 

grams  to 
pounds 
ivoirdupois. 

i 

0.1550 

10.764 

1.196 

2.471 

i 

0.01543 

IS4 

^2.36 

•S2 

74 

2.20462 

!  2 

0.3100 

21.528 

2.392 

4.942 

2 

0.03086 

308 

34.71 

7-os 

48 

4.40924 

3 

0.4650 

32.292 

3.588 

7-4I3 

3 

0.04630 

46297.07 

10.58 

22 

6.61387 

4 

O.62OO 

43.055 

4784 

9.884 

4 

0.06173 

61729.43 

14.1096 

8.81849 

15 

0.7750 

53.819 

5.980 

12355 

5 

0.07716 

) 

77161.78 

17.6370 

II.023II 

6 

0.9300 

64.583 

7.176 

14.826 

6 

0.09259 

92594.14 

21.1644 

13.22773 

7 

1.0850 

75-347 

8.372 

17.297 

7 

0.10803 

108026.49 

24.6918 

I5-43236 

8 

I.24OO 

86.ui 

9.568 

19.768 

8 

0.12346 

123458.85 

28.2192 

17.63698 

9 

1.3950 

96.875 

10.764 

22.239 

9 

0.13880 

) 

1388 

51.21 

31 

.7466 

19.84160 

CUBIC. 

WEIGHT. 

Cubic 
centimeters 
to  cubic 

Cubic 
decimeters 
to  cubic 

Cubic 
meters  to 
cubic 

Cubic 
meters  to 
cubic 

Quintals  to 
pounds  av. 

Milliers  or 
tonnes  to  pounds 

Kilograms 
to  ounces 

inches. 

inches. 

feet. 

yards. 

i 

0.06  10 

61.023 

35-3I4 

1-308 

! 

220.46 

2204.6 

32.1507 

i  2 

O.I22O 

122.047 

70.269 

2.616 

2 

440.92 

4409.2 

64.3015 

3 
4 

0.1831 
0.2441 

183.070 
244.094 

105-943 
141.258 

3-924 
5-232 

3 
4 

66t. 

881. 

39 
8S 

66  1 

88  1 

3-9 

8-S 

96.4522 
128.6030 

5 

0.3051 

305.  "7 

176.572 

6.540 

5 

1102.31 

11023.1 

160.7537 

6 

0.3661 

366.140 

211.887 

7.848 

6 

1322.77 

13227.7 

192.9045 

7 

0.4272 

427.164 

247.201 

9.156 

7 

24 

I54324 

225.0552 

8 
9 

0.4882 
0.5492 

488.187 
549-210 

282.516 
317.830 

10.464 
11.771 

8 
9 

1763.70 
1984.16 

17637.0 
19841.6 

257.2059 
289.3567 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an  International  Bureau  of  Weights  and 
Measures  has  been  established  near  Paris.  Under  the  direction  of  the  International  Committee,  two  ingots  were 
cast  of  pure  platinum-iridium  in  the  proportion  of  9  parts  of  the  former  to  i  of  the  latter  metal.  From  one  of  these 
a  certain  number  of  kilograms  were  prepared,  from  the  other  a  definite  number  of  meter  bars.  These  standards  of 
weight  and  length  were  intercompared,  without  preference,  and  certain  ones  were  selected  as  International  proto- 
type standards.  The  others  were  distributed  by  lot,  in  September,  1889,  to  the  different  governments,  and  are  called 
National  prototype  standards.  Those  apportioned  to  the  United  States  were  received  in  1890,  and  are  kept  at  the 
Bureau  of  Standards  in  Washington,  D.  C. 

The  metric  system  was  legalized  in  the  United  States  in  1866. 

The  International  Standard  Meter  is  derived  from  the  Metre  des  Archives,  and  its  length  is  defined  by  the 
distance  between  two  lines  at  o°  Centigrade,  on  a  platinum-iridium  bar  deposited  at  the  International  Bureau  of 
Weights  and  Measures. 

The  International  Standard  Kilogram  is  a  mass  of  platinum-iridium  deposited  at  the  same  place,  and  its  weight 
in  vacuo  is  the  same  as  that  of  the  Kilogram  des  Archives. 

The  liter  is  equal  to  the  quantity  of  pure  water  at  4°  C,  760  mm.  Hg.  pressure  which  weighs  i  kilogram  =  1.000027 
cu.  dm.  (Trav.  et  Mem.  Bureau  Intern,  des  P.  et  M.  14,  1910,  Benoit.) 

SMITHSONIAN  TABLES. 


TABLE  3. 

EQUIVALENTS    OP   METRIC    AND    BRITISH    IMPERIAL    WEIGHTS 
AND    MEASURES.* 

(1)    METRIC   TO    IMPERIAL 


LINEAR  MEASURE. 

1  I^Tm.)  (mm°      |=      °'°3937    in- 
i  centimeter  (.01  m.)      =      0.39370     " 
i  decimeter  (.1  m)         =      3-93701 
(39-370II3  " 

I  METER    (m.)       .      .      .  =  <     3.280843  ft. 

(    1.09361425  yds. 
"W      }•    '    •=    -0.936.4 

Ih!?o™   •  •  -"^s    - 

'l^mO       •    •    •=     «*»37-fl* 
'•&£&}'    •    '=     ^.37-ile, 
i  micron              •    •    .  —      o  ooi  mm. 

MEASURE  OF  CAPACITY, 
i  mmmter  (ml.)  (.001  |  =    O>o6lo  cub.  in. 

i  centiliter  (.01  liter)        =  |  ^2g4m" 

i  deciliter  (.1  liter)  .     .  =    0.176  pint. 
i  LITER  (1,000  cub.    ) 
centimeters  or  i    >   =     1.75980  pints, 
cub.  decimeter)       ) 
i  dekaliter  (10  liters)     .   =    2.200  gallons, 
i  hectoliter  (100  "   )     .  =     2.75  bushels, 
i  kiloliter  (1,000  "  )     .  =    3.437  quarters. 

APOTHECARIES'  MEASURE. 

SQUARE  MEASURE. 

i  sq.  centimeter  .    .     .  =      0.1550  sq.  in. 

"T^t^tm.,      }-    '5.500  „.  in. 
I  sq.  meter  or  centi-  1  j  10.7639  sq.  ft. 

i    cubic    centi-  )       (    0.03520  fluid  ounce, 
meter     ^r  —  \    0.28157  fluid  drachm, 
gram  w't)       )       (  15.43236  grains  weight. 
i  cub.  millimeter  =  0.01693  minim. 

AVOIRDUPOIS   WEIGHT. 

milligram  (mgr.)   .     .  =  0.01543  grain, 
centigram  (.01  gram.)   =  0.15432      " 
decigram  (.1         "     )   =  1.54324  grains. 

GRAM          .                   .           —  1543236        " 

I  ARE  (100  sq.  m.)          =  119.60  sq.  yds. 
i  hectare  (100  ares     )  _ 
or  10,000  sq.  m.)     f~ 

CUBIC  MEASURE. 

i  cub.  centimeter         ) 
(c.c.)  (1,000  cubic  >  =    0.0610  cub.  in. 
millimeters)            ) 
i  eub.  decimeter           ) 
(c.d.)  (1,000  cubic  >  =  61.024      "      " 
centimeters)            ) 

1  ™:;  -  -i-sss** 

dekagram  (10  gram.)   =  5.64383  drams, 
hectogram    (100  "    )  =  3.52739  oz. 
C  2.2046223  lb~ 

KILOGRAM  (1,000"     )    =^15432.3564 
(    '     grains, 
myriagram  (10  kilog.)   =22.04622  Ibs. 
quintal        (100    "    )   =  1.96841  cwt. 
millier  or  tonne  )                ^^Q^« 
(1,000  kilog.)    ]'    '  =0-9842  ton. 

TROY  WEIGHT. 

(   0.03215  oz.  Troy. 
I  GRAM     .    .    =  ]   0.64301  pennyweight. 
(  15.43236  grains. 

APOTHECARIES'  WEIGHT. 

(    0.25721  drachm, 
i  GRAM     ....=<    0.77162  scruple. 
(  I  S43236  grains. 

NOTE.— The  METER  is  the  length,  at  the  temperature  of  o°  C.,  of  the  platinum-iridium  bar  deposited  at  the 
International  Bureau  of  Weights  and  Measures  at  Sevres,  near  Paris,  France. 
The  present  legal  equivalent  of  the  meter  is  39.370113  inches,  as  above  stated. 
The  KILOGRAM  is  the  ma 


The  prc 0 ., ,..,, 

KILOGRAM  is  the  mass  of  a  platinum-iridium  weight  deposited  at  the  same  place. 
The  LITER  contains  one  kilogram  weight  of  distilled  water  at  its  maximum  density  (4°  C.),  the  barometer  being 


at  760  millimeters. 

*In  accordance  with  the  schedule  adopted  under  the  Weights  and  Measures  (metric  system)  Act,  1897. 
SMITHSONIAN  TABLES. 


TABLE  3. 

EQUIVALENTS  OF   METRIC   AND   BRITISH   IMPERIAL   WEIGHTS 
AND    MEASURES. 

(2)  METRIC  TO  IMPERIAL 


LINEAR  MEASURE. 

MEASURE  OF   CAPACITY. 

Millimeters 
to 
inches. 

Meters 
to 
feet. 

Meters 
to 
yards. 

Kilo- 
meters  to 
miles. 

Liters 
to 

pints. 

Dekaliters 
to 
gallons. 

Hectoliters 
to 
bushels. 

Kiloliters 
to 
quarters. 

0-039370" 
0.07874023 
0.11811034 
0.15748045 
0.19685056 

3.28084 
6.56169 

9.84253 
I3-I2337 
16.40421 

1.09361 
2.18723 
3.28084 
4-37446 
5.46807 

0.62137 
1.24274 
1.86412 
2.48549 
3.10686 

I 
2 

3 

4 
5 

1.75980 
3.51961 
5.27941 
7.03921 
8.79902 

2.19975 
4-39951 
6.59926 
8.79902 
10.99877 

2.74969 
5-49938 
8.24908 
10.99877 
13.74846 

3-43712 
6.87423 
10.31135 
13.74846 
17-18558 

0.23622068 

0.27559079 
0.31496090 
0.35433102 

19.68506 
22.96590 
26.24674 
29.52758 

6.56169 

7.65530 
8.74891 
9-84253 

3.72823 
4.34960 
4.97097 
5.59235 

6 

I 

9 

10.55882 
12.31862 
14.07842 
15.83823 

13.19852 
15.39828 

17.59803 
19.79778 

16.49815 
19.24785 
21.99754 
24-74723 

20.62269 
24.05981 
27.49692 
30.93404 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

4 
5 

Square 
centimeters 
to  square 
inches. 

Square 
meters  to 
square 
feet. 

Square 
meters  to 
square 
yards. 

Hectares 
to  acres. 

Milli- 
grams 
to 
grains. 

Kilograms 
to  grains. 

Kilo- 
grams 
to 
pounds, 

Quintals 
to 
hundred- 
weights. 

O.I5500 
0.31000 
0.46500 
0.62000 
0.77500 

10-76393 
21.52786 
32.29179 
43-05572 
53.81965 

I.I9599 
2.39198 
3-58798 
4-78397 
5-97996 

2.4711 
4.9421 

74132 
9.8842 

12.3553 

I 
2 

3 

4 
5 

0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

15432.356 

30864.713 
46297.069 
61729.426 
77161.782 

2.20462 
4.40924 
6.61387 
8.81849 
II.O23II 

1.96841 
3.93683 
5.90524 

7.87365 
9.84206 

6 

8 
9 

0.93000 
1.08500 
I.24OOO 

'•39501 

64.58357 
75-34750 
86.11143 
96.87536 

7-17595 
8.37194 

9-56794 
10.76393 

14.8263 
17.2974 
I9-7685 
22.2395 

6 

i 

9 

0.09259 
0.10803 
0.12346 
0.13889 

92594.138 
108026.495 
123458.851 
138891.208 

13.22773 
I5-43236 
17-63698 
19.84160 

11.81048 
13.77889 
I5-74730 
17.71572 

CUBIC  MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 
(cont.) 

TROY  WEIGHT. 

APOTHE- 
CARIES' 
WEIGHT. 

Cubic 
decimeters 
to  cubic 
inches. 

Cubic 
meters  to 
cubic 
feet. 

Cubic 
meters  to 
cubic 
yards. 

Cub.  cen- 
timeters 
to  fluid 
drachms. 

Milliers  or 
tonnes  to 
tons. 

Grams 
to  ounces 
Troy. 

Grams 

to  penny- 
weights. 

Grams 
to 
scruples. 

I 

3 

4 
5 

61.02390 
122.04781 
183.07171 
244.09561 
305."952 

35-3I476 
70.62952 
105.94428 
141.25904 
176.57379 

L30795 
2.61591 
3.92386 
5.23182 
6-53977 

0.28157 
0.56314 
0.84471 
I.I2627 
1.40784 

I 

2 

3 

4 
5 

0.98421 
1.96841 
2.95262 

3.93683 
4.92103 

0.03215 
0.06430 
0.09645 
0.12860 
0.16075 

0.64301 
1.28603 
1.92904 
2.57206 
3.21507 

0.77162 

1.54324 
2.31485 

3.08647 
3.85809 

6 

I 

9 

366.14342 
427.16732 
488.19123 
549.21513 

211.88855 
247.20331 
282.51807 
3I7-»3283 

7.84772 
9.15568 
10.46363 
11.77159 

1.68941 
1.97098 
2.25255 
2.53412 

6 

8 
9 

5.90524 
6.88944 

& 

0.19290 
0.22506 
0.23721 
0.28936 

3.85809 
4.50110 
5.14412 
578713 

4.62971 
5.40132 
6.17294 
6.94456 

SMITHSONIAN  TABLES. 


TABLE  3. 

EQUIVALENTS  OF   BRITISH   IMPERIAL   AND   METRIC  WEIGHTS 
AND   MEASURES. 

(3)    IMPERIAL  TO    METRIC. 


9 


LINEAR  MEASURE. 

MEASURE   OF  CAPACITY. 

(  25.400  milli- 

gill    —  1.42  deciliters. 

1  mch    =  |      meters. 

i  foot  (12  in.)     .     .  =       0.30480  meter. 

pint  (4  gills)  .     .     .  =  0.568  liter, 
quart  (2  pints)    .     .  =  1.136     liters. 

i  YARD  (3  ft.)     .     .  =       0.914399    " 
I  pole  (5!  yd.)    .    .  =       5.0292  meters. 

GALLON  (4  quarts)  =  4.5459631  " 
peck  (  2  galls.)    .     .  =  9.092     '     « 

I  chain  (22  yd.  or)            2QIl68       « 

bushel  (8  galls.)     .  =  3.637  dekaliters. 

100  links)         \ 
i  furlong  (220  yd.)  =    201.168 

quarter  (8  bushels)  =  2.909  hectoliters. 

(    1.6093  kilo- 

i  mile  (1,760  yd.)   .  =  |     meters. 

AVOIRDUPOIS   WEIGHT. 

SQUARE  MEASURE. 

igrain  .                          <64.8milli- 

6.4516  sq.  cen- 

i  souare  inch               —  —           ^v 

1      grams, 
dram  ....       —       1  772  grams. 

timeters. 
,     ,                                  9-2903  sq.  deci- 

ounce  (16  dr.)  .     .=      28.350      '* 

I  sq.  ft.  (144  sq.  in.)    =         *  meters. 

(    0.836126  sq. 
i  SQ.  YARD  (9  sq.  ft.)  =    i        meters.  4 

™(g±sfh       0.45359^43  Mogr. 

stone  (  14  Ib.)  .     .=       6.350                " 

i  perch  (301  sq.  yd.)  =  |    -5-93  sq.  me- 

quarter  (28  Ib.)     .=      12.70 
hundredweight  )            (  50.80                  " 

i  rood  (40  perches)    =       10.117  ares. 

(ii2lb.)          )            (    0.5080  quintal. 

i  ACRE  (4840  sq.  yd.)  =        0.40468  hectare. 

(  1.0160  tonnes 

i  sq.  mile  (640  acres)  =  j  259.00  hectares. 

Moo^cwt).-!^^  s 

TROY  WEIGHT. 

CUBIC   MEASURE. 

I  cub.  inch=   16.387  cub.  centimeters, 
i  cub.  foot  (1728  )       (0.028317  cub.  me- 
cub.  in.)           f—  <      ter,    or     28.317 
f      cub.  decimeters, 
i  CUB    YARD  (27  1^0.76455  cub.  meter. 

i  Troy  OUNCE  (480)   =3I.IO35  grams. 
grains  avoir.)      ) 
I  pennyweight  (24  1   __                     « 
grains)                 )    " 

NOTE.  —  The  Troy  grain  is  of  the  same  weight  as 
the  Avoirdupois  grain. 

APOTHECARIES'  MEASURE. 

APOTHECARIES'  WEIGHT. 

i  gallon  (8  pints  or  J            4.5459631  liters. 
160  fluid  ounces)  )             •••aw  o 
i  fluid  ounce,  f  3  1             28.4123  cubic 
(8  drachms)       f                centimeters. 
I   fluid  drachm,  f  3  )              3-55x5  cubic 
(60  minims)         J  *          centimeters, 
i  minim,  m  (0.91146  i  0.05919  cubic 

i  ounce  (8  drachms)   =31.1035  grams, 
i  drachm,  3  i  (  3  scru-  {  ggg         «< 
pies)                      J         3- 
i   scruple    91   (20  J     _                    « 
grains)                ) 

grain  weight)       )               centimeters. 

NOTE.  —  The  Apothecaries'  ounce  is  of  the  same 
weight  as  the  Troy  ounce.      The   Apothecaries' 

NOTE.  —  The  Apothecaries'  gallon  is  of  the  same 

grain  is  also  of  the  same  weight  as  the  Avoirdupois 

capacity  as  the  Imperial  gallon. 

grain. 

NOTE.  —  The  YARD  is  the  length  at  62°  Fahr. ,  marked  on  a  bronze  bar  deposited  with  the  Board  of  Trade. 

The  POUND  is  the  weight  of  a  piece  of  platinum  weighed  in  vacuo  at  the  temperature  of  o°  C.,  and  which  is  also 
deposited  with  the  Board  of  Trade. 

The  GALLON  contains  10  Ib.  weight  of  distilled  water  at  the  temperature  of  62°  Fahr.,  the  barometer  being  at 
30  Inches. 

SMITHSONIAN  TABLES. 


IO  TABLE  3. 

EQUIVALENTS  OF   BRITISH    IMPERIAL   AND   METRIC  WEIGHTS 
AND   MEASURES. 

(4)   IMPERIAL  TO  METRIC. 


r 

LINEAR  MEASURE. 

MEASURE  OF  CAPACITY. 

_ 

I 

2 

3 

4 
5 

Inches 
to 
centimeters. 

Feet 
to 
meters. 

Yards 
to 
meters. 

Miles 
to  kilo- 
meters. 

2 

3 

4 

5 

Quarts 
to 
liters. 

Gallons 
to 
liters. 

Bushels 
to 
dekaliters. 

Quarters 
to 
hectoliters. 

2-S39998 
5.079996 
7.619993 
10.159991 
12.699989 

0.30480 
0.60960 
0.91440 
1.21920 
1.52400 

0.91440 
1.82880 
2.74320 
3.65760 

4.57200 

1.60934 
3.21869 
4.82803 

6-43737 
8.04671 

1.13649 
2.27298 
3-40947 
4-54596 
5.68245 

4.54596 
9.09193 

I3-63789 
18.18385 
22.72982 

3-63677 
7-27354 
10.91031 

14.54708 
18.18385 

2.90942 
5.81883 
8.72825 
11.63767 
14.54708 

6 

I 

9 

IS-239987 
17.779984 
20.319982 
22.859980 

1.82880 
2.13360 
2.43840 
2.74320 

5.48640 

7.3I5I9 
8.22959 

9.65606 
11.26540 

12.87474 
14.48408 

6 

8 
9 

6.81894 

7-95544 
9.09193 
10.22842 

27.27578 
31.82174 
36.36770 
40.91367 

21.82062 

25-45739 
29.09416 

32-73093 

17.45650 
20.3659  1 

23.27533 
26.18475 

SQUARE  MEASURE. 

WEIGHT  (AVOIRDUPOIS). 

Square 
inches 
to  square 
centimeters. 

Square 
feet 
to  square 
decimeters. 

Square 
yards  to 
square 
meters. 

Acres  to 
hectares. 

Grains 
to  milli- 
grams. 

Ounces  to 
grams. 

Pounds 
to  kilo- 
grams. 

Hundred- 
weights to 
quintals. 

I 
2 

3 
4 
5 

6.45159 
12.90318 

19-35477 
25.80636 
32.25794 

9.29029 
18.58058 
27.87086 
37.16115 
46.45144 

0.83613 
1.67225 
2.50838 

3-3445° 
4.18063 

0.40468 
0.80937 
1.21405 
1.61874 
2.02342 

I 
2 

3 

4 
5 

64.79892 
129.59784 

194.39675 
259-1  9567 
323-99459 

28.34953 
56.69905 
85.04858 
113.39811 
141.74763 

0-45359 
0.90718 
1.36078 
1.81437 
2.26/96 

0.50802 
1.01605 
1.52407 
2.03209 
2.54012 

6 

8 
9 

38.70953 
45.16112 
51.61271 
58.06430 

55-74I73 
65.03201 
74.32230 
83.61259 

5.01676 
5.85288 
6.68901 
7-525I3 

2.42811 
2.83279 
3.23748 
3.64216 

6 
9 

388.79351 
453-59243 
518.39135 
583.19026 

170.09716 
198.44669 
226.79621 

255-H574 

2.72155 

3-I75I5 
3.62874 
4.08233 

3.04814 
3-556I6 
4.06419 
4.57221 

CUBIC  MEASURE. 

APOTHE- 
CARIES' 
MEASURE. 

AVOIRDUPOIS 
(font.). 

TROY  WEIGHT. 

APOTHK- 
CARJES' 
WEIGHT. 

Cubic 
inches 
to  cubic 
centimeters. 

Cubic  feet 
to 
cubic 
meters. 

Cubic 
yards 
to  cubic 
meters. 

Fluid 
drachms 
to  cubic 
centi- 
meters. 

Tons  to 
milliers  or 
tonnes. 

Ounces  to 
grams. 

Penny- 
weights to 
grams. 

Scruples 
to 
grams. 

I 
2 

3 
4 
5 

16.38702 

32.77404 
49.16106 
65.54808 
81.93511 

0.02832 
0.05663 
0.08495 
0.11327 
0.14158 

0.76455 
1.52911 
2.29366 
3.05821 
3.82276 

3-55I53 
7.10307 
10.65460 
14.20613 
17.75767 

I 

2 

3 

4 
5 

1.01605 
2.03209 
3.04814 
4.06419 
5.08024 

31.10348 
62.20696 
93.31044 
124.41392 
155.51740 

I-555I7 
3-II035 
4.66552 
6.22070 
777587 

1.29598 
2.59196 
3.88794 

5-18391 
6.47989 

6 

i 

9 

98.32213 
114.70915 
131.09617 
147.48319 

0.16990 
0.19822 
0.22653 
0.25485 

4.58732 

5-35I87 
6.11642 
6.88098 

21.30920 
24.86074 
28.41227 
31.96380 

6 

I 

9 

6.09628 
7-II233 
8.12838 
9.14442 

186.62088 
217.72437 
248.82785 
279-93T33 

9-33  1  °4 
10.88622 
12.44139 
I3-99657 

777587 
9.07185 
10.36783 
11.66381 

SMITHSONIAN  TABLES. 


TABLE  4. 


II 


VOLUME  OF  A  CLASS  VESSEL  FROM  THE  WEIGHT  OF  ITS  EQUIVALENT 
VOLUME    OF    MERCURY   OR   WATER. 

If  a  glass  vessel  contains  at  t°  C,  P  grammes  of  mercury,  weighted  with  brass  weights  in  air  at 
760  mm.  pressure,  then  its  volume  in  c.  cm. 

at  the  same  temperature,  t,  :    V  =  PR    =  Py 
at  another  temperature,  /i,  :   V  =  PR\  =  P  fid  \  i  +  y  (t\  -  /)  ( 
/  =  the  weight,  reduced  to  vacuum,  of  the  mass  €>f  mercury  or  water  which,  weighed  with  brass 

weights,  equals  i  gram ; 
d  ==•  the  density  of  mercury  or  water  at  t°  C, 
and  7  =  o.ooo  025,  is  the  cubical  expansion  coefficient  of  glass. 


Temper- 
ature 
t 

WATER. 

MERCURY. 

R. 

Xi,  *i  =  10°. 

j?i,  ^  =  20°. 

ft. 

J?!,  ^  =  10°. 

Xlt  /!  =  20°. 

0° 

I.OOII92 

1.001443 

I.OOI693 

0-0735499 

0.0735683 

0.0735867 

I 

"33 

1358 

l6O9 

5633 

5798 

5982 

2 

1092 

1292 

1542 

5766 

59*4 

6098 

3 

1068 

1243 

1493 

5900 

6029 

6213 

4 

1060 

I2IO 

I46O 

§033 

6144 

6328 

5 

1068 

"93 

H43 

6167 

6259 

6443 

6 

7 

1.001092 
1131 

1.001192 
1206 

I.OOI442 
1456 

0.0736301 
6434 

0.0736374 
6490 

0.0736558 

8 

1184 

1234 

1485 

6568 

6605 

6789 

9 

1252 

1277 

1527 

6702 

6720 

6904 

10 

1333 

'333 

1584 

6835 

6835 

7020 

ii 

1.001428 

1.001403 

I.OOI653 

0.0736969 

0.0736951 

0.0737135 

12 

1536 

1486 

1736 

7103 

7066 

7250 

13 

1657 

1582 

1832 

7236 

7181 

7365 

H 

1790 

1690 

1940 

7370 

7297 

7481 

«s 

1935 

1810 

2060 

75°4 

7412 

7596 

16 

1.002092 

1.001942 

I.002I93 

0.0737637 

0.0737527 

0.07377II 

17 

2261 

2086 

2337 

7771 

7642 

7826 

18 

2441 

2241 

2491 

7905 

7757 

7941 

19 

2633 

2407 

2658 

8039 

7872 

8057 

20 

2835 

2584 

2835 

8172 

7988 

8l72 

21 

1.003048 

1.002772 

1.003023 

0.0738306 

0.0738103 

O.O738288 

22 

3271 

2970 

322O 

8440 

8218 

8403 

23 

24 
25 

3504 
3748 
4001 

3178 
3396 
3624 

3429 
3647 
3875 

8573 
8707 
8841 

8333 
8449 

8564 

8518 

& 

26 

27 

1.004264 
4537 

1.003862 
4110 

I.OO4II3 
4361 

0.0738974 

0.0738679 
8794 

0.0738864 
8979 

28 

4818 

4366 

46l6 

9242 

8910 

9094 

29 

5110 

4632 

4884 

9376 

9025 

92IO 

30 

4908 

5159 

95*o 

9140 

9325 

Taken  from  Landolt,  Bornstein,  and  Meyerhoffer's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


12 


TABLE  5. 
DERIVATIVES  AND  INTEGRALS.* 


J  .-„, 

^n+i 

d  dx 

a  ax 

ya;  cte 

tt-f-I 

d  uv 

/    fa       du\   , 

rdx 

=  log  a: 

u 

/  du       dv\ 

d*» 

=•  nxn~1  dx 

/*<*"* 

_I  go;r 

a 

_d/(w)   du 

as 

d/(«) 

fx  eax  dx 

=^2"  («*-!) 

de* 

=  e*dx 

flog  x  dx 

=  *  log  x—x 

de*x 

=  a  eax  dx 

fu  dv 

=  w  v—fv  du 

d  loge  * 

x 

f(a+bx}n  dx 

_(a+bx)n+1 

(w+i)6 

dx* 

=  xx  (  i  -1-  loge  a?) 

dsina 

=  cos  x  dx 

/(a2-!-*2)-1  dx 

=  -  tan-i  -  = 

a             a 

i  sin-.       * 

0                    V#2_j_a2 

d  cos  x 

=  —sin  x  dx 

/(a2-*2)-1*** 

=  I-log^ 

2a       a—  a; 

dtznx 

—  sec2  x  dx 

/(a2-a;2)-l  dx 

=  sin—1   -,  or  —  cos~  l  — 

a'                    a 

dcotx 

=  —esc2  x  dx 

fx(az±x*~)-ldx 

=  ±(a2±«2)> 

dsecx 

=  tan  x  sec  x  dx 

/sin2  x  dx 

=  —  |  cos  a;  sin  x+%  x 

dcscx 

—  —cot  x  .  scs  a:  dx 

/cos2  x  dx 

=  |  sin  x  cos  a;+£  x 

d  sin-1  x 

=  (i  —  **)  -*  d* 

/sin  a:  cos  x  dx 

=  £  sin2  a; 

d  cos-1  x 

=  -(i-a:2)-*  da; 

f  (sin  a;  cos  a;)-1  da;  =  log  tan  x 

d  tan-1  x 

=  (i+a;2)"1^ 

/tan  x  dx 

=  —log  cos  x 

d  cot—1  x 

=  —  (i+a:2)"1^ 

/tan2  x  dx 

=  tan  a;—  a: 

d  sec-1  x 

:=  a;  —  1  (a;2  —  i)  —  ^  dx 

/cot  a;  da; 

=  log  sin  x 

d  esc-1  *] 

:=  —  x  —  1  (#2  —  i)  —  ^  dx 

/cot2  *  da; 

=  —  cot  x—x 

d  sinh  x 

=  cosh  x  dx      M 

/esc  x  dx 

=  log  tan  f  a: 

d  cosh  a; 

=  sinh  x  dx 

fx  sin  a;  da: 

=  sin  a;—  a;  cos  x 

d  tanh  a; 

=  sech2  x  dx 

fx  cos  a;  da: 

=  cosa:+a;  sin* 

d  coth  x 

=  —csch2  a:  dx 

/tanh  a;  da; 

=  log  cosh  x 

d  sech  a; 

=  —sech  jc  tanh  dx 

/coth  a;  da: 

=  log  sinh  x 

d  csch  x 

=  -csch  a:  .  coth  x  dx 

/sech  a;  da: 

=  2  tan-1  e*=gd  u 

d  sinh-1  a; 

=  (*2+i)-Jd* 

/csch  a:  da; 

=  log  tanh  - 

d  cosh-  a: 

=  (x2—  i)—*  da: 

fx  sinh  a;  da; 

=  x  cosh  a;—  sinh  * 

d  tanh-    x 

=  (j  —a?)-1  dx 

fx  cosh  a;  da; 

=  x  sinh  a:—  cosh  a; 

d  coth-  a; 

=  (i—  a;2)"1  da; 

/sinh2  x  dx 

=  £  (sinh  a;  cosh  a;—  a;) 

d  sech—  a; 

=  _£-i  (i—  a;2)  -»  d« 

/cosh2  a;  da: 

=  |  (sinh  a;  cosh  a;+a;) 

d  csch-  * 

=  _,-i(a:,+I)-» 

/sinh  a;  cosh  a;  da; 

=|  cosh  (2  a;) 

*  See  also  accompanying  table  of  derivatives.    For  example  :  /cos.  x  dx  —  sin.  x  +  constant. 
SMITHSONIAN  TABLES. 


TABLE  6. 
SERIES. 


(x  +  y)n  =  xn  +  HL  xn-l  y  +  n  ^    V  *n-2  ^2  +  .  .  . 

LI xn—m  ym+ 

Wl ! 

(I±»).  =  I±IW+  «0ti^  ±  «(»-H»-«)«'  +  ---  +  (±'j*t»'^  +  ... 


(n- 

±  a;)"1  =  i 


±  *)~2  =  i  T  2o;+3o;2  T 


/<«+*)-/ W+*/' («)  + ^7"  (»)+.;..  +  D /<»(*)+;..  ^'"series. 

Maclaurin's 
),"t*  •  •  •  series. 


. 


x  —  i      i  /x  —  iV      I  A  —  J V 


log  (i  +  x)  =  x  -  \tf 


w  3!      5!      7! 

cos  a;  =  ^  (eia5  +  e-«>)  =  i_^-+L_|_  +  .  .  .  =  x  _  versin  a; 


7T  I  I  I 


SMITHSONIAN  TABLES. 


TABLE  6   (continued). 
SERIES. 


cosh  * 

-  1  ,  +  _»  -      *  '~^~^~ 

1 

2  ^                              2!    '    4!  +  6!  +  '  " 

^          ' 

tanh  x 

I                   2                     17 

(3-2  ^  iTT2) 

sinh~  l  x 

-3_1?L8  +  I.3.^_£.3.5*7, 

(*2  <C  I  ) 

23        245        2467 

—  IOCT  2v  4-                         I3I,I35 
f   2   2*         2  4  4*<  +   2  4  6   6*« 

<*>0 

cosh"1  x 

=  togM_i-L        '2_L        13|    i 

2    2X*          2  4  4**          240   0*° 

(,'>.) 

tanh-1  x 

=  ^+1^30.1^511^.71 

r    2         v 

3                  5                  7 

T                        T                       fS  T 

gd*  = 

0  —  X      '   ~~  •#*    1            #5                   X*    I 

(*  small) 

6           24          5040 

—  —                   CAnli     <v                                                     ^ 

(*  large) 

2                                     23                  245 

x 

=    gd-1  0  =  04-^3+±05+^I_)/)74.... 

H) 

f(*) 

I    .                                 TTX                             2TTX 

=  -  b0  +  b.  cos    h  b,  cos    h  •  .  . 

2                                     C                                C 

.      TTX                           ZTTX 

+  ai  sm  \-  az  cos  h  .  .  . 

[  —  c<#<c) 

c                     c 

am 

--  /^+c  /Msin  W?r*<7* 

-  cy  _  c  j  w  si    c 

b- 

1    /*  +  C     /•  /    \             WT*j 

CJ   -CJ  W  cos      c      ^ 

TABLE  7. -MATHEMATICAL  CONSTANTS, 


e  =  2.71828  18285 

Numbers. 
TT  =  3.I4I59    26536 

Logarithms. 
0.49714   98727 

g-i  =  0.36787  94412 

IT2   =  9.86960    44OII 

0.99429  97454 

M  =  logioe  =  0.43429  44819 

-  =  0.31830    98862 

9.50285  01273 

(M)-1  =  loge  10  =  2.30258  50930 

X/1T  =    1.77245    38509 

0.24857  49363 

l°gio  logio^  ==  9-63778  43II3 

—  =  0.88622    69255 

9-94754  49407 

Iogi02  =  0.30102  99957 

—^  =  0.56418    95835 

9.75142  50637 

Ioge2  ==  0.69314  71806 

—  =    I.I2837    91671 

0.05245  50593 

loglol  =  M.log^ 

^^  =  I-2533I  41373 

0.09805  99385 

I°g5*  =  l°ge*-  I°g5£ 

•%/-  =  0.79788  45608 

9.90194  00615 

=  loge*-MogeB 

j.      *  =  0.78539  81634 

9.89508  98814 

logeir  =  1.14472  98858 

—  =  0.44311  34627 
4 

9.64651  49450 

p  =  0.47693  62762 

f  7T    =  4.18879    O2048 

0.62208  86093 

logp  =  9.67846  03565 

^T==    =    1.08443    75514 

0.03520  45477 

SMITHSONIAN  TABLES. 


TABLES.  15 

VALUES  OF  RECIPROCALS,  SQUARES,  CUBES,  SQUARE  ROOTS,  OF 

NATURAL  NUMBERS. 


« 

lOOO.i 

n^ 

«3 

j» 

n 

I000.£ 

H* 

«« 

4n 

10 

IOO.OOO 

IOO 

1000 

3-1623 

65 

15.3846 

4225 

274625 

8.0623 

II 

90.9091 

121 

J33r 

3.3166 

66 

1S-151S 

4356 

287496 

8.1240 

12 

83-3333 

1  44 

1728 

3.4641 

67 

14.9254 

4489 

300763 

8.1854 

I3 

76.9231 

169 

2197 

3.6056 

68 

14.7059 

4624 

3  i  4432 

8.2462 

14 

71.4286 

196 

2744 

3-74I7 

69 

14.4928 

476l 

328509 

8.3066 

15 

66.6667 

225 

3375 

3-873° 

70 

14-2857 

4900 

343000 

8.3666 

16 

62.5000 

256 

4096 

4.0000 

7i 

14.0845 

5041 

357911 

8.4261 

17 

58-8235 

289 

§J3 

4.1231 

72 

13.8889 

5^4 

373248 

8.4853 

18 

55-5556 

324 

32 

4.2426 

73 

13.6986 

5329 

389017 

8.5440 

'9 

52.6316 

36i 

59 

4.3589 

74 

13.5135 

5476 

405224 

8.6023 

20 

50.0000 

400 

8000 

4.4721 

75 

13-3333 

5625 

421875 

8.6603 

21 

47.6190 

441 

9261 

4.5826 

76 

i3-I579 

5776 

438976 

8.7178 

22 

45-4545 

484 

10648 

4.6904 

77 

12.9870 

5929 

456533 

8-775° 

23 

434783 

529 

12167 

4-7958 

78 

12.8205 

6084 

474552 

8.8318 

24 

41.6667 

576 

13824 

4.8990 

79 

12.6582 

6241 

493039 

8.8882 

25 

40.0000 

625 

15625 

5.0000 

80 

12.5000 

6400 

512000 

8-9443 

26 

38.4615 

676 

17576 

5.0990 

81 

12.3457 

6561 

53r44i 

9.0000 

27 

37-0370 

729 

19683 

5.1962 

82 

12.1951 

6724 

551368 

9-0554 

28 

35-7M3 

784 

21952 

5-29I5 

83 

12.0482 

6889 

571787 

9.1104 

29 

344828 

841 

24389 

5-3852 

84 

11.9048 

7056 

592704 

9.1652 

30 

33-3333 

900 

27000 

5-4772 

85 

11.7647 

7225 

614125 

9.2195 

3* 

32.2581 

961 

29791 

5-5678 

86 

11.6279 

7396 

636056 

9.2736 

32 

31.2500 

1024 

32768 

5-6569 

87 

11.4943 

7569 

658503 

9-3274 

33 

30-3030 

1089 

35937 

5-7446 

88 

11.3636 

7744 

681472 

9.3808 

34 

29.4118 

1156 

39304 

5-8310 

89 

11.2360 

7921 

704969 

9.4340 

35 

28.5714 

1225 

42875 

5.9161 

90 

n.ini 

8100 

729000 

9.4868 

36 

27.7778 

1296 

46656 

6.0000 

91 

10.9890 

8281 

753571 

9-5394 

37 

27.0270 

1369 

50653 

6.0828 

92 

10.8696 

8464 

778688 

9-59J7 

33 

26.3158 

1444 

54872 

6.1644 

93 

10.7527 

8649 

804357 

9-6437 

39 

25.6410 

1521 

59319 

6.2450 

94 

10.6383 

8836 

830584 

9.6954 

40 

25.0000 

1600 

64000 

6.3246 

95 

10.5263 

9025 

857375 

9.7468 

4i 

24.3902 

1681 

68921 

6.4031 

96 

10.4167 

9216 

884736 

9.7980 

42 

23.8095 

1764 

74088 

6.4807 

97 

10.3093 

9409 

912673 

9.8489 

43 

23.2558 

1849 

79507 

6-5574 

98 

10.2041 

9604 

941192 

9.8995 

44 

22.7273 

1936 

85184 

6.6332 

99 

10.1010 

9801 

970299 

9-9499 

45 

22.2222 

2025 

91125 

6.7082 

100 

IO.OOOO 

1  0000 

I  000000 

10.0000 

46 

21.7391 

2116 

97336 

6.7823 

101 

9.90099 

IO2OI 

1030301 

10.0499 

47 

21.2766 

2209 

103823 

6.8557 

102 

9.80392 

10404 

1061208 

10.0995 

48 

20.8333 

2304 

110592 

6.9282 

103 

9.70874 

10609 

1092727 

10.1489 

49 

20.4082 

2401 

117649 

7.0000 

104 

9.61538 

I08I6 

1124864 

10.1980 

50 

51 

20.0000 
19.6078 

2500 
2601 

125000 
132651 

7.0711 
7.1414 

105 

1  06 

9.52381 
9-43396 

IIO25 
11236 

1157625 

1191010 

10.2470 
10.2956 

52 

19.2308 

2704 

140608 

7.2111 

107 

9-34579 

II449 

1225043 

10.3441 

53 

18.8679 

2809 

148877 

7.2801 

108 

9-25926 

11664 

1259712 

10.3923 

54 

18.5185 

2916 

157464 

7.3485 

109 

9-I743I 

Il88l 

1295029 

10.4403 

55 

18.1818 

3025 

166375 

7.4162 

110 

9.09091 

1  2  IOO 

1331000 

10.4881 

56 

17-8571 

3136 

175616 

7-4833 

in 

9.00901 

I232I 

1367631 

!0-5357 

* 

59 

17-5439 
17.2414 
16.9492 

3249 
3364 
348i 

185193 
195112 

205379 

7-5498 
7.6158 
7.6811 

112 

"3 
114 

8.92857 
8.84956 
8.77193 

12544 
12769 
12996 

1404928 
1442897 
1481544 

10.5830 
10.6301 
10.6771 

60 

61 

16.6667 
16.3934 

3600 
372i 

216000 
226981 

7-746o 
7.8102 

115 

116 

8.69565 
8.62069 

13225 

r3456 

1520875 

1  560896 

10.7238 
10.7703 

62 

16.1290 

3844 

238328 

7.8740 

117 

8.54701 

13689 

1601613 

10.8167 

63 

15-8730 

3969 

250047 

7-9373 

118 

8.47458 

13924 

1643032 

10.8628 

64 

15.6250 

4096 

262144 

8.0000 

119 

8.40336 

14161 

1685159 

10.9087 

SMITHSONIAN   TABLES. 


I  6  TABLE  8    (continued). 

VALUES   OF   RECIPROCALS,   SQUARES,   CUBES,  SQUARE   ROOTS, 
OF    NATURAL    NUMBERS. 


n 

*W 

»2 

# 

V- 

n 

1000.? 

- 

«3 

J 

120 

121 
122 

8-33333 
8.26446 
8.19672 

14400 
14641 
14884 

I728OOO 
1771561 
1815848 

10.9545 
1  1  .0000 
11.0454 

175 

176 

177 

5.71429 
5.68182 
5-64972 

30625 
30976 

5359375 
545»776 
5545233 

13.2288 
13.2665 
'3-304I 

123 

8.13008 

15129 

1860867 

11.0905 

178 

5.61798 

3!684 

i3-34!7 

124 

8.06452 

15376 

1906624 

179 

5-58659 

32041 

5735339 

U-379! 

125 

8.00000 

15625 

i953I25 

11.1803 

180 

5-55556 

32400 

5832000 

13.4164 

126 

127 

7-93651 

7.87402 

15876 
16129 

2000376 
2048383 

11.2250 
11.2694 

181 
182 

5.52486 

5-49451 

32761 
33I24 

5929741 
6028568 

!3-4536 
13.4907 

128 
129 

7.81250 
7-75194 

16384 
16641 

2097152 
2146689 

n-3!37 
II-3578 

183 
184 

5.46448 
5-43478 

33489 
33856 

6128487 
6229504 

I3-5647 

130 

7.69231 

16900 

2197000 

11.4018 

185 

5.40541 

34225 

6331625 

13.6015 

131 

7-63359 

17161 

2248091 

n-4455 

186 

5-37634 

34596 

6434856 

13.6382 

132 

7-57576 
7.51880 

17424 
17689 

2299968 
2352637 

11.4891 
11.5326 

187 
1  88 

5-34759 

34969 
35344 

6539203 
6644672 

13.6748 

134 

7.46269 

17956 

2406104 

II-5758 

189 

5.29101 

35721 

6751269 

13-7477 

135 

136 

7.40741 
7.35294 

18225 
18496 

2460375 
2515456 

11.6190 
11.6619 

190 

191 

5.26316 
5-23560 

36100 
36481 

6859000 
6967871 

13.7840 
13.8203 

137 

7.29927 

18769 

2571353 

11.7047 

192 

5-20833 

36864 

7077888 

13.8564 

138 

7.24638 

19044 

2628072 

n-7473 

193 

5-i8i35 

37249 

7189057 

13.8924 

139 

7.19424 

19321 

2685619 

11.7898 

194 

5-I5464 

37636 

7301384 

13.9284 

140 

7.14286 

19600 

2744000 

11.8322 

195 

5.12821 

38025 

74!4875 

13.9642 

141 

7.09220 

19881 

2803221 

11.8743 

196 

5.10204 

38416 

7529536 

14.0000 

142 

7.04225 

20164 

2863288 

11.9164 

197 

5.07614 

38809 

7645373 

14-0357 

H3 

6.99301 

20449 

2924207 

11-9583 

198 

5-05051 

39204 

7762392 

14.0712 

144 

6-94444 

20736 

2985984 

I2.OOOO 

199 

5-02513 

39601 

7880599 

14.1067 

145 

6.89655 

21025 

3048625 

I2.O4I6 

200 

5.00000 

40000 

8000000 

14.1421 

146 

6.84932 

21316 

3112136 

12.0830 

201 

4.97512 

40401 

8120601 

14.1774 

147 

6.80272 

21609 

3176523 

12.1244 

2O2 

4.95050 

40804 

8242408 

14.2127 

148 

6.75676 

21904 

3241792 

12.1655 

203 

4.92611 

41209 

8365427 

14.2478 

149 

6.71141 

222OI 

3307949 

12.2066 

204 

4.90196 

41616 

8489664 

14.2829 

150 

6.66667 

225OO 

3375000 

12.2474 

205 

4-87805 

42025 

8615125 

14.3178 

151 

6.62252 

22801 

3442951 

12.2882 

206 

4-85437 

42436 

8741816 

14.3527 

152 

6.57895 

23104 

3511808 

12.3288 

207 

4.83092 

42849 

8869743 

14-3875 

6-53595 

23409 

358  *  577 

12.3693 

208 

4.80769 

43264 

8998912 

14.4222 

*54 

6-493  5  ! 

23716 

3652264 

12.4097 

209 

4-78469 

43681 

9129329 

14.4568 

155 

6.45161 

24025 

3723875 

12.4499 

210 

4.76190 

44100 

9261000 

14.4914 

156 

6.41026 

24336 

3796416 

12.4900 

211 

4-73934 

44521 

939393  ! 

i4-5258 

157 

6-36943 

24649 

3869893 

12.5300 

212 

4.71698 

44944 

9528128 

14.5602 

158 

6.32911 

24964 

3944312 

12.5698 

213 

4.69484 

45369 

9663597 

14-5945 

159 

6.28931 

25281 

4019679 

12.6095 

214 

4.67290 

45796 

9800344 

14.6287 

160 

6.25000 

25600 

4096000 

12.6491 

215 

4.65116 

46225 

9938375 

14.6629 

161 

6.21118 

25921 

4173281 

12.6886 

216 

4.62963 

46656 

10077696 

14.6969 

162 

6.17284 

26244 

4251528 

12.7279 

217 

4.60829 

47089 

10218313 

14.7309 

163 

6.13497 

26569 

4330747 

12.7671 

218 

4.58716 

47524 

10360232 

14.7648 

164 

6-09756 

26896 

4410944 

1  2.8062 

219 

4.56621 

4796i 

10503459 

14.7986 

165 

1  66 

6.06061 

6.02410 

27225 
27556 

4492125 
4574296 

12.8452 
12.8841 

220 

221 

4-54545 
4.52489 

48400 
48841 

10648000 
10793861 

14.8324 
14.8661 

167 

5.98802 

27889 

4657463 

12.9228 

222 

4.50450 

49284 

10941048 

14.8997 

168 

5.95238 

28224 

4741632 

12.9615 

223 

4.48430 

49729 

11089567 

14-9332 

169 

5.91716 

28561 

4826809 

13.0000 

224 

4.46429 

50176 

11239424 

14.9666 

170 

5-88235 

28900 

4913000 

13.0384 

225 

4-44444 

50625 

11390625 

1  5.0000 

171 

5-84795 

29241 

5000211 

13.0767 

226 

4.42478 

51076 

11543176 

I5-0333 

172 

5-8i395 

29584 

5088448 

13.1149 

227 

4-40529 

51529 

11697083 

15.0665 

173 

174 

5-78035 
5-747I3 

29929 
30276 

5I777I7 
5268024 

13.1909 

228 
229 

4-38596 
4.36681 

52441 

"852352 
12008989 

15.0997 

SMITHSONIAN  TABLES. 


TABLE  8  (continued).  IJ 

VALUES  OF  RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE  ROOTS,  OF 

NATURAL    NUMBERS. 


n 

iooc4 

** 

«» 

ff 

n 

loooJ 

»2 

«8 

v» 

230 

231 

4-34783 
4.32900 

52900 
5336i 

I2I67000 
12326391 

15.1658 
15.1987 

285 

286 

3-50877 
3-49650 

81225 
81796 

23149125 
23393656 

16.8819 

16.9115 

232 

4-3I034 

53824 

12487168 

r5-23i5 

287 

3-48432 

82369 

23639903 

16.9411 

233 

4.29185 

54289 

12649337 

15.2643 

288 

3.47222 

82944 

23887872 

16.9706 

234 

4-2735° 

54756 

12812904 

15.2971 

289 

3.46021 

83521 

24137569 

17.0000 

235 

4-25532 

55225 

12977875 

1  5-3297 

290 

3.44828 

84100 

24389000 

17.0294 

236 

4.23729 

55696 

13144256 

1  5-3623 

291 

3-43643 

84681 

24642171 

17.0587 

23? 

4.21941 

56169 

1  33  i  20  53 

I5-3948 

292 

3.42466 

85264 

24897088 

17.0880 

238 
239 

4.20168 
4.18410 

56644 
57121 

13481272 
I365I9I9 

15.4272 
I5-4596 

293 

294 

3.41297 
3.40136 

85849 
86436 

25*53757 
25412184 

17.1172 
17.1464 

240 

4-16667 

576oo 

13824000 

I5-49I9 

295 

3-38983 

87025 

25672375 

17.1756 

241 

4.14938 

58081 

I399752I 

15.5242 

296 

3-37838 

87616 

25934336 

17.2047 

242 

4.13223 

58564 

14172488 

I5-5563 

297 

3.36700 

88209 

26198073 

17.2337 

243 

4-11523 

59049 

14348907 

15.5885 

298 

3-35570 

88804 

26463592 

17.2627 

244 

4.09836 

59536 

14526784 

15.6205 

299 

3-34448 

89401 

26730899 

17.2916 

245 

4.08163 

60025 

14706125 

1  5-6525 

300 

3-33333 

9OOOO 

27OOOOOO 

17.3205 

246 

4.06504 

60516 

14886936 

15.6844 

301 

3.32226 

90601 

27270901 

17.3494 

247 

4.04858 

61009 

15069223 

15.7162 

302 

3.31126 

91204 

27543608 

17.3781 

248 

4.03226 

61504 

15252992 

15.7480 

3°3 

3-30033 

91809 

27818127 

17.4069 

249 

4.01606 

62001 

15438249 

15-7797 

3°4 

3.28947 

92416 

28094464 

17.4356 

250 

4.00000 

62500 

15625000 

15.8114 

305 

3.27869 

93025 

28372625 

17.4642 

25  r 

3.98406 

63001 

15813251 

15.8430 

306 

3-26797 

93636 

28652616 

17.4929 

252 

3.96825 

63504 

16003008 

1  5-8745 

3°7 

3-25733 

94249 

28934443 

17.5214 

253 

3-95257 

64009 

16194277 

15.9060 

308 

3.24675 

94864 

292l8lI2 

17.5499 

254 

3-93701 

64516 

16387064 

1  5-9374 

309 

3.23625 

95481 

29503629 

17.5784 

255 

3-92I57 

65025 

16581375 

15.9687 

310 

3.22581 

96100 

29791000 

17.6068 

256 

3.90625 

65536 

16777216 

16.0000 

311 

3.21543 

96721 

30080231 

17.6352 

257 

3.89105 

66049 

1  697  45  93 

16.0312 

312 

3-20513 

97344 

30371328 

17.6635 

258 

3-87597  !  66564 

I7I73512 

16.0624 

3i3 

3.19489 

97969 

30664297 

17.6918 

259 

3.86100 

67081 

17373979 

16.0935 

3'4 

3.18471 

98596 

30959M4 

17.7200 

260 

3.84615 

67600 

17576000 

16.1245 

315 

3.17460 

99225 

3I255875 

17.7482 

261 

3.83142 

68121 

17779581 

16.1555 

3i6 

3.16456 

99836 

31  554490 

17.7764 

262 

3.81679 

68644 

17984728 

16.1864 

3J7 

3-x5457 

100489 

31855013 

17.8045 

263 

3.80228 

69169 

18191447 

16.2173 

3i8 

3-M465 

101124 

32I57432 

17.8326 

264 

3.78788 

69696 

18399744 

16.2481 

3^9 

3.13480 

101761 

32461759 

17.8606 

265 

3-77358 

70225 

18609625 

16.2788 

320 

3.12500 

102400 

32768000 

17.8885 

266 

3-75940 

70756 

18821096 

16.3095 

321 

3-H5'6 

103041 

33076161 

17.9165 

267 

3-74532 

71289 

19034163 

16.3401 

322 

3  I0559 

103684 

33386248 

17.9444 

268 

3-73t34 

71824 

19248832 

16.3707 

323 

3-09598 

104329 

33698267 

17.9722 

269 

3-7  i  747 

72361 

194^5109 

16.4012 

324 

3.08642 

104976 

34012224 

18.0000 

270 

3-70370 

72900 

19683000 

16.4317 

325 

3.07692 

105625 

34328125 

18.0278 

271 
272 
273 

3.69004 
3.67647 
3.66300 

73441 
73984 
74529 

19902511 
20123648 
20346417 

16.4621 
16.4924 
16.5227 

326 

327 
328 

3.06748 
3.05810 
3-04878 

106276 
106929 
107584 

34645976 
34965783 
35287552 

18.0355 
18.0831 
18.1108 

274 

3.64964 

75076 

20570824 

16.5529 

329 

3-0395I 

108241 

35611289 

18.1384 

275 

3.63636 

75625 

20796875 

16.5831 

330 

3.03030 

108900 

35937000 

18.1659 

276 

3.62319 

76176 

21024576 

16.6132 

33  i 

3.02115 

109561 

36264691 

18.1934 

277 

3.61011 

76729- 

21253933 

16.6433 

332 

3.01205 

110224 

36594368 

18.2209 

278 

3-59712 

77284 

21484952 

16.6733 

333 

3.00300 

110889 

36926037 

18.2483 

279 

3-58423 

77841 

21717639 

16.7033 

334 

2.99401 

"1556 

37259704 

18.2757 

280 

3-57I43 

78400 

21952000 

16.7332 

335 

2.98507 

112225 

37595375 

18.3030 

281 

3-55872 

78961 

22188041 

16.7631 

336 

2.97619 

112896 

37933056 

18.3303 

282 

3.54610 

79524 

22425768 

16.7929 

337 

2.96736 

113569 

38272753 

18.3576 

283 

3-53357 

80089 

22665187 

16.8226 

338 

2.95858 

114244 

38614472 

18.3848 

284 

3-52113 

80656 

22906304 

16.8523 

339 

2-94985 

114921 

38958219 

18.4120 

SMITHSONIAN  TABLES. 


i8 


TABLE  8  (continued). 


VALUES   OF   RECIPROCALS,  SQUARES,  CUBES,  AND   SQUARE    ROOTS 
OF   NATURAL    NUMBERS. 


n 

1000.1 

* 

* 

y. 

n 

10004 

* 

- 

1* 

340 

2.94118 

115600 

39304000 

18.4391 

395 

2-53165 

156025 

61629875 

19.8746 

341 

2.93255 

116281 

39651821 

18.4662 

396 

2-52525 

156816 

62099136 

19.8997 

342 

2.92398 

116964 

40001688 

18.4932 

397 

2.51889 

157609 

62570773 

19.9249 

343 

2.9*545 

117649 

40353607 

18.5203 

398 

2.51256 

158404 

63044792 

19.9499 

344 

2.90698 

118336 

40707584 

18.5472 

399 

2.50627 

159201 

63521199 

19.9750 

345 

2-89855 

119025 

41063625 

18.5742 

400 

2.50000 

160000 

64000000 

20.0000 

346 

2.89017 

119716 

41421736 

18.6011 

401 

2-49377 

160801 

64481201 

20.0250 

347 

2.88184 

120409 

41781923 

18.6279 

402 

2.48756 

161604 

64964808 

20.0499 

348 

2.87356 

121104 

42144192 

18.6548 

403 

2.48139 

162409 

65450827 

20.0749 

349 

2.86533 

121801 

42508549 

18.6815 

404 

247525 

163216 

65939264 

20.0998 

350 

2.85714 

122500 

42875000 

18.7083 

405 

2.46914 

164025 

66430125 

20.1246 

352 

2.84900 
2.84091 

123201 
123904 

4324355J 
43614208 

18.735° 
18.7617 

406 
407 

246305 
2.45700 

164836 
165649 

66923416 
67419143 

20.1494 
20.1742 

353 

2.83286 

124609 

43986977 

18.7883 

408 

2.45098 

166464 

67917312 

20.1990 

354 

2.82486 

125316 

44361864 

18.8149 

409 

2.44499 

167281 

68417929 

20.2237 

355 

2.81690 

126025 

44738875 

18.8414 

410 

2.43902 

168100 

68921000 

20.2485 

356 

2.80899 

126736 

45118016 

18.8680 

411 

2.43309 

168921 

69426531 

20.2731 

357 

2.80112 

127449 

45499293 

18.8944 

412 

2.42718 

169744 

69934528 

20.2978 

358 

2-7933° 

128164 

45882712 

18.9209 

413 

2.42131 

170569  j  70444997 

20.3224 

359 

2.78552 

128881 

46268279 

18.9473 

414 

2.41546 

171396 

70957944 

20.3470 

360 

2.77778 

129600 

46656000 

18.9737 

415 

2.40964 

172225 

7H73375 

20.3715 

361 

2.77008 

130321 

47045881 

19.0000 

416 

2.40385 

173056 

71991296 

20.3961 

362 

2-76243 

131044 

47437928 

19.0263 

417 

2.39808 

173889 

72511713 

20.4206 

363 

2.75482 

131769 

47832147 

19.0526 

418 

2.39234 

174724 

20.4450 

364 

2.74725 

132496 

48228544 

19.0788 

419 

2.38663 

I7556i 

73560059 

20.4695 

365 

2.73973 

133225 

48627125 

19.1050 

420 

2.38095 

176400 

74088000 

20.4939 

366 

2.73224 

49027896 

19.1311 

421 

2.37530 

177241 

74618461 

20.5183 

2.72480 

134689 

49430863 

19.1572 

422 

2.36967 

178084 

75I5I448 

20.5426 

368 

2.71739 

1  35424 

49836032 

19-1833 

423 

2.36407 

178929 

75686967 

20.5670 

369 

2.71003 

136161 

50243409 

19.2094 

424 

2.35849 

179776 

76225024 

20.5913 

370 

2.70270 

136900 

50653000 

I9.2354 

425 

2.35294 

180625 

76765625 

20.6155 

371 

2.69542 

137641 

51064811 

19.2614 

426 

2.34742 

181476 

77308776 

20.6398 

372 

2.68817 

138384 

51478848 

19.2873 

427 

2.34192 

182329 

77854483 

20.6640 

373 

2.68097 

139129 

5r895II7 

19.3132 

428 

2.33645 

183184 

78402752 

20.6882 

374 

2.67380 

139876 

52313624 

1  9-339  r 

429 

2.33100 

184041 

78953589 

20.7123 

375 

2.66667 

140625 

52734375 

19.3649 

430 

2-32558 

184900 

79507000 

20.7364 

376 

2-65957 

141376 

53J57376 

19.3907 

43  r 

2.32019 

185761 

80062991 

20.7665 

377 

2.65252 

142129 

53582633 

19.4165 

432 

2.31481 

186624 

80621568 

20.7846 

378 

2.64550 

142884 

54010152 

19.4422 

433 

2.30947 

187489 

81182737 

20.8087 

379 

2.63852 

143641 

54439939 

19.4679 

434 

2.30415 

188356 

81746504 

20.8327 

380 

2.63158 

144400 

54872000 

19.4936 

435 

2.29885 

189225 

82312875 

20.8567 

381 

2.62467 

145161 

55306341 

19.5192 

436 

2-29358 

190096 

82881856 

20.8806 

382 

2.61780 

145924 

55742968 

19.5448 

437 

2.28833 

190969 

83453453 

20.9045 

383 

2.61097 

146689 

56181887 

19.5704 

438 

2.28311 

191844 

84027672 

20.9284 

384 

2.60417 

1  47456 

56623104 

1  9-  5959 

439 

2.27790 

192721 

84604519 

20.9523 

385 

2.59740 

148225 

57066625 

19.6214 

440 

2.27273 

193600 

85184000 

20.9762 

386 

2.59067 

148996 

575I2456 

19.6469 

441 

2.26757 

194481 

85766121 

2I.OOOO 

387 

2.58398 

149769 

57960603 

19.6723 

442 

2.26244 

195364 

86350888 

21.0238 

388 

2-57732 

1  5°544 

58411072 

19.6977 

443 

2.25734 

196249 

86938307 

21.0476 

389 

2.57069 

151321 

58863869 

19.7231 

444 

2.25225 

197136 

87528384 

21.0713 

390 

2.56410 

152100 

59319000 

19.7484 

445 

2.24719 

198025 

88121125 

21.0950 

39  l 

2-55754 

152881 

59776471 

19-7737 

446 

2.24215 

198916 

88716536 

2I.II87 

392 

2.55102 

153664 

60236288 

19.7990 

447 

2.23714 

199809 

89314623 

21.1424 

393 

2-54453 

154449 

60698457 

19.8242 

448 

2.23214 

200704 

89915392 

21.  1660 

394 

2.53807 

155236 

61162984 

19.8494 

449 

2.22717 

201601 

90518849 

21.1896 

SMITHSONIAN  TABLES. 


TABLE  8  (continued).  I 

VALUES   OF   RECIPROCALS,   SQUARES,   CUBES,   AND   SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

lOOO.i 

* 

«3 

tf* 

n 

ioooi 

* 

»» 

J 

450 

2.22222 

2O25OO 

9II25000 

21.2132 

505 

1.98020 

255025 

128787625 

22.4722 

451 

2.21729 

203401 

9I73385I 

21.2368 

506 

1.97628 

256036 

129554216 

22.4944 

452 

2.21239 

204304 

92345408 

21.2603 

507 

1.97239 

257049 

130323843 

22.5167 

453 

2.20751 

205209 

92959677 

21.2838 

508 

1.96850 

258064 

131096512 

22.5389 

454 

2.2O264 

2o6ll6 

93576664 

21.3073 

509 

1.96464 

259081 

131872229 

22.5610 

455 

2.19780 

207025 

941963,75 

21.3307 

510 

1.96078 

260100 

132651000 

22.5832 

456 

2.19298 

207936 

948l88l6 

21.3542 

5" 

I-95695 

261121 

1  3343283  I 

22.6053 

457 

2.l88l8 

208849 

95443993 

21.3776 

512 

I-953I2 

262144 

134217728 

22.6274 

458 

2.18341 

209764 

96071912 

21.4009 

1.94932 

263169 

1  35005697 

22.6495 

459 

2.17865 

2I068I 

96702579 

21.4243 

SM 

1  -94553 

264196 

1  357967  44 

22.6716 

460 

2.17391 

2II600 

97336000 

21.4476 

515 

I.94I75 

265225 

136590875 

22.6936 

461 

2.16920 

2I252I 

97972181 

21.4709 

516 

1.93798 

266256 

137388096 

22.7156 

462 

2.16450 

213444 

9861  i  i  28 

21.4942 

5*7 

1.93424 

267289 

138188413 

22.7376 

463 

464 

2.15983 
2.I55I7 

214369 
215296 

99252847 
99897344 

21.5174 
21-5407 

518 

1.93050 
1.92678 

268324 
269361 

1  3899^32 
139798359 

22.7596 
22.7816 

465 

2.15054 

216225 

100544625 

21.5639 

520 

1.92308 

270400 

140608000 

22.8035 

466 

2.14592 

217156 

101194696 

21.5870 

521 

1.91939 

271441 

141420761 

22.8254 

467 

2.HI33 

218089 

101847563 

21.6102 

522 

272484 

142236648 

22.8473 

468 

2.13675 

219024 

102503232 

21.6333 

523 

1.91205 

273529 

143055667 

22.8692 

469 

2.13220 

219961 

103161709 

21.6564 

524 

1.90840 

274576 

143877824 

22.8910 

470 

2.12766 

22O9OO 

103823000 

21.6795 

525 

1.90476 

275625 

144703125 

22.9129 

471 

2.12314 

221841 

104487111 

21.7025 

526 

1.90114 

276676 

I4553I576 

22.9347 

472 

2.II864 

222784 

105154048 

21.7256 

527 

I-89753 

277729 

146363183 

22.9565 

473 

2.II4I6 

223729 

105823817 

21.7486 

528 

1.89394 

278784 

M7I97952 

22.9783 

474 

2.10970 

224676 

106496424 

21.7715 

529 

1.89036 

279841 

148035889 

23.0000 

475 

2.10526 

225625 

107171875 

21.7945 

530 

1.88679 

280900 

148877000 

23.0217 

476 

2.IOO84 

226576 

107850170 

21.8174 

531 

1.88324 

281961 

149721291 

23-0434 

477 

2.09644 

227529 

Io853I333 

21.8403 

S32 

1.87970 

283024 

150568768 

23.0651 

478 

2.09205 

228484 

109215352 

21.8632 

533 

1.87617 

284089 

151419437 

23.0868 

479 

2.08768 

229441 

109902239 

21.8861 

534 

1.87266 

285156 

152273304 

23.1084 

480 

2.08333 

230400 

110592000 

21.9089 

535 

1.86916 

286225 

I53I30375 

23.1301 

481 

2.07900 

231361 

111284641 

21.9317 

536 

1.86567 

287296 

153990656 

482 

2.07469 

232324 

111980168 

21.9545 

537 

1.86220 

288369 

*54»54I53 

23-I733 

483 

2.07039 

233289 

112678587 

21-9773 

538 

1.85874 

289444 

155720872 

23.1948 

484 

2.06612 

234256 

H3379904 

22.0000 

539 

1.85529 

290521 

156590819 

23.2164 

485 

2.o6l86 

235225 

114084125 

22.0227 

540 

1.85185 

291600 

157464000 

23.2379 

486 

2.05761 

236196 

114791256 

22.0454 

541 

1.84843 

292681 

158340421 

23-2594 

487 

2.05339 

237169 

115501303 

22.0681 

542 

1.84502 

293764 

159220088 

23.2809 

488 

2.O49I8 

238144 

116214272 

22.0907 

543 

1.84162 

294849 

160103007 

23.3024 

489 

2.04499 

239121 

116930169 

22.1133 

544 

1.83824 

295936 

160989184 

23-3238 

490 

2.04082 

240100 

117649000 

22.1359 

545 

1.83486 

297025 

161878625 

23-3452 

491 

492 

2.03666 
2.03252 

241081 
242064 

118370771 
119095488 

22.1585 
22.1811 

546 
547 

1.83150 
1.82815 

298116 
299209 

162771336 
163667323 

23.3666 
23.3880 

493 

2.02840 

243049 

119823157 

22.2036 

548 

1.82482 

300304 

164566592 

23.4094 

494 

2.O2429 

244036 

120553784 

22.2261 

549 

1.82149 

301401 

165469149 

234307 

495 

2.02020 

245025 

121287375 

22.2486 

550 

1.81818 

302500 

166375000 

23.4521 

496 

2.01613 

246016 

122023936 

22.2711 

551 

1.81488 

303601 

167284151 

234734 

497 
498 

499 

2.OI2O7 
2.00803 
2.00401 

247009 
248004 
249001 

122763473 
123505992 
124251499 

22.2935 

22.3159 
22.3383 

552 
553 
554 

1.81159 
1.80832 
1.80505 

304704 
305809 
306916 

168196608 
169112377 
170031464 

234947 
23.5160 
23-5372 

500 

502 
5°3 
504 

2.00000 
I.9960I 

1.98413 

250000 
25IOOI 
252004 
253009 
254016 

125000000 

i  26506008 
127263527 
128024064 

22.3607 
22.3830 
22.4054 
22.4277 
22.4499 

555 

556 
557 
558 
559 

i.  80180 
1.79856 
1-79533 
1.79211 
1.78891 

308025 
309136 
310249 

3  "364 
312481 

170953875 
171879616 
172808693 
173741112 
174676879 

23-5584 
23.5797 
23.6008 
23.6220 
23.6432 

SMITHSONIAN  TABLES. 


2O  TABLE  8  (continued). 

VALUES   OF   RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

1000.^ 

n2 

* 

v. 

n 

lOOO.i 

* 

«3 

v« 

560 

1-78571 
1-78253 

313600 
3*4721 

175616000 
176558481 

23-6643 
23.6854 

615 

616 

1.62602 

1.62338 

378225 
379456 

232608375 
233744896 

24-7992 
24.8193 

562 
563 

1.77936 

1.77620 

315844 
316969 

177504328 
178453547 

23-7065 
23-7276 

617 
618 

1.62075 
1.61812 

380689 
381924 

234885113 
236029032 

24-8395 
24.8596 

564 

1-77305 

318096 

179406144 

23.7487 

619 

1.61551 

383*61 

237176659 

24-8797 

565 

566 

1.76991 
1.76678 

319225 
320356 

180362125 
181321496 

23-7697 
23-7908 

620 

621 

1.61290 
1.61031 

384400 
385641 

238328000 
239483061 

24.8998 
24.9199 

1.76367 

321489 

182284263 

23.8118 

622 

1.60772 

386884 

240641848 

24-9399 

568 

1.76056 

322624 

183250432 

23.8328 

623 

1.60514 

388129 

241804367 

24.9600 

569 

1-75747 

323761 

184220009 

23-8537 

624 

1.60256 

389376 

242970624 

24.9800 

570 

1-75439 

324900 

185193000 

23.8747 

625 

1.60000 

390625 

244140625 

25.0000 

571 

326041 

186169411 

23.8956 

626 

1-59744 

391876 

2453M376 

25.0200 

572 

174825 

327184 

187149248 

23.9165 

627 

1.59490 

393I29 

246491883 

25.0400 

573 

1.74520 

328329 

188132517 

23-9374 

628 

1.59236 

394384 

247673152 

25-0599 

1  574 

1.74216 

329476 

189119224 

23-9583 

629 

1.58983 

395641 

248858189 

25-0799 

575 

I-739I3 

330625 

190109375 

23.9792 

630 

1.58730 

396900 

250047000 

25-0998 

576 

1.73611 

331776 

191102976 

24.0000 

631 

1.58479 

398161 

251239591 

25.1197 

577 

1.73310 

332929 

192100033 

24.0208 

632 

1.58228 

399424 

25.1396 

578 

1.73010 

334084 

I93Io°552 

24.0416 

633 

I.57978 

400689 

253636137 

25-I595 

579 

1.72712 

335241 

194104539 

24.0624 

634 

1.57729 

401956 

254840104 

25.1794 

580 

1.72414 

336400 

195112000 

24.0832 

635 

1.57480 

403225 

256047875 

25.1992 

581 

1.72117 

337561 

196122941 

24.1039 

636 

1.57233 

404496 

257259456 

25.2190 

582 

1.71821 

338724 

I97I37368 

24.1247 

637 

1.56986 

405769 

258474853 

25.2389 

583 

1.71527 

339889 

198155287 

24.1454 

638 

1.56740 

407044 

259694072 

25.2587 

584 

1-71233 

341056 

199176704 

24.1661 

639 

1.56495 

408321 

260917119 

25.2784 

585 

1.70940 

342225 

200201625 

24.1868 

640 

1.56250 

409600 

262144000 

25.2982 

586 

1.70648 

343396 

201230056 

24.2074 

641 

1.56006 

410881 

263374721 

25.3180 

587 

1.70358 

344569 

202262003 

24.2281 

642 

L55763 

412164 

264609288 

25-3377 

588 

1.70068 

345744 

203297472 

24.2487 

643 

413449 

265847707 

25-3574 

589 

1.69779 

346921 

204336469 

24.2693 

644 

1.55280 

4H736 

267089984 

590 

1.69492 

348100 

205379000 

24.2899 

645 

1.55039 

416025 

268336125 

25-3969 

591 

592 

1.69205 
1.68919 

349281 
350464 

206425071 
207474688 

24.3105 

646 
647 

1-54799 
1.54560 

417316 
418609 

269586136 
270840023 

25.4165 
25.4362 

593 

1.68634 

35^49 

208527857 

24.3516 

648 

I-54321 

419904 

272097792 

254558 

594 

1.68350 

352836 

209584584 

24-3721 

649 

1.54083 

421201 

273359449 

25-4755 

595 

1.68067 

354025 

210644875 

24.3926 

650 

1.53846 

422500 

274625000 

25.4951 

596 

1.67785 

211708736 

24.4131 

651 

1.53610 

423801 

275894451 

25-5*47 

597 

1.67504 

356409 

212776173 

24-4336 

652 

J-53374 

425104 

277167808 

25-5343 

598 

1.67224 

357604 

213847192 

24.4540 

653 

I-53I39 

426409 

278445077 

25-5539 

599 

1.66945 

3588oi 

214921799 

24-4745 

654 

1.52905 

427716 

279726264 

25.5734 

600 

601 

1.66667 
1.66389 

360000 
361201 

216000000 
217081801 

24-4949 

655 

656 

1.52672 

!•  52439 

429025 
430336 

281011375 
282300416 

25-5930 
25.6125 

602 

1.66113 

362404 

218167208 

24-5357 

657 

1.52207 

431649 

283593393 

25.6320 

603 
604 

1.65837 
1-65563 

363609 
364816 

219256227 
220348864 

24-5561 
24.5764 

658 
659 

1.51976 
I-5I745 

432964 
434281 

284890312 
286191179 

25-6515 
25.6710 

605 

606 

1.65289 
1.65017 

366025 
367236 

221445125 
222545016 

24.5967 
24.6171 

660 

661 

I.5I5J5 
1.51286 

4356oo 
436921 

.287496000 
288804781 

25.6905 
25.7099 

607 

1.64745 

368449 

223648543 

24-6374 

662 

1.51057 

438244 

290117528 

609 

1.64474 
1.64204 

369664 
37o88i 

224755712 
225866529 

24-6577 
24.6779 

663 
664 

1.50830 
1.50602 

439569 
440896 

291434247 
292754944 

25.7488 
25.7682 

610 

1-63934 

372100 

226981000 

24.6982 

665 

1.50376 

442225 

294079625 

25.7876 

611 

1.63666 

373321 

228099131 

24.7184 

666 

1.50150 

443556 

295408296 

25.8070 

612 

6.3 

I-63399 
1.63132 

374544 
375769 

229220928 
230346397 

24.7386 
24.7588 

667 
668 

1.49925 
1.49701 

444889 
446224 

296740963 
298077632 

25.8263 

25.8457 

614 

1.62866 

376996 

23H75544 

24.779° 

669 

1.49477 

44756i 

299418309 

25.8650 

SMITHSONIAN  TABLES. 


TABLE  8    (continued).  2  I 

VALUES   OF   RECIPROCALS,  SQUARES,  CUBES,  AND  SQUARE    ROOTS 
OF    NATURAL    NUMBERS. 


n 

lOOO.i 

«2 

«3 

*• 

n 

1000.1 

* 

n* 

V* 

670 

1.49254 

448900 

300763000 

25.8844 

725 

1-3793* 

525625 

381078125 

26.9258 

671 
672 
673 
674 

1.49031 
1.48810 
1.48588 
1.48368 

450241 

45^84 
452929 
454276 

302III7II 
303464448 
3O482I2I7 
306l82024 

25-9037 
25.9230 
25.9422 
25.9615 

726 

727 
728 
729 

1-3774* 
1-37552 
I-37363 
1-37*74 

527076 
528529 
529984 
53*44* 

382657176 
384240583 
385828352 
387420489 

26.9444 
26.9629 
26.9815 
27.0000 

675 

676 

1.48148 
1.47929 

455625 
456976 

307546875 
308915776 

26.OOOO 

730 

73* 

1.36986 
1.36799 

532900 
53436i 

389017000 
390617891 

27.0185 
27.0379 

677 

1.47710 

458329 

310288733 

26.OI92 

732 

1.36612 

535824 

392223168 

27-0555 

678 
679 

1-47493 
I-47275 

459684 
461041 

3II665752 
313046839 

26.O384 
26.0576 

733 
734 

1.36426 
1.36240 

537289 
538756 

393832837 
395446904 

27.0740 
27.0924 

680 

1.47059 

462400 

314432000 

26.0768 

735 

1.36054 

540225 

397065375 

27.1109 

68  1 

1.46843 

463761 

3I582I24I 

26.O96O 

736 

1  -35870 

54*696 

398688256 

27.1293 

682 
683 

1.46628 
1.46413 

465124 
466489 

3I72I4568 
3I86II987 

26.1151 
26.1343 

737 
738 

1.35685 
I-355°* 

543i69 
544644 

400315553 
401947272 

27.1477 

27.1662 

684 

1.46199 

467856 

320013504 

26.1534 

739 

546121 

4035834*9 

27.1846 

685 

I-45985 

469225 

32I4I9I25 

26.1725 

740 

I-35*35 

5476oo 

405224000 

27.2029 

686 
687 

1-45773 
1.45560 

470596 
471969 

322828856 
324242703 

26.I9I6 
26.2IO7 

742 

1-34953 
1-3477* 

549081 
550564 

406869021 
408518488 

27.2213 

27.2397 

688 

1-45349 

473344 

325660672 

26.2298 

743 

1.34590 

552049 

410172407 

27.2580 

689 

i  -45J38 

474721 

327082769 

26.2488 

744 

1.34409 

553536 

411830784 

27.2764 

690 

1.44928 
1.44718 

476100 

477481 

3285O9OOO 
32993937* 

26.2679 
26.2869 

745 

746 

1.34228 
1.34048 

555025 
5565*6 

413493625 
415160936 

27.2947 
27.3130 

692 
693 

1.44509 
1.44300 

478864 
480249 

33*373888 
332812557 

26.3059 
26.3249 

747 
748 

1.33869 
1.33690 

558009 
559504 

416832723 
418508992 

27-3496 

694 

1.44092 

481636 

334255384 

26.3439 

749 

1-335*1 

561001 

420189749 

/   ^"J-/ 

27.3679 

695 

1.43885 

483025 

335702375 

26^629 

750 

'•33333 

562500 

421875000 

27.3861 

696 

697 
698 

1.43678 
1.43472 
1.43266 

484416 
485809 
487204 

337153536 
338608873 
340368392 

26.3818 
26.4008 
26.4197 

752 
753 

1.32979 

1.32802 

564001 

565504 
567009 

423564751 
425259008 
426957777 

27.4044 
27.4226 
27.4408 

699 

1.43062 

488601 

341532099 

26.4386 

754 

1.32626 

568516 

428661064 

27.4591 

700 

1.42857 

490000 

343000000 

26.4575 

755 

1.32450 

570025 

430368875 

27-4773 

701 

1.42653 

491401 

344472IOI 

26.4764 

756 

1-32275 

571536 

432081216 

27-4955 

702 

1.42450 

492804 

345948408 

26.4953 

757 

1.32100 

573049 

433798093 

27.5136 

703 

1.42248 

494209 

347428927 

26.5141 

758 

1.31926 

574564 

4355*95*2 

704 

1.42045 

495616 

348913664 

26.5330 

759 

1-3*752 

576081 

437245479 

27.5500 

705 

706 

1.41844 
1.41643 

497025 
498436 

350402625 
35l8958l6 

26.5518 
26.5707 

760 

761 

1-3*579 
1.31406 

577600 
579121 

438976000 
440711081 

27.5681 
27.5862 

707 

1.41443 

499849 

353393243 

26.5895 

762 

*-3I234 

580644 

442450728 

27.6043 

708 

1.41243 

501264 

354894912 

26.6083 

763 

1.31062 

582169 

444194947 

27.6225 

709 

1.41044 

502681 

356400829 

26.6271 

764 

1.30890 

583696 

445943744 

27.6405 

710 

1.40845 

504100 

3579IIOOO 

26.6458 

765 

1.30719 

585225 

447697125 

27.6586 

711 

1.40647 

50552* 

359425431 

26.6646 

766 

1.30548 

586756 

449455096 

27.6767 

712 

1.40449 

506944 

360944128 

26.6833 

767 

I-30378 

588289 

451217663 

27-6948 

713 

1.40252 

508369 

362467097 

26.7O2I 

768 

1.30208 

589824 

452984832 

27.7128 

7H 

1.40056 

509796 

363994344 

26.7208 

769 

1.30039 

591361 

454756609 

27.7308 

715 

1.39860 

511225 

365525875 

26.7395 

770 

1.29870 

592900 

456533000 

27.7489 

716 

1.39665 

512656 

367O6l696 

26.7582 

77* 

1.29702 

59444* 

458314011 

27.7669 

717 

1.39470 

514089 

36860I8I3 

26.7769 

772 

1-29534 

595984 

460099648 

27.7849 

718 

1.39276 

5*5524 

370146232 

26.7955 

773 

1.29366 

597529 

461889917 

27.8029 

719 

1.39082 

516961 

371694959 

26.8142 

774 

1.29199 

599076 

463684824 

27.8209 

720 

1.38889 

518400 

373248000 

26.8328 

775 

1.29032 

600625 

465484375 

27.8388 

721 

1.38696 

519841 

374805361 

26.8514 

776 

1.28866 

602176 

467288576 

27.8568 

722 

1.38504 

521284 

376367048 

26.87OI 

777 

1.28700 

603729 

469097433 

27-8747 

723 

1-38313 

522729 

377933067 

26.8887 

778 

1-28535 

605284 

470910952 

27.8927 

724 

1.38122 

524176 

379503424 

26.9072 

779 

1.28370 

606841 

472729*39 

27.9106 

SMITHSONIAN  TABLES. 


2  2  TABLE  8  (continued). 

VALUES  OF   RECIPROCALS,   SQUARES,   CUBES,   AND   SQUARE   ROOTS 
OF   NATURAL    NUMBERS. 


n 

IOOO.J 

»2 

fft 

V* 

n 

iooo4 

«2 

«8 

tf* 

780 

1.28205 

608400 

474552000 

27.9285 

835 

1.19760 

697225 

582182875 

28.8964 

781 

1.28041 

609961 

476379541 

27.9464 

836 

1.19617 

698896 

584277056 

28.9137 

782 

1.27877 

611524 

478211768 

27.9643 

837 

1.19474 

700569 

586376253 

28.9310 

783 

1.27714 

613089 

480048687 

27.9821 

838 

1.19332 

702244 

588480472 

28.9482 

784 

1-27551 

614656 

481890304 

28.0000 

839 

1.19190 

703921 

590589719 

28.9655 

785 

1.27389 

616225 

483736625 

28.0179 

840 

1.19048 

705600 

592704000 

28.9828 

786 

1.27226 

617796 

485587656 

28.0357 

841 

1.18906 

707281 

594823321 

29.0000 

787 

1.27065 

619369 

487443403 

28.0535 

842 

1.18765 

708964 

596947688 

29.0172 

788 

1.26904 

620944 

489303872 

28.0713 

843 

1.18624 

710649 

599077107 

29-0345 

789 

1.26743 

622521 

491169069 

28.0891 

844 

1.18483 

712336 

601211584 

29.0517 

790 

1.26582 

624100 

493039000 

28.1069 

845 

1-18343 

714025 

603351125 

29.0689 

791 

1.26422 

625681 

494913671 

28.1247 

846 

1.18203 

715716 

605495736 

29.0861 

792 

1.26263 

627264 

496793088 

28.1425 

847 

1.18064 

717409 

607645423 

29.1033 

792 

1.26103 

628849 

498677257 

28.1603 

848 

1.17925 

719104 

609800192 

29.1204 

794 

1.25945 

630436 

500566184 

28.1780 

849 

1.17786 

720801 

611960049 

29.1376 

795 

1.25786 

632025 

502459875 

28.1957 

850 

1.17647 

722500 

614125000 

29.1548 

796 

1.25628 

633616 

504358336 

28.2135 

851 

1.17509 

724201 

616295051 

29.1719 

797 

1.25471 

635209 

506261573 

28.2312 

852 

1.17371 

725904 

618470208 

29.1890 

793 

I-253I3 

636804 

508169592 

28.2489 

853 

1.17233 

727609 

620650477 

29.2062 

799 

1.25156 

638401 

510082399 

28.2666 

854 

1.17096 

729316 

622835864 

29.2233 

800 

1.25000 

640000 

5I2OOOOOO 

28.2843 

855 

1.16959 

731025 

625026375 

29.2404 

80  1 

1.24844 

641601 

5I392240I 

28.3019 

856 

1.16822 

732736 

627222016 

29-2575 

802 

1.24688 

643204 

515849608 

28.3196 

857 

1.16686 

734449 

629422793 

29.2746 

803 

J-24533 

644809 

517781627 

28.3373 

858 

1.16550 

736164 

631628712 

29.2916 

804 

1.24378 

646416 

519718464 

28.3549 

859 

1.16414 

73788i 

633839779 

29.3087 

805 

1.24224 

648025 

521660125 

28.3725 

860 

1.16279 

739600 

636056000 

29.3258 

806 

1.24069 

649636 

523606616 

28.3901 

861 

1.16144 

74i321 

638277381 

29.3428 

807 

1.23916 

651249 

525557943 

28.4077 

862 

1.16009 

743°44 

640503928 

29-3598 

808 

1.23762 

652864 

527514112 

28.4253 

863 

1.15875 

744769 

642735647 

29.3769 

809 

1.23609 

654481 

529475129 

28.4429 

864 

1.15741 

746496 

644972544 

29-3939 

810 

1  -23457 

656100 

53I44IOOO 

28.4605 

865 

1.15607 

748225 

647214625 

29.4109 

811 

1-23305 

657721 

5334II73I 

28.4781 

866 

1.15473 

749956 

649461896 

29.4279 

812 

1-23153 

659344 

535387328 

28.4956 

867 

1.15340 

751689 

651714363 

29.4449 

813 

1.23001 

660969 

537367797 

28.5132 

868 

1.15207 

753424 

653972032 

29.4618 

814 

1.22850 

662596 

539353M4 

28.5307 

869 

1.15075 

755'6i 

656234909 

29.4788 

815 

1.22699 

664225 

541343375 

28.5482 

870 

1.14943 

756900 

658503000 

29-4958 

816 

1.22549 

665856 

543338496 

28.5657 

871 

1.14811 

758641 

660776311 

295127 

817 

1.22399 

667489 

5453385r3 

28.5832 

872 

1.14679 

760384 

663054848 

29.5296 

818 
819 

r.  22249 

I.22IOO 

669124 
670761 

547343432 
549353259 

28.6007 
28.6182 

g73 
874 

1.14548 

1.14416 

762129 
763876 

665338617 
667627624 

29.5466 
29'5635 

820 

I.2I95I 

672400 

551368000 

28.6356 

875 

1.14286 

765625 

669921875 

29.5804 

821 

1.21803 

674041 

55338766r 

28.6531 

876 

1-14155 

767376 

672221376 

29-5973 

822 

1.21655 

675684 

555412248 

28.6705 

877 

1.14025 

769129 

674526133 

29.6142 

823 

1.21507 

677329 

557441767 

28.6880 

878 

I-I3895 

770884 

676836152 

29.6311 

824 

I-2I359 

678976 

559476224 

28.7054 

879 

1.13766 

772641 

6791  5  J  439 

29.6479 

825 

I.2I2I2 

680625 

561515625 

28.7228 

880 

1.13636 

774400 

681472000 

29.6648 

826 

I.2I065 

682276 

563559976 

28.7402 

88  1 

I-I35°7 

776161 

683797841 

29.6816 

827 

1.20919 

683929 

565609283 

28.7576 

882 

I-I3379 

777924 

686128968 

29.6985 

828 

1.20773 

685584 

567663552 

28.7750 

883 

1.13250 

779689 

688465387 

29.7153 

829 

1.20627 

687241 

569722789 

28.7924 

884 

1.13122 

781456 

690807104 

29.7321 

830 

1.20482 

688900 

571787000 

28.8097 

885 

1.12994 

783225 

693^4125 

29.7489 

831 

1.20337 

690561 

573856191 

28.8271 

886 

1.12867 

784996 

695506456 

29.7658 

832 

I.2OI92 

692224 

575930368 

28.8444 

887 

1.12740 

786769 

697864103 

29.7825 

833 

1.20048 

693889 

578009537 

28.8617 

888 

1.12613 

788544 

700227072 

29-7993 

834 

I.I9904 

695556 

580093704 

28.8791 

889 

1.12486 

790321 

702595369 

29.8161 

SMITHSONIAN  TABLES. 


TABLE  8  (continued}.  2 

VALUES   OF   RECIPROCALS,  SQUARES,  CUBES,  AND   SQUARE   ROOTS 
OF   NATURAL    NUMBERS. 


n 

1000.1 

»2 

«3 

4" 

n 

1000.4 

«2 

«3 

J* 

890 

891 

1.12360 
1.12233 

792100 
79388l 

704969000 
707347971 

29.8329 
29.8496 

945 

946 

1.05820 
1.05708 

893025 

894916 

843908625 
846590536 

30.7409 
307571 

892 

.12108 

795664 

709732288 

29.8664 

947 

1-05597 

896809 

849278123 

30-7734 

893 

.11982 

797449 

712121957 

29.8831 

948 

1.05485 

898704 

85I97I392 

30.7896 

894 

.11857 

799236 

714516984 

29.8998 

949 

1-05374 

900601 

854670349 

30.8058 

895 

896 

.11732 
.11607 

801025 
802816 

716917375 
719323136 

29.9166 
29-9333 

950 

951 

1.05263 
1.05152 

902500 
904401 

857375000 
860085351 

30.8221 
30.8383 

897 

.11483 

804609 

721734273 

29.9500 

952 

1.05042 

906304 

862801408 

30-8545 

898 

•TI359 

806404 

724150792 

29.9666 

953 

1.04932 

908209 

865523177 

30-8707 

899 

•11235 

808201 

726572699 

29-9833 

954 

1.04822 

910116 

868250664 

30.8869 

900 

.inn 

810000 

729000000 

30.0000 

955 

1.04712 

912025 

870983875 

30.9031 

901 

.10988 

811801 

731432701 

30.0167 

956 

i  .04603 

9^936 

873722816 

30.9192 

902 

.10865 

813604 

733870808 

30.0333 

957 

1.04493 

915849 

876467493 

30-9354 

903 

.10742 

815409 

7363H327 

30.0500 

958 

1.04384 

917764 

879217912 

30.9516 

904 

.10619 

817216 

738763264 

30.0666 

959 

1.04275 

919681 

881974079 

30.9677 

905 

.10497 

819025 

741217625 

30.0832 

960 

1.04167 

921600 

884736000 

30-9839 

906 

•10375 

820836 

743677416 

30.0998 

961 

i  .04058 

923521 

887503681 

31.0000 

907 

.10254 

822649 

746142643 

30.1164 

962 

1.03950 

925444 

890277128 

31.0161 

908 

.10132 

824464 

748613312 

3°-  i  330 

963 

1.03842 

927369 

893056347 

31.0322 

909 

.10011 

826281 

751089429 

30.1496 

964 

1.03734 

929296 

895841344 

31.0483 

910 

.09890 

828100 

753571000 

30.1662 

965 

1.03627 

931225 

898632125 

31.0644 

91  1 
912 

.09769 
.09649 

829921 
831744 

756058031 
758550528 

30.1828 

3°-  i  993 

966 
967 

1.03520 
1-03413 

933^6 
935089 

901428696 
904231063 

31.0805 
31.0966 

9T3 

.09529 

833569 

761048497 

30.2159 

968 

1.03306 

937024 

907039232 

31.1127 

914 

.09409 

835396 

763551944 

30.2324 

969 

1.03199 

938961 

909853209 

31.1288 

915 

1.09290 

837225 

766060875 

30.2490 

970 

1.03093 

940900 

912673000 

31.1448 

916 

1.09170 

839056 

768575296 

30-2655 

971 

1.02987 

942841 

915498611 

31.1609 

917 

1.09051 

840889 

771095213 

30.2820 

972 

1.02881 

944784 

918330048 

31.1769 

918 

1.08032 

842724 

773620632 

30.2985 

973 

1.02775 

946729 

921167317 

31.1929 

919 

1.08814 

844561 

776I5I559 

30-3150 

974 

1.02669 

948676 

924010424 

31.2090 

920 

1.08696 

846400 

778688000 

30.3315 

975 

1.02564 

950625 

926859375 

31.2250 

921 

1.08578 

848241 

781229961 

30.3480 

976 

1.02459 

952576 

929714176 

31.2410 

922 

1.08460 

850084 

783777448 

30-3645 

977 

1.02354 

954529 

932574833 

31.2570 

923 

1.08342 

851929 

786330467 

30.3809 

978 

1.02249 

956484 

935441352 

31.2730 

924 

1.08225 

853776 

788889024 

30-3974 

979 

1.02145 

958441 

9383^739 

31.2890 

925 

1.08108 

855625 

791453125 

30.4138 

980 

1.02041 

960400 

941192000 

31-3050 

926 

1.07991 

857476 

794022776 

30.4302 

981 

1.01937 

962361 

944076141 

31.3209 

927 

1.07875 

859329 

796597983 

30.4467 

982 

1.01833 

9643J4 

946966168 

3I-3369 

928 
929 

1.07759 
1.07643 

861184 
863041 

799178752 
801765089 

30.4631 
30-4795 

983 
984 

1.01729 
1.01626 

966289 
968256 

949862087 
952763904 

3I-3528 
31-3688 

930 

1.07527 

864900 

804357000 

30-4959 

985 

1-01523 

970225 

955671625 

3  i  -3847 

93i 
932 

1.07411 
1.07296 

866761 
868624 

806954491 
809557568 

30-5123 
30.5287 

986 
987 

1.01420 
1.01317 

972196 
974169 

958585256 
961  504803 

31.4006 
31.4166 

933 
934 

1.07181 
1.07066 

870489 
872356 

812166237 
814780504 

30-5450 
30.5614 

988 
989 

1.01215 

I.OIII2 

976144 
978121 

964430272 
967361669 

3M325 
31.4484 

935 

936 
937 
938 
939 

1.06952 
1.06838 
1.06724 
i.  066  10 
1.06496 

874225 
876096 
877969 

879844 
881721 

817400375 
820025856 
822656953 
825293672 
827936019 

30-5778 
30.594I 
30.6105 
30.6268 
30.6431 

990 

991 
992 
993 
994 

I.OIOIO 

1.00908 
1.00806 
1.00705 
1.00604 

980100 
982081 
984064 
986049 
988036 

970299000 
973242271 
976191488 
979146657 
982107784 

3  i  4643 
31.4802 
31.4960 

3i.5"9 
31.5278 

940 

941 
942 
943 
944 

1.06383 
1.06270 
1.06157 
1.06045 
1.05932 

883600 
885481 
887364 
889249 
891136 

830584000 
833237621 
835896888 
838561807 
841232384 

30-6594 
30.6757 
30.6920 
30.7083 
30.7246 

995 

996 

999 

1.00503 
I.OO4O2 
I.OO3OI 
I  .OO2OO 
I.OOIOO 

990025 
992016 
994009 
996004 
998001 

985074875 
988047936 
991026973 
994011992 
997002999 

3!-5436 
31-5595 
31-5753 
3^-59^ 
31.6070 

SMITHSONIAN  TABLES. 


TABLE  9. 
LOGARITHMS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

100 

0000 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

o°35 

0039 

0043 

101 

0043 

0048 

0052 

0056 

0060 

0065 

0069 

0073 

0077 

0082 

0086 

102 

0086 

0090 

0095 

0099 

0103 

OIO7 

01  1  1 

0116 

OI2O 

0124 

0128 

103 

0128 

0133 

0141 

0145 

0149 

0154 

0158 

Ol62 

0166 

0170 

104 

0170 

0175 

0179 

0183 

0187 

0191 

0199 

0204 

0208 

O2I2 

105 

0212 

0216 

0220 

0224 

0228 

0233 

0237 

0241 

0245 

0249 

0253 

1  06 

107 

0253 
0294 

0257 
0298 

026l 
0302 

0265 
0306 

0269 
0310 

0273 

°3T4 

0278 
0318 

0282 
0322 

0286 
0326 

0290 
0330 

0294 
0334 

108 

0334 

0338 

0342 

0346 

°35° 

0354 

0358 

0362 

0366 

0370 

0374 

109 

0374 

0378 

0382 

0386 

0390 

0394 

0398 

0402 

0406 

0410 

0414 

110 

0414 

'  0418 

O422 

0426 

0430 

0434 

0438 

0441 

0445 

0449 

0453 

in 

0453 

0457 

0461 

0465 

0469 

0473 

0477 

0481 

0484 

0488 

0492 

112 

0492 

0496 

0500 

0504 

0508 

0512 

0515 

0519 

0523 

0527 

0531 

"3 

0531 

°535 

0538 

0542 

0546 

0550 

°554 

0558 

0561 

0565 

0569 

114 

0509 

0573 

0577 

0580 

0584 

0588 

0592 

0596 

0599 

0603 

0607 

115 

0607 

0611 

0615 

0618 

0622 

0626 

0630 

°633 

0637 

0641 

0645 

116 

0645 

0648 

0652 

0656 

0660 

0663 

0667 

0671 

0674 

0678 

0682 

"7 

0682 

0686 

0689 

0693 

0697 

0700 

0704 

0708 

O7II 

0715 

0719 

118 

0719 

0722 

0726 

0730 

0734 

0737 

0741 

0745 

0748 

0752 

°755 

"9 

°755 

0759 

0763 

0766 

0770 

0774 

0777 

0781 

0785 

0788 

0792 

120 

0792 

0795 

0799 

0803 

0806 

0810 

0813 

0817 

0821 

0824 

0828 

121 

0828 

0831 

0835 

0839 

0842 

0846 

0849 

0853 

0856 

0860 

0864 

122 

0864 

0867 

0871 

0874 

0878 

0881 

0885 

0888 

0892 

0896 

0899 

I23 

124 

0899 
0934 

0903 
0938 

0906 
0941 

0910 
0945 

0913 
0948 

0917 
0952 

0920 
°955 

0924 
°959 

0927 
0962 

0$ 

0934 
0969 

125 

0969 

0973 

0976 

0980 

0983 

0986 

0990 

0993 

0997 

1000 

1004 

126 

1004 

1007 

ion 

1014 

1017 

IO2I 

1024 

1028 

I03I 

1035 

1038 

127 

1038 

1041 

1045 

1048 

1052 

IO55 

I059 

1062 

1065 

1069 

1072 

128 

1072 

1075 

1079 

1082 

1086 

1089 

1092 

1096 

1099 

1103 

1106 

129 

1106 

1109 

1113 

ii  16 

1119 

II23 

1126 

1129 

"33 

1136 

"39 

130 

"39 

"43 

1146 

"49 

"53 

1156 

"59 

1163 

1166 

1169 

"73 

131 

"73 

1176 

"79 

1183 

1186 

Il89 

"93 

1196 

"99 

I2O2 

1206 

132 

1206 

1209 

1212 

1216 

1219 

1222 

1225 

1229 

1232 

I235 

I239 

1239 

1242 

1245 

1248 

1252 

1255 

1258 

1261 

.1265 

1268 

1271 

134 

1271 

1274 

1278 

1281 

1284 

1287 

1290 

1294 

1297 

1300 

1303 

135 

1303 

1307 

1310 

J3r3 

1316 

1319 

1323 

1326 

1329 

1332 

1335 

136 

1335 

1339 

1342 

T345 

1348 

'351 

'355 

1358 

1361 

1364 

1367 

137 

1367 

1370 

1374 

1377 

1380 

1383 

1386 

1389 

1392 

1396 

1399 

138 

*399 

1402 

1405 

1408 

1411 

1414 

1418 

1421 

1424 

1427 

143° 

139 

1430 

1433 

I436 

1440 

M43 

1446 

M49 

1452 

1455 

1458 

1461 

140 

1461 

1464 

1467 

1471 

1474 

1477 

1480 

1483 

1486 

1489 

1492 

141 

1492 

M95 

1498 

1501 

T5°4 

1508 

1511 

15*4 

1517 

1520 

1523 

142 

1523 

1526 

1529 

1532 

*535 

1538 

I54I 

1544 

1547 

1550 

1553 

144 

1553 
1584 

1556 
1587 

r559 
1590 

1562 
1593 

1565 
1596 

1569 
1599 

1602 

i|75 
1605 

1608 

1581 
1611 

1584 
1614 

145 

146 

1614 
1644 

1617 
1647 

1620 
1649 

1623 
1652 

1626 

1629 
1658 

1632 
1661 

'635 
1664 

1638 
1667 

1641 
1670 

1644 
1673 

147 

1673 

1676 

1679 

1682 

1685 

1688 

1691 

1694 

1697 

1700 

1703 

148 

1703 

1706 

1708 

1711 

1714 

1717 

1720 

1723 

1726 

1729 

1732 

H9 

1732 

1735 

1738 

1741 

1744 

1746 

1749 

1752 

1755 

1758 

1761 

SMITHSONIAN  TABLES, 


TABLE   9  (continued). 

LOGARITHMS. 


N. 

0 

1 
I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

150 

1761 

1764 

1767 

1770 

1772 

1775 

1778 

1781 

1784 

1787 

1790 

I5I 

1790 

1796 

1798 

1801 

1804 

1807 

1810 

1813 

1816 

1818 

I52 

1818 

1821 

1824 

1827 

1830 

1833 

1836 

1838 

1841 

1844 

1847 

153 

1847 

1850 

1853 

1855 

1858 

1861 

1864 

1867 

1870 

1872 

1875 

154 

1875 

1878 

1881 

1884 

1886 

1889 

1892 

1895 

1898 

1901 

1903 

155 

1903 

1906 

1909 

1912 

1915 

1917 

1920 

1923 

1926 

1928 

I93I 

156 

I931 

1934 

1940 

1942 

1945 

1948 

1951 

*953 

1956 

'959 

J57 

1959 

1962 

1965 

1967 

1970 

1976 

1978 

1981 

1984 

1987 

158 

1987 

I989 

1992 

1995 

1998 

2OOO 

2003 

2006 

2009 

2OII 

2014 

159 

2014 

2OI7 

2019 

2022 

2025 

2028 

2030 

2033 

2036 

2038 

2041 

160 

2041 

2044 

2047 

2049 

2052 

2055 

2057 

2060 

2063 

2066 

2068 

161 

2068 

2O7I 

2074 

2076 

2079 

2082 

2084 

2087 

2090 

2O92 

2095 

162 

2095 

2098 

2IOI 

2103 

2106 

2109 

2III 

2114 

2117 

2119 

2122 

163 

2122 

2125 

2127 

2130 

2133 

2135 

2138 

2140 

2143 

2140 

2148 

164 

2148 

2151 

2154 

2156 

2159 

2l62 

2164 

2167 

2170 

2172 

2175 

165 

2175 

2177 

2180 

2183 

2185 

2188 

2191 

2193 

2196 

2198 

22OI 

1  66 

22OI 

2204 

2206 

22O9 

2212 

2214 

2217 

2219 

2222 

2225 

2227 

167 

2227 

2230 

2232 

2235 

2238 

224O 

2243 

2245 

2248 

225I 

2253 

1  68 

2253 

2256 

2258 

226l 

2263 

2266 

2269 

2271 

2274 

2276 

2279 

169 

2279 

228l 

2284 

2287 

2289 

2292 

2294 

2297 

2299 

2302 

2304 

170 

2304 

2307 

2310 

23I2 

2315 

2317 

2320 

2322 

2325 

2327 

233° 

171 

233° 

2333 

2335 

2338 

2340 

2343 

2345 

2348 

2350 

2353 

2355 

172 

2355 

2358 

2360 

2363 

2365 

2368 

2370 

2373 

2375 

2378 

2380 

J73 

2380 

2383 

2385 

2388 

2390 

2393 

2395 

2398 

24OO 

2403 

2405 

174 

2405 

2408 

2410 

24U 

2415 

24l8 

2420 

2423 

2425 

2428 

2430 

175 

176 

2430 

2455 

2433 

2458 

2435 
2460 

2438 
2463 

2440 
2465 

2443 
2467 

2445 
2470 

2448 
2472 

2450 
2475 

2453 
2477 

2455 
2480 

177 

2480 

2482 

2485 

2487 

2490 

2492 

2494 

2497 

2499 

25O2 

2504 

178 

2504 

2507 

2509 

25I2 

25M 

2516 

2519 

2521 

2524 

2526 

2529 

179 

2529 

2531 

2533 

2536 

2538 

2541 

2543 

2545 

2548 

2550 

2553 

180 

2553 

2555 

2558 

2560 

2562 

2565 

2567 

2570 

2572 

2574 

2577 

181 

182 

2577 
2601 

2579 

2582 
2605 

2584 
2608 

2586 
26lO 

2589 
2613 

2591 
2615 

2594 
2617 

262O 

2598 
2622 

2601 
2625 

183 
184 

2625 
2648 

2651 

2629 
2653 

2632 
2655 

2634 
2658 

2636 
2660 

l$2 

2641 
2665 

2643 
2667 

2646 
2669 

2648 
2672 

185 

2672 

2674 

2676 

2679 

268l 

2683 

2686 

2688 

2690 

2693 

2695 

186 

2695 

2697 

27OO 

27O2 

2704 

2707 

2709 

2711 

2714 

2716 

2718 

187 

27l8 

2721 

2723 

2725 

2728 

2730 

2732 

2735 

2737 

2739 

2742 

188 

2742 

2744 

2746 

2749 

2751 

2753 

2755 

2758 

2760 

2762 

2705 

189 

2765 

2767 

2769 

2772 

2774 

2776 

2778 

2781 

2783 

2785 

2788 

190 

191 
192 

193 
194 

2788 
28lO 

2833 
2856 
2878 

2790 
2813 
2835 
2858 

2792 
2838 
2882 

2794 
2817 
2840 
2862 
2885 

2797 
2819 
2842 
2865 
2887 

2799 
2822 

2844 
2867 
2889 

2801 
2824 
2847 
2869 
2891 

2804 
2826 
2849 
2871 
2894 

2806 
2828 
2851 

2808 
2831 

2853 
2876 
2898 

2810 

2833 
2856 
2878 
2900 

195 

196 

199 

2900 
2923 

2945 
2967 

2903 
2925 
2947 
2969 
2991 

2905 
2927 

2949 
2971 

2993 

2907 
2929 

295T 
2973 
2995 

2909 

2931 

2953 
2975 
2997 

2911 

2934 
2956 
2978 
2999 

2914 
2936 

2CX8 

2980 
3002 

2916 
2938 
2960 
2982 
3004 

2918 
2940 
2962 
2984 
3006 

2920 
2942 
2964 
2986 
3008 

2923 
2945 
2967 
2989 
3010 

SMITHSONIAN  TABLES. 


26 


TABLE  10. 
LOGARITHMS. 


O-ioo       4.     S     fi       7     ft     Q 

P.I 

> 

X     A     O       V.    -  9     "9        /      O     57 

1 

2 

3 

4 

5 

10 

0000    0043  0086  0128    0170  0212  0253    0294  0334  0374 

4 

8 

12 

17 

21 

II 

0414   0453  °492  °53I   0569  0607  0645   0682  0719  0755 

4 

8 

II 

15 

19 

12 

0792   0828  0864  0899   0934  0969  1004   IO38  1072  1106 

3 

7 

IO 

M 

17 

13 
H 

"39   "73  1206  1239   1271  1303  1335   1367  1399  1430 
1461   1492  1523  1553   1584  1614  1644   1673  r703  1732 

3 
3 

6 
6 

IO 

9 

13 

12 

16 
15 

15 

1761   1790  1818  1847   J875  1903  1931   1959  1987  2014 

3 

6 

8 

II 

14 

16 

2041     2068   2095   2122     2145   2175   2201     2227  2253   2279 

3 

5 

8 

II 

U 

17 

2304     2330  2355   2380     2405   2430  2455     2480  2504   2529 

2 

5 

7 

10 

12 

18 

'9 

2553   2577  2601  2625   2648  2672  2695   27  J8  2742  2765 
2788   2810  2833  '2856   2878  2900  2923   2945  2967  2989 

2 

2 

5 
4 

7 

7 

9 
9 

12 
II 

20 

3010   3032  3054  3075   3096  3118  3139   3160  3181  3201 

2 

4 

6 

8 

II 

21 

3222   3243  3263  3284   3304  3324  3345   3365  3385  3404 

2 

4 

6 

8 

10 

22 

3424   3444  3464  3483   3502  3522  3541   3560  3579  3598 

2 

4 

6 

8 

10 

23 

24 

3617   3636  3655  3674   3692  3711  3729   3747  3766  3784 
3802   3820  3838  3856   3874  3892  3909   3927  3945  3962 

2 

2 

4 
4 

5 

5 

7 
7 

9 
9 

25 

3979   3997  4014  4031   4048  4065  4082   4099  4116  4133 

2 

3 

5 

7 

9 

26 

4150   4166  4183  4200   4216  4232  4249   4265  4281  4298 

2 

3 

5 

7 

8 

2£ 

4314   4330  4346  4362   4378  4393  4409   4425  4440  4456 

2 

3 

5 

6 

8 

28 

4472   4487  45°2  45  J  8   4533  4548  4564   4579  4594  4609 

2 

3 

5 

6 

8 

29 

4624   4639  4654  4669   4683  4698  4713   4728  4742  4757 

I 

3 

4 

6 

7 

30 

4771   4786  4800  4814   4829  4843  4857   4871  4886  4900 

3 

4 

6 

7 

3i 

4914   4928  4942  4955   4969  4983  4997   5011  5024  5038 

3 

4 

6 

7 

32 

5051   5065  5079  5092   5105  5119  5132   5145  5159  5172 

3 

4 

5 

7 

33 

5l85   5198  5211  5224   5237  525°  5263   5276  5289  5302 

3 

4 

5 

6 

34 

5315   5328  5340  5353   5366  5378  539i   5403  54i6  5428 

3 

4 

5 

6 

35 

544i   5453  5465  5478   549°  55°2  55T4   5527  5539  5551 

2 

4 

5 

6 

36 

5563   5575  5587  5599   56ir  5623  5635   5647  5658  567Q 

2 

4 

5 

6 

37 

5682   5694  5705  5717   5729  5740  5752   5763  5775  5786 

2 

3 

5 

6 

38 
39 

5798   5809  5821  5832   5843  5855  5866   5877  5888  5899 
59"   5922  5933  5944   5955  5966  5977   5988  5999  6010 

2 
2 

3 
3 

5 
4 

6 
6 

40 

4i 

6021   6031  6042  6053   6064  6075  6085   6096  6107  6117 
6128   6138  6149  6160   6170  6180  6191   6201  6212  6222 

2 
2 

3 
3 

4 
4 

5 

5 

42 

6232   6243  6253  6263   6274  6284  6294   6304  6314  6325 

2 

3 

4 

5 

43 
44 

6335   6345  6355  6365   6375  6385  6395   6405  6415  6425 
6435   6444  6454  6464   6474  6484  6493   6503  6513  6522 

2 

2 

3 
3 

4 
4 

5 
5 

45 

46 

6532   6542  6551  6561   6571  6580  6590   6599  6609  6618 
6628   6637  6646  6656   6665  6675  6684   6693  6702  6712 

2 

2 

3 

3 

4 
4 

5 
5 

47 

6721   6730  6739  6749   6758  6767  6776   6785  6794  6503 

2 

3 

4 

5 

d8 

6812   6821  6830  6839   6848  6857  6866   6875  6884  6893 

2 

3 

4 

4 

49 

6902   6911  6920  6928   6937  6946  6955   6964  6972  6981 

2 

3 

4 

4 

50 

6990   6998  7007  7016   7024  7033  7042   7050  7059  7067 

2 

3 

3 

4 

51 

7076   7084  7093  7101   7110  7118  7126   7135  7143  7152 

2 

3 

3 

4 

52 

7160   7168  7177  7185   7193  7202  7210   7218  7226  7235 

2 

2 

3 

4 

53 

7243   7251  7259  7267   7275  7284  7292   73°°  73°8  73l6 

2 

2 

3 

4 

54 

7324   7332  7340  7348   7356  7364  7372   7380  7388  7396 

2 

2 

3 

4 

SMITHSONIAN  TABLES. 


TABLE    10  (continued). 
LOGARITHMS. 


N. 

0     123     456     789 



] 

p.  r 

> 

1 

2 

3 

4 

5 

55 

7404   7412  7419  7427   7435  7443  7451   7459  7466  7474 

7 

2 

2 

3 

4 

56 

57 

7482   7490  7497  7505   7513  7520  7528   7536  7543  7551 
7559   7566  7574  75§2   7589  7597  7604   7612  7619  7627 

2 
2 

2 

2 

3 
3 

4 
4 

58 

7634   7642  7649  7657   7664  7672  7679   7686  7694  7701 

2 

3 

4 

59 

7709   7716  7723  7731   7738  7745  7752   7760  7767  7774 

2 

3 

4 

60 

7782   7789  7796  7803   7810  7818  7825   7832  7839  7846 

2 

3 

4 

61 

7853   7860  7868  7875   7882  7889  7896   7903  7910  7917 

2 

3 

4 

62 

7924   793  1  7938  7945   7952  7959  7966   7973  798o  7987 

2 

3 

3 

63 

7993   8000  8007  8014   8021  8028  8035   8041  8048  8055 

2 

3 

3 

64 

8062   8069  8075  8082   8089  8096  8102   8109  8116  8122 

2 

3 

3 

65 

8129   8136  8142  8149   8156  8162  8169   8176  8182  8189 

2 

3 

3 

66 

8195   8202  8209  8215   8222  8228  8235   8241  8248  8254 

2 

3 

3 

67 

8261   8267  8274  8280   8287  8293  8299   8306  8312  8319 

2 

3 

3 

68 

8325   8331  8338  8344   8351  8357  8363   8370  8376  8382 

2 

3 

3 

69 

8388   8395  8401  8407   8414  8420  8426   8432  8439  8445 

2 

3 

3 

70 

8451   8457  8463  8470   8476  8482  8488   8494  8500  8506 

2 

2 

3 

7i 
72 

8513   8519  8525  8531   8537  8543  8549   8555  8561  8567 
8573   8579  8585  8591   8597  8603  8609   8615  8621  8627 

2 

2 

2 
2 

3 

3 

73 

8633   8639  8645  8651   8657  8663  8669   8675  8681  8686 

2 

2 

3 

74 

8692   8698  8704  8710   8716  8722  8727   8733  8739  8745 

2 

2 

3 

75 

875,1   8756  8762  8768   8774  8779  8785   8791  8797  8802 

2 

2 

3 

76 

8808   8814  8820  8825   8831  8837  8842   8848  8854  8859 

2 

2 

3 

77 

8865   8871  8876  8882   8887  8893  8899   8904  8910  8915 

2 

2 

3 

78 

8921   8927  8932  8938   8943  8949  8954   8960  8965  8971 

2 

2 

3 

79 

8976   8982  8987  8993   8998  9004  9009   9015  9020  9025 

2 

2 

3 

80 

9031   9036  9042  9047   9053  9058  9063   9069  9074  9079 

2 

2 

3 

81 

9085   9090  9096  9101   9106  9112  9117   9122  9128  9133 

2 

2 

3 

82 

9138   9143  9149  9154   9159  9165  9170   9175  9180  9186 

2 

2 

3 

83 

9191   9196  9201  9206   9212  9217  9222   9227  9232  9238 

I 

2 

2 

3 

84 

9243   9248  9253  9258   9263  9269  9274   9279  9284  9289 

I 

2 

2 

3 

85 

9294   9299  9304  9309   9315  9320  9325   9330  9335  9340 

2 

2 

3 

86 

9345   935°  9355  936o   9365  9370  9375   93go  9385  939° 

2 

2 

3 

87 

9395   9400  9405  94io   9415  9420  9425   9430  9435  9440 

0 

2 

2 

88 

9445   9450  9455  9460   9465  9469  9474   9479  9484  9489 

o 

2 

2 

89 

9494   9499  95<H  95Q9   95'3  95*8  9523   9528  9533  9538 

o 

2 

2 

90 

9542   9547  9552  9557   9562  9566  9571   9576  9581  9586 

o 

2 

2 

9i 

959°   9595  9600  9605   9609  9614  9619   9624  9628  9633 

o 

2 

2 

92 

9638   9643  9647  9652   9657  9661  9666   9671  9675  9680 

o 

2 

2 

93 

9685   9689  9694  9699   9703  9708  9713   9717  9722  9727 

o 

2 

2 

94 

9731   9736  974i  9745   9750  9754  9759   9763  9768  9773 

0 

2 

2 

95 

96 

9777   9782  9786  9791   9795  9800  9805   9809  9814  9818 
9823   9827  9832  9836   9841  9845  9850   9854  9859  9863 

0 
0 

2 

2 

2 
2 

9868   9872  9877  9881   9886  9890  9894   9899  9903  9908 

0 

2 

2 

98 

9912   9917  9921  9926   9930  9934  9939   9943  994»  9952 

0 

2 

2 

99 

9956   9961  9965  9969   9974  9978  9983   9987  9991  9996 

0 

2 

2 

SMITHSONIAN  TABLES. 


28 


TABLE  11. 
ANTILOGARITHMS. 


01      o     o       4.     ^     fi        7     ft     Q 

] 

P.  F 

i 

J,     •      w        t      3      O         /      O      9 

1 

2 

3 

4 

5 

.00 

IOOO     IOO2  IOO5  IOO7     IOO9  IOI2   IOI4     IOl6  IOI9  IO2I 

o 

0 

.01 

1023     1026  1028   1030     1033  1035  1038     1040   1042   1045 

o 

o 

.02 

1047   I05°  I052  I054   I057  I059  Io62   IO^4  Io67  I0^9 
1072   1074  1076  1079   Io81  Io84  Io86   Io89  I09I  I094 

0 
0 

o 

0 

.04 

1096   1099  1102  1104   1107  1109  iii2   1114  1117  1119 

o 

I 

.05 

1122     1125   1127   1130     1132   1135   1138     1140  1143  1146 

0 

.o6 

1148   1151  1153  1156   1159  1161  1164   1167  1169  1172 

o 

.07 

1175   1178  1180  1183   1186  1189  1191    1194  1197  1199 

o 

.o8 

1202     1205   1208  I2II     1213  I2l6  1219     1222  1225   I227 

0 

.09 

1230     1233  1236  1239     1242  1245  1247     1250  1253  1256 

0 

.10 

1259     1262   1265  1268     1271   1274  1276     1279  1282  1285 

o 

i 

.ii 

1288     1291   1294  1297     1300  1303  1306     1309  1312   1315 

0 

2 

.12 

1318     1321   1324  1327     1330  1334  1337     1340  1343   1346 

o 

2 

•13 
.14 

1349    1352   1355   1358     1361   1365   1368     1371   1374  1377 
1380     1384  1387   1390     1393   1396  1400     1403  1406  1409 

o 
o 

2 

2 

.15 

.i6 

1413     1416  1419  1422     1426  1429  1432     1435  1439  1442 

1445   1449  1452  1455   *459  J462  1466   1469  1472  1476 

0 

o 

2 
2 

.17 

1479   J483  !4°6  M89   J493  J496  1500   1503  1507  1510 

0 

2 

.18 

1514   1517  1521  1524   1528  1531  1535   1538  1542  1545 

o 

2 

.19 

1549   1552  1556  1560   1563  1567  1570   1574  1578  1581 

o 

2 

.20 

1585   1589  1592  1596   1600  1603  1607   1611  1614  1618 

0 

i 

2 

.21 

1622   1626  1629  1633   1637  1641  1644   1648  1652  1656 

o 

2 

2 

.22 

1660   1663  1667  1671    1675  1679  1683   J687  1690  1694 

0 

2 

2 

•23 

1698   1702  1706  1710   1714  1718  1722   1726  1730  1734 

0 

2 

2 

.24 

1738   1742  1746  1750   1754  1758  1762   1766  1770  1774 

o 

2 

2 

.25 

1778   1782  1786  1791   1795  *799  l8°3   l8°7  l8n  l8l6 

0 

2 

2 

.26 

1820   1824  1828  1832   1837  1841  1845   1849  l854  l858 

o 

2 

2 

.27 

1862   1866  1871  1875   l879  l884  l888   l892  l897  I9°I 

o 

2 

2 

.28 

I9°S   I9I°  I914  I9I9   X923  J928  J932   I93&  1941  1945 

0 

2 

2 

.29 

I95°   *954  X9S9  J9^3   1968  1972  1977   1982  1986  1991 

o 

2 

2 

.30 

1995   2000  2004  2009   2014  2018  2023   2028  2032  2037 

0 

2 

2 

•31 

2042   2046  2051  2056   2061  2065  2070   2075  2o8°  2o84 

o 

2 

2 

•32 

2089   2094  2099  2104   2109  2113  2118   2123  2128  2133 

o 

2 

2 

•33 

2138   2143  2148  2153   2158  2163  2168   2173  2178  2183 

0 

2 

2 

•34 

2188   2193  2198  2203   2208  2213  2218   2223  2228  2234 

1 

2 

2 

3 

.35 

2239   2244  2249  2254   2259  2265  2270   2275  2280  2286 

2 

2 

3 

•36 

2291   2296  2301  2307   2312  2317  2323   2328  2333  2339 

2 

2 

3 

•37 

2344   235°  2355  2360   2366  2371  2377   2382  2388  2393 

2 

2 

3 

•38 

2399   2404  2410  2415   2421  2427  2432   2438  2443  2449 

2 

2 

3 

•39 

2455   2460  2466  2472   2477  2483  2489   2495  2500  2506 

2 

2 

3 

.40 

.41 

.42 

2512   2518  2523  2529   2535  2541  2547   2553  2559  2564 
257°   2576  2582  2588   2594  2600  2606   2612  2618  2624 
2630   2636  2642  2649   2655  2661  2667   2673  2679  2685 

2 

2 

2 

2 
2 
2 

3 
3 
3 

•43 

2692   2698  2704  2710   2716  2723  2729   2735  2742  2748 

2 

3 

3 

•44 

2754   2761  2767  2773   2780  2786  2793   2799  2805  2812 

2 

3 

3 

.45 

2818   2825  2831  2838   2844  2851  2858   2864  2871  2877 

2 

3 

3 

.46 

2884   2891  2897  2904   2911  2917  2924   2931  2938  2944 

2 

3 

3 

•47 

2951   2958  2965  2972   2979  2985  2992   2999  3006  3013 

2 

3 

3 

.48 

3020   3027  3034  3041   3048  3055  3062   3069  3076  3083 

2 

3 

4 

•49 

3090   3097  3105  3112   3119  3126  3133   3141  3148  3155 

2 

3 

4 

SMITHSONIAN  TABLES. 


TABLE    1  1    (continued). 
ANTILOGARITHMS. 


0123      456      789 

I 

».  P 

•L      «       O          IK      *J      U          /      O      *7 

1 

2 

3 

4 

5 

.50 

3162   3170  3177  3184   3192  3199  3206   3214  3221  3228 

i 

2 

3 

4 

•51 

3236   3243  325!  3258   3266  3273  3281   3289  3296  3304 

2 

2 

3 

4 

•52 

3311   33*9  3327  3334   3342  3350  3357   3365  3373  3381 

2 

2 

3 

4 

•53 

3388   3396  3404  3412   3420  3428  3436   3443  3451  3459 

2 

2 

3 

4 

•54 

3467   3475  3483  349i   3499  35o8  3516   3524  3532  354O 

2 

2 

3 

4 

.55 

3548   3556  3565  3573   3581  3589  3597   3606  3614  3622 

2 

2 

3 

4 

•56 

3631   3639  3648  3656   3664  3673  3681   3690  3698  3707 

2 

3 

3 

4 

•57 

37i5   3724  3733  374i   3750  3758  3767   3776  3784  3793 

2 

3 

3 

4 

.58 

3802   3811  3819  3828   3837  3846  3855   3864  3873  3882 

2 

3 

4 

4 

•59 

3890   3899  3908  3917   3926  3936  3945   3954  39^3  3972 

2 

3 

4 

5 

.60 

3981   3990  3999  4009   4018  4027  4036   4046  4055  4064 

2 

3 

4 

5 

.61 

4074   4083  4093  4102   4111  4121  4130   4140  4150  4159 

2 

3 

4 

5 

.62 

4169   4178  4188  4198   4207  4217  4227   4236  4246  4256 

2 

3 

4 

5 

•63 

4266   4276  4285  4295   4305  4315  4325   4335  4345  4355 

2 

3 

4 

5 

.64 

4365   4375  4385  4395   44°6  4416  4426   4436  4446  4457 

2 

3 

4 

5 

.65 

.66 

4467   4477  4487  4498   4508  4519  4529   4539  4550  4560 
4571   4581  4592  4603   4613  4624  4634   4645  4656  4667 

2 
2 

3 
3 

4 
4 

5 
5 

.67 

4677   4688  4699  4710   4721  4732  4742   4753  4764  4775 

2 

3 

4 

5 

.68 

4786   4797  4808  4819   4831  4842  4853   4864  4875-4887 

2 

3 

4 

6 

.69 

4898   4909  4920  4932   4943  4955  4966   4977  4989  5000 

2 

3 

5 

6 

.70 

5012   5023  5035  5047   5058  5070  5082   5093  5105  5117 

2 

4 

5 

6 

•71 

.72 

5129   5140  5152  5164   5176  5188  5200   5212  5224  5236 
5248   5260  5272  5284   5297  5309  5321   5333  5346  53<>8 

2 

2 

4 
4 

5 
5 

6 
6 

•73 

5370   5383  5395  5408   5420  5433  5445   5458  547Q  54»3 

3 

4 

5 

6 

•74 

5495   5508  5521  5534   5546  5559  5572   5585  5598  5610 

3 

4 

5 

6 

.75 

.76 

5623   5636  5649  5662   5675  5689  5702   5715  5728  5741 
5754   5768  5781  5794   5808  5821  5834   5848  5861  5875 

3 
3 

4 
4 

5 
5 

7 
7 

•78 

5888   5902  5916  5929   5943  5957  5970   5984  5998  6012 
6026   6039  6053  6067   6081  6095  6109   6124  6138  6152 

3 
3 

4 
4 

I 

7 
7 

•79 

6166   6180  6194  6209   6223  6237  6252   6266  6281  6295 

3 

4 

6 

7 

.80 

6310   6324  6339  6353   6368  6383  6397   6412  6427  6442 

i 

3 

4 

6 

7 

.81 

6457   6471  6486  6501   6516  6531  6546   6561  6577  6592 

2 

3 

5 

6 

8 

.82 

6607   6622  6637  6653   6668  6683  6699   6714  6730  6745 

2 

3 

5 

6 

8 

•83 

6761   6776  6792  6808   6823  6839  6855   6871  6887  6902 

2 

3 

5 

6 

8 

.84 

6918   6934  6950  6966   6982  6998  7015   7031  7047  7063 

2 

3 

5 

6 

8 

.85 

7079   7096  7112  7129   7145  7161  7178   7194  7211  7228 

2 

3 

5 

7 

8 

.86 

7244   7261  7278  7295   7311  7328  7345   7362  7379  7396 

2 

3 

5 

7 

8 

.87 

7413   743°  7447  7464   7482  7499  7516   7534  7551  7568 

2 

3 

5 

7 

9 

oo 
.00 

7586   7603  7621  7638   7656  7674  7691   7709  7727  7745 

2 

4 

5 

7 

9 

.89 

7762   7780  7798  7816   7834  7852  7870   7889  7907  7925 

2 

4 

5 

7 

9 

.90 

.91 

7943   7962  7980  7998   8017  8035  8054   8072  8091  8110 
8128   8147  8166  8185   8204  8222  8241   8260  8279  8299 

2 
2 

4 
4 

6 
6 

I 

9 
9 

.92 
•93 
•94 

8318   8337  8356  8375   8395  8414  8433   8453  ff2  8492 
8511   8s  31  8551  8570   8590  8610  8630   8650  8670  8690 
8710   8730  8750  8770   8790  8810  8831   8851  8872  8892 

2 
2 
2 

4 
4 

4 

6 
6 
6 

8 
8 
8 

10 

10 

IO 

.95 

8913   8933  8954  8974   8995  9016  9036   9057  9078  9099 

2 

4 

6 

8 

10 

.96 

•97 

9120   9141  9162  9183   9204  9226  9247   9265  9290  9311 
9333   9354  9376  9397   9419  944*  9462   9484  95°6  9528 

2 
2 

4 
4 

. 
7 

9 

1  1 

II 

.98 
•99 

9550   9572  9594  9616   9638  9661  9683   9705  9727  9750 
9772   9795  9817  9840   9863  9886  9908   993i  9954  9977 

2 

2 

4 
5 

7 
7 

9 
9 

II 

II 

SMITHSONIAN  TABLES. 


30 


TABLE  12. 
ANT1LOGARITHMS, 




0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.900 

7943 

/  S-T*J 

7945 

7947 

7949 

7951 

7952 

7954 

7956 

7958 

7960 

7962 

.901 

7962 

7963 

7965 

7967 

7969 

7971 

7973 

7974 

7976 

7978 

7980 

.902 

7980 

7982 

7984 

7985 

7987 

7989 

799  i 

7993 

7995 

7997 

7998 

•9°3 

7998 

8000 

8002 

8004 

8006 

8008 

8009 

8011 

8013 

8015 

8017 

.904 

8017 

8019 

8020 

8022 

8024 

8026 

8028 

8030 

8032 

8033 

8035 

.905 

8035 

8037 

8039 

8041 

8043 

8045 

8046 

8048 

8050 

8052 

8054 

.906 

8054 

8056 

8057 

8059 

8061 

8063 

8065 

8067 

8069 

8070 

8072 

.907 

8072 

8074 

8076 

8078 

8080 

8082 

8084 

8085 

8087 

8089 

8091 

.908 

8091 

8093 

8095 

8097 

8098 

8100 

8102 

8104 

8106 

8108 

81  10 

.909 

8110 

8111 

8113 

8115 

8117 

8119 

8121 

8123 

8125 

8126 

8128 

.910 

8128 

8130 

8132 

8134 

8136 

8138 

8140 

8141 

8143 

8145 

8i47 

.911 

8147 

8149 

8151 

8i53 

8155 

8156 

8158 

8160 

8162 

8164 

8166 

.912 

8166 

8168 

8170 

8171 

8i73 

8i75 

8177 

8179 

8181 

8183 

8185 

•913 

8185 

8187 

8188 

8190 

8192 

8194 

8196 

8198 

8200 

8202 

8204 

.914 

8204 

8205 

8207 

8209 

8211 

8213 

8215 

8217 

8219 

8221 

8222 

.915 

8222 

8224 

8226 

8228 

8230 

8232 

8234 

8236 

8238 

8239 

8241 

.916 

8241 

8243 

8245 

8247 

8249 

8251 

8253 

8255 

8257 

8258 

8260 

.917 

8260 

8262 

8264 

8266 

8268 

8270 

8272 

8274 

8276 

8278 

8279 

.918 

8279 

8281 

8283 

8285 

8287 

8289 

8291 

8293 

8295 

8297 

8299 

.919 

8299 

8300 

8302 

8304 

8306 

8308 

8310 

8312 

83H 

8316 

8318 

.920 

8318 

8320 

8321 

8323 

8325 

8327 

8329 

8331 

8333 

8335 

8337 

.921 

8337 

8339 

8341 

8343 

8344 

8346 

8348 

8350 

8352 

8354 

8356 

.922 

8356 

8358 

8360 

8362 

8364 

8366 

8368 

8370 

8371 

8373 

8375 

•923 

8375 

8377 

8379 

8381 

8383 

8385 

8387 

8389 

8391 

8393 

8395 

.924 

8395 

8397 

8398 

8400 

8402 

8404 

8406 

8408 

8410 

8412 

8414 

.925 

8414 

8416 

8418 

8420 

8422 

8424 

8426 

8428 

8429 

8431 

8433 

.926 
.927 

8433 
8453 

8435 
8455 

8437 
8457 

8439 
8459 

8441 
8461 

8443 
8463 

8445 
8464 

8447 
8466 

8449 
8468 

8451 
8470 

8453 
8472 

.928 

8472 

8474 

8476 

8478 

8480 

8482 

8484 

8486 

8488 

8490 

8492 

•929 

8492 

8494 

8496 

8498 

8500 

8502 

8504 

8506 

8507 

8509 

8511 

.930 

•93  i 

8511 

8513 
8533 

8515 

8535 

8517 
8537 

8519 
8539 

8521 
8541 

8523 
8543 

8525 
8545 

8527 
8547 

8529 
8549 

8531 

855i 

•932 

8551 

8553 

8555 

8557 

8559 

8561 

8562 

8564 

8566 

8568 

8570 

•933 

8570 

8572 

8574 

8576 

8578 

8580 

8582 

8584 

8586 

8588 

8590 

•934 

8590 

8592 

8594 

8596 

8598 

8600 

8602 

8604 

8606 

8608 

8610 

.935 

8610 

8612 

8614 

8616 

8618 

8620 

8622 

8624 

8626 

8628 

8630 

•936 

8630 

8632 

8634 

8636 

8638 

8640 

8642 

8644 

8646 

8648 

8650 

•937 

8650 

8652 

8654 

8656 

8658 

8660 

8662 

8664 

8666 

8668 

8670 

•938 

8670 

8672 

8674 

8676 

8678 

8680 

8682 

8684 

8686 

8688 

8690 

•939 

8690 

8692 

8694 

8696 

8698 

8700 

8702 

8704 

8706 

8708 

8710 

.940 

8710 

8712 

8714 

8716 

8718 

8720 

8722 

8724 

8726 

8728 

8730 

.941 

8730 

8732 

8734 

8736 

8738 

8740 

8742 

8744 

8746 

8748 

875° 

.942 

8750 

8752 

8754 

8756 

8758 

8760 

8762 

8764 

8766 

8768 

8770 

•943 

8770 

8772 

8774 

8776 

8778 

8780 

8782 

8784 

8786 

8788 

8790 

•944 

8790 

8792 

8794 

8796 

8798 

8800 

8802 

8804 

8806 

8808 

8810 

.945 

8810 

8813 

8815 

8817 

8819 

8821 

8823 

8825 

8827 

8829 

8831 

.946 

8831 

8833 

8835 

8837 

8839 

8841 

8843 

8845 

8847 

8849 

8851 

•947 

8851 

8853 

8855 

8857 

8859 

8861 

8863 

8865 

8867 

8870 

8872 

.948 

8872 

8874 

8876 

8878 

8880 

8882 

8884 

8886 

8888 

8890 

8892 

•949 

8892 

8894 

8896 

8898 

8900 

8902 

8904 

8906 

8908 

8910 

8913 

SMITHSONIAN  TABLES, 


TABLE  1 2  («MtfeimO. 
ANTILOGARITHMS, 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.950 

8913 

8915 

8917 

8919 

8921 

8923 

8925 

8927 

8929 

8931 

8933 

•951 

8933 

8935 

8937 

8939 

8941 

8943 

8945 

8947 

8950 

8952 

8954 

•952 

8954 

8956 

8958 

8960 

8962 

8964 

8966 

8968 

8970 

8972 

8974 

•953 

8974 

8976 

8978 

8980 

8983 

8985 

8987 

8989 

8991 

8993 

8995 

•954 

8995 

8997 

8999 

9001 

9003 

9005 

9007 

9009 

9012 

9014 

9016 

.955 

9016 

9018 

9020 

9022 

9024 

9026 

9028 

9030 

9032 

9034 

9036 

.956 

9036 

9039 

9041 

9043 

9°45 

9047 

9049 

9051 

9053 

9055 

9057 

•957 

9057 

9°59 

9061 

9064 

9066 

9068 

9070 

9072 

9074 

9076 

9078 

•958 

9078 

9080 

9082 

9084 

9087 

9089 

9091 

9093 

9095 

9097 

9099 

•959 

9099 

9101 

9103 

9^5 

9108 

9110 

9112 

9114 

9116 

9118 

9120 

.960 

9120 

9122 

9124 

9126 

9129 

9131 

9133 

9J35 

9T37 

9139 

9141 

.961 

9141 

9H3 

9M5 

9M7 

9150 

9152 

9J54 

9158 

9160 

9162 

.962 

9162 

9164 

9166 

9169 

9171 

9J73 

9175 

9177 

9179 

9181 

9183 

•963 

9^3 

9185 

9188 

9190 

9192 

9194 

9196 

9198 

9200 

9202 

9204 

.964 

9204 

9207 

9209 

9211 

9213 

9215 

9217 

9219 

9221 

9224 

9226 

.965 

9226 

9228 

9230 

9232 

9234 

9236 

9238 

9241 

9243 

9245 

9247 

.966 

9247 

9249 

9251 

9253 

9256 

9258 

9260 

9262 

9264 

9266 

9268 

.967 

9268 

9270 

9273 

9275 

9277 

9279 

9281 

9283 

9285 

9288 

9290 

.968 

9290 

9292 

9294 

9296 

9298 

9300 

93°3 

9305 

93°7 

9309 

93" 

.969 

9311 

9315 

93^8 

9320 

9322 

9324 

9326 

9328 

933° 

9333 

,970 

9333 

9335 

9337 

9339 

934i 

9343 

9345 

9348 

9350 

9352 

9354 

•97  i 

9354 

9356 

9358 

9361 

9363 

9365 

9367 

9369 

937i 

9373 

9376 

.972 

9376 

9378 

9382 

9384 

9386 

9389 

939  i 

9393 

9395 

9397 

•973 

9397 

9399 

9402 

9404 

9406 

9408 

9410 

9412 

9415 

9417 

9419 

•974 

9419 

942i 

9423 

9425 

9428 

943° 

9432 

9434 

9436 

9438 

9441 

.975 

9441 

9443 

9445 

9447 

9449 

945  i 

9454 

9456 

9458 

9460 

9462 

.976 

9462 

9465 

9467 

9469 

947i 

9473 

9475 

9478 

9480 

9482 

9484 

•977 

9484 

9486 

9489 

949  i 

9493 

9495 

9497 

9499 

9502 

9504 

9506 

.978 

9506 

9508 

95*3 

95^7 

9519 

9521 

9524 

9526 

9528 

•979 

9528 

9530 

9532 

9535 

9537 

9539 

954i 

9543 

9546 

9548 

9550 

980 

955° 

9552 

9554 

9557 

9559 

956r 

9563 

9565 

9568 

9570 

9572 

.981 

9572 

9574 

9576 

9579 

9581 

9583 

9585 

9587 

9590 

9592 

9594 

.982 
•983 

9594 
9616 

9618 

9621 

9601 
9623 

9603 
9625 

9627 

9607 
9629 

96? 

9612 
9634 

9614 
9636 

9616 
9638 

•984 

9638 

9641 

9643 

9645 

9647 

9649 

9652 

9654 

9656 

9658 

9661 

.985 

9661 

9663 

9665 

9667 

9669 

9672 

9674 

9676 

9678 

9681 

9683 

.986 

9683 

9685 

9687 

9689 

9692 

9694 

9696 

9698 

9701 

9703 

9705 

.987 

9705 

9707 

9710 

9712 

97H 

9716 

9719 

9721 

9723 

9725 

9727 

.988 

9727 

973° 

9732 

9734 

97  36 

9739 

974i 

9743 

9745 

9748 

975° 

.989 

975° 

9752 

9754 

9757 

9759 

9761 

9763 

9766 

9768 

9770 

9772 

.990 

9772 

9775 

9777 

9779 

9781 

9784 

9786 

9788 

9790 

9793 

9795 

.991 
.992 
•993 
•994 

9795 
9817 
9840 
9863 

9797 
9820 
9842 
9865 

9799 
9822 

9845 
9867 

9802 
9824 

9847 
9870 

9804 
9827 
9849 
9872 

9806 
9829 
9851 
9874 

9808 
983' 
9854 
9876 

9811 

9833 
9856 

9879 

9813 

9858 
9881 

9815 
9838 
9861 

9883 

9817 
9840 
9863 
9886 

.995 

9886 

9888 

9890 

9892 

9895 

9897 

9899 

9901 

9904 

9906 

9908 

.996 

9908 

9911 

99'3 

99T5 

9917 

9920 

9922 

9924 

9927 

9929 

993  J 

•997 

993  r 

9933 

9936 

9938 

9940 

9943 

9945 

9947 

9949 

9952 

9954 

•998 

9954 

99  56 

9959 

9963 

9966 

9968 

9970 

9972 

9975 

9977 

•999 

9977 

9979 

9984 

9986 

9988 

999  i 

9993 

9995 

9998 

oooo 

SMITHSONIAN  TABLES. 


TABLE  13. 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 

(Taken  from  B.  O.  Peirce's  "  Short  Table  of  Integrals,"  Ginn  &  Co.) 


^C/j 

«i 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

SH 

0 

Nat.    Log. 

Nat.    Log. 

Nat.    Log. 

Nat.      Log. 

o.oooo 

o°oo' 

.0000    00 

I.OOOO  O.OOOO 

.0000    oo 

00        00 

9o°oo' 

1.5708 

0.0029 

10 

.0029  7.4637 

I.OOOO   .OOOO 

.0029  7.4637 

343-77   2.5363 

50 

I-5679 

0.0058 

20 

.0058   .7648 

I.OOOO   .0000 

.0058   .7648 

171.89    .2352 

40 

I-5650 

0.0087 

30 

.0087   .9408 

I.OOOO   .0000 

.0087   .9409 

114.59    .0591 

30 

1.5621 

0.0116 

40 

.0116  8.0658 

.9999  .0000 

.0116  8.0658 

85.940  1.9342 

20 

L5592 

0.0145 

5° 

.0145   .1627 

.9999  .0000 

.0145   .1627 

68.750   -8373 

IO 

0.0175 

I°00' 

.0175  8.2419 

.9998  9-9999 

.0175  8.2419 

57.290  1.7581 

89°oo' 

I-5S33 

0.0204 

10 

.0204   .3088 

•9998  -9999 

.0204   .3089 

49.104   .6911 

50 

1-5504 

0.0233 

20 

.0233   .3668 

•9997  -9999 

•0233   -3669 

42.964   .6331 

40 

J-5475 

0.0262 

3° 

.0262   .4179 

•9997   -9999 

.0262   .4181 

38.188   .5819 

30 

1.5446 

0.0291 

40 

.0291   .4637 

.9996  .9998 

.0291   .4638 

34-368   .5362 

20 

I-54I7 

0.0320 

5° 

.0320   .5050 

•9995  -9998 

•0320   .5053 

31.242   .4947 

IO 

1.5388 

0.0349 

2°00/ 

.0349  8.542*8 

•9994  9-9997 

•0349  8.5431 

28.636  1.4569 

88°oo' 

'•5359 

0.0378 

10 

•0378   .5776 

•9993  -9997 

•0378   .5779 

26.432   .4221 

50 

1-5330 

0.0407 

20 

.0407   .6097 

.9992  .9996 

.0407   .6lOI 

24.542   .3899 

40 

0.0436 
0.0465 

30 
40 

.0436   .6397 
.0465   .6677 

.9990  -9996 
.9989  .9995 

.0437   .6401 
.0466   .6682 

22.904   -3599 
21.470   .3318 

30 

20 

1.5272 
1.5243 

0.0495 

50 

.0494   .6940 

.9988  .9995 

•0495   .6945 

20.206   -3055 

IO 

J-52I3 

0.0524 

3°oo' 

.0523  8.7188 

.9986  9.9994 

.0524  8.7194 

19.081  1.2806 

87°oo' 

1.5184 

0-0553 

10 

.0552   .7423 

•9985  -9993 

•°553   7429 

18.075   -2571 

5° 

1.5155 

0.0582 

20 

.0581   .7645 

.9983  .9993 

.0582   .7652 

17.169   .2348 

40 

1.5126 

0.06  1  1 

30 

.O6l0   .7857 

.9981   .9992 

.0612   .7865 

16.350   .2135 

3° 

I-5097 

0.0640 

40 

.0640   .8059 

.9980  .9991 

.0641   .8067 

15.605   .1933 

20 

1.5068 

0.0669 

50 

.0669   .8251 

•9978  .9990 

.0670   .8261 

14.924   .1739 

10 

I-5039 

0.0698 

4°oo' 

.0698  8.8436 

•9976  9-9989 

.0699  8.8446 

14-301   I.I554 

86°oo' 

1.5010 

0.0727 

IO 

.0727   .8613 

•9974  -9989 

.0729   .8624 

J3-727   -1376 

5° 

1.4981  1 

0.0756 

20 

.0756   .8783 

.997  1   .9988 

.0758   .8795 

13.197   .1205 

40 

1.4952 

0.0785 

30 

.0785   .8946 

.9969  .9987 

.0787   .8960 

12.706   .1040 

3° 

1.4923 

0.0814 

40 

.0814   .9104 

.9967   .9986 

.0816   .9118 

12.251   .0882 

20 

1.4893 

0.0844 

50 

.0843   .9256 

.9964  .9985 

.0846   .9272 

11.826   .0728 

10 

1.4864 

0.0873 

5°oo' 

•0872  8.9403 

.9962  9.9983 

.0875  8.9420 

11.430  1.0580 

85°oo' 

1-4835 

0.0902 

IO 

.0901   .9545 

•9959  -9982 

.0904   .9563 

11.059   .0437 

5° 

1.4806 

0.0931 

20 

•0929   .9682 

•9957  -9981 

•°934   -9701 

10.712   .0299 

40 

1-4777 

0.0960 
0.0989 

30 
40 

•0958   .9816 
•0987   -9945 

•9954  -9980 
•995  i  -9979 

.0963   .9836 
.0992   .9966 

10.385   .0164 
10.078   .0034 

30 

20 

1.4748 
1.4719 

0.1018 

50 

.1016  9.0070 

.9948  .9977 

.IO22  9.0093 

9.7882  0.9907 

IO 

1.4690 

0.1047 
0.1076 

6°oo 

IO 

.1045  9.0192 
.1074   .0311 

•9945  9-9976 
•9942  .9975 

.1051  9.0216 
.1080   .0336 

9.5144  0.9784 
9.2553  .9664 

84°oo' 
50 

1.4661 
1.4632 

0.1105 

20 

.1103   .0426 

•9939  -9973 

.mo  .045  3 

9.0098  .9547 

40 

1.4603 

0.1134 

30 

.1132   .0539 

.9936  .9972 

•IJ39  -0567 

8.7769  .9433 

3° 

1-4574 

0.1164 

40 

.Il6l   .0648 

.9932  .9971 

.1169  .0678 

8-5555  -9322 

20 

•4544 

0.1193 

50 

•U9Q  .0755 

•9929  -9969 

.1198  .0786 

8.3450  .9214 

10 

4515 

0.1222 

7°oo' 

.1219  9.0859 

.9925  9.9968 

.1228  9.0891 

8.1443  0.9109 

83°oo' 

.4486 

O.I25I 
0.1280 

IO 
20 

.1248  .0961 
.1276  .1060 

.9922   .9966 
.9918  .9964 

.i2«  .0995 
.1287  .1096 

7.9530  .9005 
7.7704  .8904 

50 
40 

•4457 
.4428 

o.  1  309 

30 

•'305  -"57 

•99  i  4  -9963 

.1317  .1194 

7.59.58  .8806 

30 

-4399 

0.1338 

40 

.1334  .1252 

.9911   .9961 

.1346  .1291 

7.4287  .8709 

20 

•4370 

0.1367 

50 

.1363  .1345 

•9907   -9959 

•1376  .1385 

7.2687  .8615 

IO 

•4341 

0.1396 

8°oo' 

.1392  9-1436 

.9903  9.9958 

.1405  9.1478 

7.1154  0.8522 

82°00' 

•4312 

0.1425 

10 

.1421  .1525 

.9899  .9956 

•1435  •I569 

6.9682  .8431 

50 

•4283 

0.1454 

20 

.1449  .1612 

.9894  .9954 

.1465  .1658 

6.8269  .8342 

40 

•4254 

0.1484 

30 

.1478  .1697 

.9890  .9952 

.1495  -£745 

6.6912  .8255 

30 

.4224 

o^S^ 

40 

.1507  .1781 

.9886  .9950 

.1524  .1831 

6.5606  .8169 

20 

•4195 

0.1542 

50 

•1536  .1863 

.9881   .9948 

•1554  -WS 

6.4348  .8085 

10 

.4166 

0.1571 

9°oo' 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997 

6.3138  0.8003 

8i°oo' 

I.4I37 

Nat.   Log. 

Nat.    Log. 

Nat.    Log. 

Nat.      Log. 

IM 

J.  . 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

Wy 

Qctf 

O 

x< 

SMITHSONIAN  TABLES. 


TABLE    13   (continued). 

CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


33 


& 

(A 

& 

SINES. 

COSINES: 

TANGENTS. 

COTANGENTS. 

x< 

^te 
O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.1571 

9°oo/ 

.1564  9.1943 

.9877  9.9946 

.1584  9.1997 

6.3138  0.8003 

$I°00' 

I4I37 

o.i  600 

10 

.1593   .2022 

.9872  .9944 

.1614   .2078 

6.1970   .7922 

5° 

1.4108 

0.1629 

20 

.1622   .2IOO 

.9868  .9942 

.1644   .2158 

6.0844   .7842 

40 

1.4079 

0.1658 

3° 

.1650   .2176 

.9863  .9940 

.1673   .2236 

5.9758   .7764 

3° 

1.4050 

0.1687 

40 

.1679   -2251 

.9858  .9938 

.1703   .2313 

5.8708   .7687 

2O 

1.4021 

0.1716 

50 

.1708   .2324 

•9853  -9936 

•1733   -2389 

5.7694   .7611 

10 

1.3992 

0.1745 

io°oo' 

•*736  9-2397 

.9848  9.9934 

.1763  9.2463 

5-6713  0-7537 

8o°oo' 

I-3963 

0.1774 

IO 

.1765   .2468 

•9843  -993  * 

•!793  -2536 

5.5764  .7464 

5° 

T-3934 

0.1804 

20 

.1794   .2538 

.9838  .9929 

.1823  .2609 

5.4845  .7391 

40 

1.3904 

0-1833 

30 

.1822   .2606 

•9833  -9927 

.1853  .2680 

5-3955  -7320 

30 

L3875 

0.1862 

40 

.1851   .2674 

.9827  .9924 

.1883  .2750 

5-3093  -7230 

20 

1.3846 

0.1891 

50 

.1880   .2740 

.9822  .9922 

.1914  .  .2819 

5.2257  .7181 

10 

1.3817 

0.1920 

II°00' 

.1908  9.2806 

.9816  9.9919 

.1944  9.2887 

5.1446  0.7113 

79°oo' 

1.3788 

0.1949 

IO 

.1937   .2870 

.9811   .9917 

•1974  .2953 

5.0658  .7047 

50 

J-3759 

0.1978 

20 

.1965   -2934 

.9805  .9914 

.2004  .3020  4.9894  .6980 

40 

1-3730 

0.2007 

3° 

.1994   .2997 

•9799  -99  J  2 

.2035  .3085  4.9  1  52  .6915 

30 

1.3701 

0.2036 

40 

.2022   .3058 

•9793  -9909 

.2065  .3149 

4.8430  .6851 

20 

1.3672 

0.2065 

50 

.2O5I    .3H9 

.9787  .9907 

.2095  .3212 

4.7729  .6788 

IO 

1-3643 

0.2094 

I2°00' 

.2079  9.3179 

.9781  9.9904 

.2126  9.3275 

4.7046  0.6725 

78°oo' 

1.3614 

0.2123 

10 

.2108   .3238 

•9775  -9901 

.2156  .3336 

4.6382  .6664 

50 

1.3584 

0.2153 

20 

.2136   .3296 

.9769  .9899 

•2186  .3397 

4.5736  .6603 

40 

1-3555 

0.2182 

3° 

•2164   .3353 

.9763  .9896 

•2217  .3458 

4.5107  .6542 

30 

i.3526 

O.22II 

40 

.2193   .3410 

•9757   -9893 

•2247  -3517 

4.4494  .6483 

20 

1-3497 

O.224O 

50 

.2221    .3466 

.9750  .9890 

.2278  .3576 

4.3897  .6424 

10 

1.3468 

0.2269 

i3°oo' 

.2250  9.3521 

.9744  9.9887 

.2309  9.3634 

4.3315  0.6366 

77°oo' 

1-3439 

0.2298 

IO 

•2278   .3575 

•9737   -9884 

•2339  -3691 

4.2747  .6309 

50 

1.3410 

0.2327 

20 

.2306   .3629 

.9730  .9881 

.2370  .3748 

4.2193  .6252 

40 

i.338i 

0.2356 
0-2385 

30 
40 

.2334   .3682 

•2363  -3734 

.9724  .9878 
•9717   -9875 

.2401   .3804 
•2432  -3859 

4.1653  .6196 
4.1126  .6141 

30 

20 

1-3352 
I-3323 

0.2414 

50 

-.2391   .3786 

.9710  .9872 

.2462  .3914 

4.0611  .6086 

10 

1-3294 

0.2443 
0.2473 

i4°oo' 

IO 

•2419  9-3837 
.2447   .3887 

•9703  9-9869 
.9696  .9866 

•2493  9-3968 
.2524  .4021 

4.0108  0.6032 
3.9617  .5979 

76°oo' 
50 

1-3265 
L3235 

0.2502 
0.2531 

20 

30 

•2476  -3937 
.2504  .3986 

.9689   .9863 
.9681   .9859 

.2555  .4074 

3.9136  .5926 
3.8667  .5873 

40 
30 

1.3206 
i.3i77 

0.2560 

40 

•2532  4035 

.9674   .9856 

.2617  .4178 

3.8208  .5822 

20 

1.3148 

0.2589 

50 

.2560  .4083 

.9667   .9853 

.2648  .4230 

3.7760  .5770 

10 

1.3119 

0.26l8 

1  5°oo' 

.2588  9.4130 

.9659  9.9849 

.2679  9.4281 

3-7321  0.5719 

75°oo' 

1.3090 

0.2647 

IO 

.2616  .4177 

.9652   .9846 

•2711   -433  * 

3.6891  .5669 

50 

1.3061 

0.2676 

20 

.2644  .4223 

.9644  .9843 

.2742  .4381 

3.6470  .5619 

40 

1-3032 

0.2705 

3° 

.2672  .4269 

.9636  .9839 

•2773  -443° 

3-6059  -5570 

30 

1-3003 

0.2734 

40 

.2700  .4314 

.9628  .9836 

.2805  .4479 

3.5656  .5521 

20 

1.2974 

0.2763 

50 

.2728  .4359 

.9621   .9832 

.2836  .4527 

3.5261  .5473 

10 

1.2945 

0.2793 

i6°oo' 

.2756  9.4403 

.9613  9.9828 

.2867  9-4575 

3.4874  0.5423 

74°oo' 

1.2915 

0.2822 

IO 

.2784  .4447 

.9605  .9825 

•2899  -4622 

3-4495  -5378 

5° 

O  - 

0.2851 

20 

.2812  .4491 

.9596  .9821 

.2931   .4669 

3.4124  .5331 

40 

1<2s5£ 

0.2880 

3° 

.2840  .4533 

.9588  .9817 

.2962  .4716 

3-3759  -5284 

30 

1.2828 

0.2909 

40 

.2868  .4576 

.9580  .9814 

.2994  .4762 

3.3402  .5238 

20 

1.2799 

0.2938 

5° 

.2896  .4618 

•9572  -9810 

.3026  .4808 

3.3052  .5192 

10 

1.2770 

0.2967 

i7°oo' 

.2924  9.4659 

.9563  9.9806 

-3°57  94853 

3.2709  0.5147 

73°oo, 

1.2741 

0.2906 

10 

.2952  .4700 

•9555  -9802 

.3089  .4898 

3.2371   .5102 

5° 

1.2712 

0.3025 

0-30^4 
0.3083 

0.3H3 

20 

3° 
40 

5° 

.2979  .4741 
.3007   .4781 
.3035  .4821 
.3062  .4861 

.9546  .9798 
•9537  -9794 
.9528  .9790 
.9520  .9786 

.3121   .4943 
•3J53  4987 
•3185  -5031 
.3217  .5075 

3.2041   .5057 
3.1716  .5013 
3.1397  .4969 
3.1084  -4925 

40 
30 

20 
10 

1.2683 

1.2654 

1.2625 

1-2595 

0.3142 

i8°oo' 

.3090  9.4900 

.9511  9.9782 

•3249  9-5"8 

3.0777  0.4882 

72°00' 

1.2566 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

t/5 

AH 

1 

Q£ 

COSINES 

SINES. 

COTAN- 
GENTS. 

TANGENTS 

W^ 
Qtf 
O 

S< 

SMITHSONIAN  TABLES. 


34 


TABLE   1  3  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS, 


§* 

$ 

gw 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS 

x< 

&& 
O 

Nat.    Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.3142 

i8°oo' 

.3090  9.4900 

.9511  9.9782 

.3249  9.5118 

3.0777  0.4882 

72°00' 

.2566 

0.3171 

10 

.3118   .4939 

•95°2   .9778 

.3281   .5161 

3.0475   .4839 

50 

•2537 

0.3200 

20 

.3145   .4977 

.9492   .9774 

.3314   .5203 

3.0178   .4797 

40 

.2508 

0.3229 

3° 

•3  '73  -5015 

.9483   .9770 

.3346   .5245 

2.9887   .4755 

3° 

.2479 

0.3258 
0.3287 

40 
50 

.3201   .5052 
.3228  .5090 

.9474   .9765 
.9465   .9761 

•3378   .5287 
•3411   .5329 

2.9600   .4713 
2.9319   .4671 

20 
10 

•2450 
.2421 

0.3316 

i9°oo' 

.3256  9.5126 

•9455  9-9757 

•3443  9-5370 

2.9042  0.4630 

7i°oo' 

.2392 

0-3345 

10 

.3283  .5163 

•9446  .9752 

.3476  -54" 

2.8770   .4589 

5° 

•2363 

0-3374 

20 

•33"   .5'99 

.9436  .9748 

•3508  .5451 

2.8502   .4549 

40 

•2334 

0.3403 

3° 

•3338  .5235 

.9426  .9743 

•3541   -549I 

2.8239   .4509 

30 

•2305 

0-3432 

40 

.3365  .5270 

•9417  -9739 

•3574  -5531 

2.7980   .4469 

20 

0.3462 

50 

•3393  -5306 

.9407  -9734 

•3607  -557I 

2.7725   .4429 

10 

.2246 

0.3491 

20°00' 

.3420  9.5341 

•9397  9-9730 

.3640  9.5611 

2.7475  0.4389 

70°oo' 

.2217 

0.3520 

10 

•3448  -5375 

•9387  -9725 

•3673  -5650 

2.7228   .4350 

50 

.2188 

0-3549 

20 

•3475  -5409 

•9377  -9721 

.3706  .5689 

2.6985   .4311 

40 

.2159 

0.3578 

3° 

.3502  -5443 

•9367  -9716 

•3739  -5727 

2.6746   .4273 

30 

.2130 

0.3607 

40 

•3529  -5477 

•9356  -97" 

.3772  .5766 

2.6511   .4234 

20 

.2IOI 

0.3636 

50 

•3557  -55*0 

.9346  .9706 

.3805  .5804 

2.6279   .4196 

10 

.2072 

0.3665 

2I°00' 

•3584  9-5543 

.9336  9.9702 

•3839  9-5842 

2.6051  0.4158 

69°oo' 

.2043 

0.3694 

IO 

•36n   .5576 

•9325  -9697 

.3872  .5879 

2.5826   .4121 

50 

.2014 

0-3723 

20 

.3638  .5609 

.9315  .9692 

•39o6  .5917 

2.5605   .4083 

40 

.1985 

0.3752 

30 

.3665  .5641 

.9304  .9687 

•3939  -5954 

2.5386   .4046 

3° 

.1956 

0.3782 

40 

.3692  .5673 

.9293  .9682 

•3973  -599' 

2.5172   .4009 

20 

.1926 

0.3811 

50 

•37  19  -5704 

.9283  .9677 

.4006  .6028 

2.4960   .3972 

10 

.1897 

0.3840 

22°00' 

•3746  9-5736 

.9272  9.9672 

.4040  9.6064 

2.4751  0.3936 

68°oo' 

.1868 

0.3869 

IO 

•3773  -5767 

.9261   .9667 

.4074  .6100 

2-4545   -3900 

5° 

.1839 

0.3898 

2O 

.3800  .5798 

.9250  .9661 

.4108  .6136 

2.4342   .3864 

40 

.l8lO 

0.3927 

3° 

.3827   .5828 

.9239  .9656 

.4142  .6172 

2.4142   .3828 

3° 

.1781 

0-3956 

40 

•3854  -5859 

.9228  .9651 

.4176  .6208 

2-3945  -3792 

20 

•1752 

0-39^5 

50 

.3881   .5889 

.9216  .9646 

.4210  .6243 

2.3750  -3757 

10 

.1723 

0.4014 

23°00' 

•3907  9-59I9 

.9205  9.9640 

.4245  9.6279 

2-3559  0.3721 

67°oo' 

.1694 

0.4043 
0.4072 

10 

20 

•3934  -5948 
.3961   .5978 

•9194  -9635 
.9182  .9629 

.4279  .6314 
.4314  .6348 

2.3369  .3686 
2-3I83  .3652 

50 
40 

.1665 
.1636 

0.4102 

3° 

.3987  .6007 

.9171   .9624 

•4348  .6383 

2.2998  .3617 

3° 

.1606 

0.4131 

40 

.4014  .6036 

.9159  .9618 

.4383  .6417 

2.2817   .3583 

20 

•1577 

0.4160 

50 

.4041   .6065 

.9147   .9613 

.4417   .6452 

2.2637   .3548 

IO 

.1548 

0.4189 

24°OO' 

.4067  9.6093 

.9135  9.9607 

.4452  9.6486 

2.2460  0.3514 

66°oo' 

-1S*9 

0.4218 

10 

.4094  .6121 

.9124  .9602 

.4487   .6520 

2.2286  .3480 

5° 

.1490 

0.4247 

20 

.4120  .6149 

.9112  .9596 

•4522  .6553 

2.2113  -3447 

40 

.1461 

0.4276 

30 

.4147  .6177 

.9100  .9590 

4557  -6587 

2.1943  .3413 

3° 

.1432 

04305 

40 

.4173  .6205 

.9088  .9584 

.4592  .6620 

2-1775  -3380 

20 

1403 

0.4334 

50 

.4200  .6232 

•9°75  -9579 

.4628  .6654 

2.1609  .3346 

IO 

•1374 

o.4363 

25°OO' 

.4226  9.6259 

•9063  9-9573 

.4663  9.6687 

2.1445  0.3313 

65°oo' 

•1345 

0.4392 

10 

.4253  .6286 

.9051   .9567 

.4699  .6720 

2.1283  .3280 

5° 

1316 

0.4422 

20 

.4279  .6313 

.9038  .9561 

•4734  -6752 

2.1123  .3248 

40 

1286 

0.4451 

30 

.4305  .6340 

•9026  .9555 

.4770  .6785 

2.0965  .3215 

3° 

•1257 

0.4480 

40 

.433  i   .6366 

.9013  .9549 

.4806  .6817 

2.0809  -3  T  83 

20 

1228 

0.4509 

50 

4358  .6392 

.9001  .9543 

.4841   .6850 

2-0655  .3150 

IO 

1199 

0.4538 

26°00/ 

.4384  9.6418 

•8988  9-9537 

.4877  9.6882 

2.0503  0.3118 

64°oo' 

1170 

0.4567 

IO 

.4410  .6444 

•8975  -9530 

.4913  .6914 

2-0353  -3086 

50 

1141 

0-4596 

20 

.4436  .6470 

.8962  .9524 

.4950  .6946 

2.0204  .3054 

40 

III2 

0.4625 

30 

.4462  .6495 

.8949  .9518 

.4986  .6977 

2.0057  .3023 

30 

1083 

0.4654 

40 

.4488  .6521 

.8936  .9512 

.5022  .7009 

1.9912  .2991 

20 

1054 

0.4683 

5° 

-45H  -6546 

•8923  .9505 

•5°59  -7040 

1.9768  .2960 

IO 

I025 

0.4712 

27°00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072 

1.9626  0.2928 

63°oo' 

1.0996 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

c/i 

r'iW 

n^ 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

WM 

Q* 

o 

P 

SMITHSONIAN  TABLES. 


TABLE  1  3  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


35 


¥ 

w 

wg 

O  j 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

*< 

Q& 

O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.4712 

27°00' 

.4540  9.6570 

.8910  9.9499 

.5095  9.7072 

1.9626  0.2928 

63°oo' 

1.0996 

0.4741 
0.4771 

IO 

2O 

.4566   .6595 
.4592   .6620 

.8897   .9492 
.8884   .9486 

•5I32  .7103 
•5l69  -7134 

1.9486   .2897 
1.9347   .2866 

50 
40 

1.0966 
1.0937 

0.4800 

3° 

.4617   .6644 

•8870   .9479 

.5206  .7165 

1.9210   .2835 

3° 

1.0908 

0.4829 

40 

.4643  .6668 

•8857   .9473 

.5243  .7196 

1.9074   .2804 

20 

1.0879 

0.4858 

5° 

.4669  .6692 

.8843   -9466 

.5280  .7226 

1.8940   .2774 

10 

1.0850 

0.4887 

2S°00' 

.4695  9.6716 

.8829  9.9459 

•53!7  9-7257 

1.8807  0.2743 

62°00' 

I.082I 

0.4916 

10 

.4720  .6740 

.8816   .9453 

•5354  -7287 

1.8676   .2713 

5° 

1.0792 

0.4945 

20 

.4746  .6763 

.8802   .9446 

•5392  -73*7 

1.8546   .2683 

40 

1.0763 

0.4974 

3° 

.4772   .6787 

.8788   -9439 

.5430  .7348 

1.8418   .2652 

3° 

I-°734 

0.5003 

40 

.4797   .6810 

.8774   .9432 

-5467  .7378 

1.8291   .2622 

20 

1.0705 

0.5032 

50 

.4823  .6833 

.8760   .9425 

•5505  -74o8 

1.8165   .2592 

10 

1.0676 

0.5061 

29°00' 

.4848  9.6856 

.8746  9.9418 

•5543  97438 

1.8040  0.2562 

6i°oo' 

1.0647 

0.5091 

10 

.4874  -6878 

.8732   .9411 

.5581   .7467 

I-79I7   -2533 

5° 

1.0617 

0.5120 

20 

.4899  .6901 

.8718   .9404 

.5619  .7497 

1.7796  .2503 

40 

1.0588 

0.5149 

3° 

.4924  .6923 

.8704   .9397 

•5658  .7526 

1.7675  .2474 

30 

I-°559 

0.5178 

40 

.4950  .6946 

.8689   .9390 

.5696  .7556 

1.7556  .2444 

20 

I-053Q 

0.5207 

50 

•4975  -6968 

•8675   -9383 

•5735  -7585 

1.7437  .2415 

10 

1.0501 

0.5236 

0.5265 

3o°oo' 

IO 

.5000  9-6990 
.5025  .7012 

•8660  9.9375 
.8646   .9368 

•5774  9-76i4 
.5812  .7644 

1.7321  0.2386 
1.7205  .2356 

6o°oo' 
5° 

1.0472 
1.0443 

0.5294 

20 

•5050  -7033 

.8631   .9361 

•5851   -7673 

1.7090  .2327 

40 

1.0414 

0.5323 

30 

•5°75  -7055 

.8616   .9353 

.5890  .7701 

1.6977  -2299 

30 

1.0385 

0.5352 

40 

.5100  .7076 

.8601   .9346 

•593°  -7730 

1.6864  .2270 

20 

1-0356 

0-5381 

50 

•5I25  -7097 

•8587   .9338 

•5969  -7759 

1.6753  -2241 

10 

1.0327 

0.5411 

3i°oo' 

.5150  9.7118 

•8572  9-9331 

.6009  9.7788 

1.6643  0.2212 

59°oo' 

1.0297 

0.5440 

IO 

•5!75  -7139 

•8557  -9323 

.6048  .7816 

1.6534   .2184 

50 

1.0268 

0.5469 

20 

.5200  .7160 

.8542  .9315 

.6088  .7845 

1.6426   .2155 

40 

1.0239 

0.5498 

3° 

•5225  -7181 

.8526  .9308 

.6128  .7873 

1.6319   .2127 

30 

I.O2IO 

0-5527 

40 

.5250  .7201 

.8511  .9300 

.6168  .7902 

I.62I2   .2098 

20 

1.0181 

0.5556 

5° 

.5275  .7222 

.8496  .9292 

.6208  .7930 

I.6lO7   .2O7O 

IO 

1.0152 

0-5585 

32°00' 

.5299  9.7242 

.8480  9.9284 

•6249  9-7958 

1.6003  0.2042 

58°oo' 

1.0123 

0.5614 

10 

.5324  .7262 

.8465  .9276 

.6289  .7986 

1.5900   .2014 

5° 

1.0094 

0-5643 

20 

.5348  .7282 

.8450  .9268 

.6330  .8014 

1.5798   .1986 

40 

1.0065 

0.5672 

3° 

•5373  -7302 

.8434  .9260 

.637  1   .8042 

1.5697   .1958 

30 

1.0036 

0.570.1 

40 

.5398  .7322 

.8418  .9252 

.6412  .8070 

*-5597  -193° 

20 

1  .0007 

o.573o 

5° 

.5422  .7342 

.8403  .9244 

.6453  .8097 

1.5497  .1903 

IO 

0.9977 

0.5760 

33000' 

.5446  9.7361 

•8387  9-9236 

.6494  9.8125 

1.5399  0.1875 

57°oo' 

0.9948 

0.5789 

10 

•5471   -7380 

.8371   .9228 

•6536  -8153 

1.5301   .1847 

50 

0.9919 

0.5818 

20 

.5495  .7400 

•8355  -9219 

.6577  .8180 

1.5204  .1820 

40 

0.9890 

0.5847 

3° 

•55r9  .7419 

.8339  .9211 

.6619  .8208 

1.5108  .1792 

30 

0.9861 

0.5876 

40 

.5544  .7438 

.8323  .9203 

.6661   .8235 

1.5013  .1765 

20 

0.9832 

0-5905 

50 

.5568  .7457 

.8307  .9194 

.6703  .8263 

1.4919  .1737 

10 

0.9803 

0-5934 

34°oo' 

.5592  9-7476 

.8290  9.9186 

.6745  9.8290 

1.4826  0.1710 

56°oo' 

0-9774 

0-5963 

IO 

.5616  .7494 

.8274  .9177 

.6787  .8317 

1.4733  .1683 

5° 

0.9745 

0.5992 

20 

.5640  .7513 

.8258  .9169 

.6830  .8344 

1.4641  .1656 

40 

0.9716 

0.602  1 
0.6050 

30 
40 

.5664  .7531 
.5688  .7550 

.8241   .9160 
.8225  .9151 

•6873  -8371 
.6916  .8398 

1.4550  .1629 
1.4460  .1602 

3° 
20 

0.9687 
0.9657 

0.6080 

5° 

.5712  .7568 

.8208  .9142 

.6959  .8425 

1-4370  .1575 

10 

0.9628 

0.6109 

35°oo' 

•5736  9-7586 

.8192  9.9134 

.7002  9.8452 

1.4281  0.1548 

550oo' 

0.9599 

0.6138 
0.6167 

IO 

20 

.5760  .7604 
.5783  .7622 

•8175  -9125 
.8158  .9116 

.7046  .8479 
.7089  .8506 

1.4193  .1521 
1.4106  .1494 

50 
40 

0.9570 
0.9541 

0.6196 

3° 

.5807  .7640 

.8141  .9107 

.7133  -8533 

1.4019  .1467 

3° 

0.9512 

0.6225 

40 

•5831  -7657 

.8124  .9098 

•7i77  -8559 

1.3934  .1441 

20 

0.9483 

0.6254 

50 

•5854  .7675 

.8107  .9089 

.7221   .8586 

1.3848  .1414 

IO 

0.9454 

0.6283 

36°oo' 

.5878  9.7692 

.8090  9.9080 

.7265  9.8613 

1.3764  0.1387 

54°oo' 

0.9425 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

J 

i 

Q£ 

COSINES. 

SINES. 

COTAN- 
GENTS. 

TANGENTS. 

W  M 
O« 
O 

<< 

(** 

SMITHSONIAN  TABLES. 


TABLE  1  3  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


I 

c/5 

i  y 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS 

^ 

O 

Nat.   Log. 

Nat.   Log. 

Nat.   Log. 

Nat.    Log. 

0.6283 

36°oo' 

.5878  9.7692 

.8090  9.9080 

.7265  9.8613 

1.3764  0.1387 

54°oo' 

0.9425 

0.6312 

IO 

.5901   .7710 

.8073   -9070 

.7310   .8639 

1.3680   .1361 

5° 

0.9396 

0.6341 

20 

.5925   .7727 

.8056   .9061 

-7355  -8666 

J-3597   -1334 

40 

0.9367 

0.6370 

3° 

.5948   .7744 

.8039   .9052 

.7400  .8692 

1.3514  .1308 

30 

0-9338 

0.6400 

40 

.5972   .7761 

.8021   .9042 

.7445  .8718 

1.3432  .1282 

20 

0.9308 

0.6429 

50 

•5995  7778 

.8004   .9033 

.7490  .8745 

i-335i  -I255 

IO 

0.9279 

0.6458 

37°oo' 

•6018  9.7795 

.7986  9.9023 

•7536  9-877I 

1.3270  0.1229 

53°oo' 

0.9250 

0.6487 

10 

.6041  .7811 

.7969   .9014 

.7581   .8797 

1.3190  .1203 

50 

0.9221 

0.6516 

20 

.6065  .7828 

•795  i   -9004 

.7627   .8824 

1.3111   .1176 

40 

0.9192 

0.6545 

3° 

.6088  .7844 

•7934  -8995 

.7673  -8850 

1.3032  .1150 

30 

0.9163 

0.6574 

0.6603 

40 

.6111  .7861 

.6134  .7877 

.7916  .8985 
.7898  .8975 

.7720  .8876 
.7766  .8902 

1.2954  .1124 
1.2876  .1098 

20 

IO 

0.9134 
0.9105 

0.6632 

38°oo' 

•6157  9-7893 

.7880  9.8965 

.7813  9.8928 

1.2799  0.1072 

52°00' 

0.9076 

0.6661 

10 

.6180  .7910 

.7862  .8955 

.7860  .8954 

1.2723  .1046 

5° 

0.9047 

0.6690 

20 

.6202   .7926 

.7844  .8945 

.7907   .8980 

1.2647  .1020 

40 

0.9018 

0.6720 

3° 

.6225  .7941 

•7826  .8935 

•7954  -9006 

1.2572  .0994 

30 

0.8988 

0.6749 

40 

.6248  .7957 

.7808  .8925 

.8002  .9032 

1.2497  .0968 

20 

0.8959 

0.6778 

5° 

.6271  .7973 

.7790  .8915 

.8050  .9058 

1.2423  .0942 

IO 

0.8930 

0.6807 

39°oo' 

.6293  9.7989 

.7771  9.8905 

.8098  9.9084 

1.2349  0.0916 

5i°oo' 

0.8901 

0.6836 

10 

.6316  .8004 

•7753  -8895 

.8146  .9110 

1.2276  .0890 

5° 

0.8872 

0.6865 

0.6894 

20 
3° 

.6338  .8020 
.6361  .8035 

-7735  -8884 
.7716  .8874 

•8i95  -9135 
.8243  .9161 

1.2203  .0865 
1.2131   .0839 

40 
3° 

0.8843 
0.8814 

0.6923 

40 

.6383  .8050 

.7698  .8864 

.8292  .9187 

1.2059  .0813 

20 

0.8785 

0.6952 

50 

.6406  .8066 

-7679  -8853 

.8342  .9212 

1.1988  .0788 

10 

0.8756 

0.6981 

4o°oo' 

.6428  9.8081 

.7660  9.8843 

•8391  9-9238 

1.1918  0.0762 

5o°oo' 

0.8727 

0.7010 

IO 

.6450  .8096 

.7642  .8832 

.8441   .9264 

1.1847  -0736 

5° 

0.8698 

0.7039 

20 

.6472  .8111 

.7623  .8821 

.8491   .9289 

1.1778  .0711 

40 

0.8668 

0.7069 

30 

.6494  .8125 

.7604  .8810 

•8541   .9315 

1.1708  .0685 

3° 

0.8639 

0.7098 

40 

.6517   .8140 

.7585  .8800 

•8591   -9341 

1.1640  .0659 

20 

0.8610 

0.7127 

50 

•6539  -8155 

.7566  .8789 

.8642  .9366 

1.1571   .0634 

10 

0.8581 

0.7156 

4i°oo' 

.6561  9.8169 

•7547  9-8778 

•8693  9-9392 

1.1504  0.0608 

49°oo' 

0.8552 

0.7185 

IO 

.6583  .8184 

•7528  .8767 

.8744  .9417 

1.1436  .0583 

50 

0.8523 

0.7214 

20 

.6604  .8198 

.7509  .8756 

.8796  .9443 

1.1369  .0557 

40 

0.8494 

0.7243 

30 

.6626  .8213 

.7490  .8745 

.8847   .9468 

1.1303  .0532 

3° 

0.8465 

0.7272 

40 

.6648  .8227 

•7470  .8733 

.8899  .9494 

1.1237  .0506 

20 

0.8436 

0.7301 

50 

.6670  .8241 

-7451   -8722 

•8952  -95*9 

1.1171   .0481 

IO 

0.8407 

0.7330 

42°00' 

.6691  9.8255 

.7431  9.8711 

.9004  9.9544 

1.1106  0.0456 

48°oo' 

0.8378 

0.7359 

IO 

.6713   .8269 

.7412  .8699 

•9057  -9570 

1.1041   .0430 

5° 

0.8348 

0.7389 

20 

.6734  .8283 

.7392  -8688 

.9110  .9595 

1.0977   .0405 

40 

0.8319 

0.7418 

30 

.6756  .8297 

•7373  -8676 

.9163  .9621 

1.0913  .0379 

3° 

0.8290 

0.7447 

40 

.6777  .8311 

•7353  -8665 

.9217   .9646 

1.0850  .0354 

20 

0.8261 

0.7476 

50 

.6799  .8324 

•7333  -8653 

.9271   .9671 

1.0786  .0329 

IO 

0.8232 

0.7505 

43°oo' 

.6820  9.8338 

.7314  9.8641 

•9325  9-9697 

1.0724  0.0303 

47°oo' 

0.8203 

0.7534 

IO 

.6841   .8351 

.7294  .8629 

.9380  .9722 

1.0661   .0278 

50 

0.8174 

0.7563 

20 

.6862  .8365 

.7274  .8618 

•9435  -9747 

1.0599  .0253 

40 

0.8145 

0.7592 

30 

.6884  .8378 

.7254  .8606 

.9490  .9772 

1.0538  .0228 

3° 

0.8116 

0.7621 

40 

.6905  .8391 

.7234  .8594 

•9545  -9798 

1.0477  .0202 

20 

0.8087 

0.7650 

50 

.6926  .8405 

.7214  .8582 

.9601   .9823 

1.0416  .0177 

10 

0.8058 

0.7679 

44°oo' 

•6947  9-8418 

.7193  9.8569 

.9657  9.9848 

1.0355  o-OI52 

46°oo' 

0.8029 

0.7709 

IO 

.6967  .8431 

•7173  -8557 

.97  13  .9874 

1.0295  .0126 

50 

0-7999 

0.7738 

20 

.6988  .8444 

•7153  -8545 

.9770  .9899 

1.0235  .0101 

40 

0.7970 

0.7767 

30 

.7009  .8457 

•7133  -8532 

.9827   .9924 

1.0170  .0076 

30 

0.7941 

0.7796 

40 

.7030  .8469 

.7112  .8520 

.9884  .9949 

1.0117  .0051 

20 

0.7912 

:  0.7825 

50 

.7050  .8482 

.7092  .8507 

.9942  .9975 

1.0058  .0025 

IO 

0.7883 

0.7854 

45°oo' 

.7071  9.8495 

.7071  9.8495 

I  .OOOO  O.OOOO 

1.  0000  0.0000 

45°oo' 

0.7854 

Nat.   Log.  . 

Nat    Log. 

Nat.    Log. 

Nat.    Log. 

en 

i  y. 

-co- 

COSINES. 

SINES. 

COTAN- 
GENTS, 

TANGENTS. 

O 

l< 

SMITHSONIAN  TABLES. 


TABLE  14. 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


37 


RADIANS. 

SINES. 

COSINES. 

TANGENTS 

COTANGENTS. 

DEGREES.  1 

Nat.      Log. 

Nat.     Log. 

Nat.      Log. 

Nat.       Log. 

O.OO 
.01 
.02 

•°3 

.04 

0.00000    —  oo 

.01000  7-99999 
.02000  8.30100 
.03000   .47706 
.03999   .60194 

1.  00000   0.00000 

0-99995  9-99998 
.99980   .99991 
•99955   -99980 
.99920   .99965 

—  oo     —  oo 

o.o  i  ooo  8.00001 

.02000    .30109 

.03001   .47725 

.04002   .60229 

00         OO 

99-997   1-99999 
49-993    -69891 
33-323    -52275 
24.987    .39771 

oo°oo' 

0034 

oi  09 

01  4$ 
02  18 

0.05 
.06 

.09 

0.04998  8.69879 

•05996   -77789 
.06994   .84474 
.07991   .90263 
.08988   .95366 

0.99875  9.99946 
.99820   .99922 

•99755   -99894 
.99680   .99861 

•99595   -99824 

0.05004  8.69933 

.06007   -77867 
.07011   .84581 
.08017   .90402 

.09024  .95542 

19.983   1.30067 
16.647    -22133 
14.262    -15419 
12.473    -09598 
1  1.  08  1    .04458 

02°52' 

03  26 

04  oi 

0435 
0509 

0.10 

.11 

.12 

•13 

.14 

0.09983  8.99928 
.10978  9.04052 
.11971   .07814 
.12963   .11272 
.13954   .I4471 

0.99500  9.99782 
.99396   .99737 
.99281   .99687 
.99156   .99632 
.99022   .99573 

0.10033  9.00145 

.11045   .04315 
.12058   .08127 
.13074   .11640 
.14092   .14898 

9.9666  0.99855 
9.0542   .95685 

8-2933   -91873 
7.6489   .88360 
7.0961   .85102 

05°44' 
06  18 

0653 
07  27 
08  oi 

O.T5 
.16 

•I? 
.18 
.I9 

0.14944  9-17446 
.15932   .20227 
.16918   .22836 
.17903   .25292 
.18886   .27614 

0.98877  9.99510 
.98723   .99442 
.98558   .99369 
.98384   .99293 
.98200   .99211 

0.15114  9.17937 

.16138   .20785 
.17166   .23466 
.18197   .26000 
.19232   .28402 

6.6166  0.82063 
6.1966   .79211; 
5.8256   .76534 
5-4954   .74000 
5-1997   .71598 

o8°36' 
09  10 
0944 
10  19 
J053 

O.2O 
.21 

.22 

•23 
.24 

0.19867  9.29813 
.20846   -31902 
.21823   .33891 
•22798   .35789 
•23770   .37603 

0.98007  9.99126 
.97803   .99035 
•9759°   .98940 
•97367   .98841 
.97134   .98737 

0.20271   9.30688 

.21314  .32867 
•22362  .34951 

.23414   .36948 
.24472   .38866 

4.9332  0.69312 
4.6917   .67133 
4.4719   .65049 
4.2709   .63052 
4.0864   .61134 

JI°28' 
12  O2 
12  36 
I3  II 
1345 

°% 

•11 

.29 

0.24740  9.39341 
.25708   .41007 
.26673   .42607 
.27636   .44147 
.28595   .45629 

0.96891  9.98628 
•96639   -985!  5 
•96377   -98397 
.96106   .98275 
.95824   .98148 

0.25534  9.40712 

.26602   .42491 
.27676   .44210 

.28755  -45872 

.29841   .47482 

3.9163  0.59288 
3-7592   .57509 
3-6i33   -55790 
3.4776   .54128 
3.3511   .52518 

I40i9' 

1454 
15  28 
1603 
1637 

0.30 
•31 

•32 
•33 
•34 

0.29552  9.47059 
.30506   .48438 

•3r457   .49771 
.32404   .51060 

•33349   -52308 

0-95534  9-98016 
•95233   -97879 
•94924   -97737 
.94604   .97591 
•94275   -97440 

0-30934  9-49043 
•32033  -50559 
•33139  -52034 
.34252  .53469 

•35374   -54868 

3-2327  0.50957 
3.1218   .49441 
3.0176   .47966 
2.9195   .46531 
2.8270   .45132 

I7°n' 
17  46 
18  20 

1854 
19  29 

•$ 

3 

•39 

0.34290  9.53516 
.35227   .54688 
.36162   -55825 
.37092   .56928 
.38019   .58000 

0-93937  9-97284 
•93590   -97123 
•93233   -96957 
.92866   .96786 
.92491   .96610 

0.36503  9-56233 
.37640   .57565 
.38786   .58868 
.39941   .60142 
.41105   .61390 

2-7395  0.43767 
2.6567   42435 
2.5782   .41132 
2-5037   -39858 
2.4328   .38610 

20°03' 
20  38 
21  12 
21  46 
22  21 

0.40 
.41 
.42 
•43 
•44 

0.38942  9.59042 
.39861   -60055 
.40776   .61041 
.41687   .62000 
.42594   .62935 

0.92106  9.96429 
.91712   .96243 
.91309   .96051 
.90897   .95855 
•90475   -95653 

0.42279  9.62613 
.43463   -63812 
.44657   .64989 
.45862   .66145 
.47078   .67282 

2.3652  0.37387 
2.3008   .36188 
2-2393   -350H 
2.1804   -33855 
2.1241   .32718 

22*55' 

23  29 
24  04 

2438 
25  13 

•3 
3 

•49 

0-43497  9-63845 
.44395   .64733 
.45289   .65599 
.46178   .66443 
.47063   .67268 

0.90045  9.95446 
.89605   .95233 
•89157   -95015 
.88699   .94792 
.88233   .94563 

0.48306  9.68400 
-49545   -6950° 
.50797   .70583 
.52061   .71651 

•53339   -72704 

2.0702  0.31600 
2.0184   .30500 
1.9686   .29417 
1.9208   .28349 
1.8748   .27296 

25°47' 

26  21 
26  56 

27  3° 
28  04 

050 

0-47943  9-68072 

0.87758  9.94329 

0.54630  9-73743 

1.8305  0.26257 

2S°39' 

SMITHSONIAN  TABLES. 


TABLE    1  4  (contimtecf). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


RADIANS. 

SINES. 

COSINES. 

TANGENTS 

COTANGENTS. 

DEGREES. 

Nat.      Log. 

Nat.      Log. 

Nat.      Log. 

Nat.      Log. 

0.50 

•51 

•52 
•53 
•54 

0-47943  9-68072 
.48818   .68858 
.49688   .69625 

•5°553   -70375 
.51414   .71108 

0.87758   9.94329 
.87274    .94089 
.86782    .93843 
.86281    .93591 
•85771   -93334 

0.54630   9-73743 
•55936    .74769 
.57256    75782 
.58592    .76784 
•59943   -77774 

1.8305    0.26257 
.7878     .25231 
.7465     .24218 
.7067     .23216 
.6683     .22226 

28°39' 

29  '3 
2948 

30  22 

3°  56 

ajl 
:P 

•59 

0.52269  9.71824 
.53119   .72525 
•53963   -73210 
.54802   .73880 
-55636   74536 

0.85252  9.93071 
.84726   .92801 
.84190   .92526 
.83646   .92245 
•83094   •9I957 

0.61311   9-78754 
•62695   .79723 
.64097   .80684 
.65517   .81635 
.66956   .82579 

1.6310    0.21246 
.5950     .20277 
.5601     -19316 
.5263     .18365 
.4935     .17421 

3'°3i' 
32  05 
32  40 
33M 
33  48 

0.60 
.61 
.62 

•63 
.64 

0.56464  9.75177 
.57287   .75805 
.58104   .76420 
.58914   .77022 
.59720   .77612 

0-82534  9.91663 
.81965   .91363 
.81388   .91056 
.80803   -90743 
.80210   .90423 

0.68414  9.83514 
.69892   .84443 
.71391   .85364 
.72911   .86280 
.74454   .87189 

1.4617    0.16486 
•4308     .15557 
.4007     .14636 
•3715     .13720 
.3431     .12811 

34°23' 
34  57 
353i 
36  06 
36  40 

0.65 
.66 
.67 
.68 
.69 

0.60519  9.78189 
.61312   .78754 
.62099   .79308 
.62879   .79851 
.63654   .80382 

0.79608  9.90096 
.78999   .89762 
.78382   .89422 

•77757   .89074 
.77125   .88719 

0.76020  9.88093 
.77610   .88992 
.79225   .89886 
.80866   .90777 
.82534   .91663 

1.3154    0.11907 
.2885     .11008 
.2622     .IOII4 
.2366     .09223 
.2Il6     -08337 

37°i5' 
37  49 
38  23 
3858 
3932 

0.70 

•7i 

.72 

•73 
•74 

0.64422  9.80903 
.65183   .81414 
.65938   .81914 
.66687   .82404 
.67429   .82885 

0.76484  9.88357 
.75836   .87988 
.75181   .87611 
.74517   .87226 
.73847   .86833 

0.84229  9-92546 
•85953   -93426 
•87707   -94303 
.89492   .95178 
.91309   .96051 

1.1872    0.07454 
.1.634     .06574 
.1402     .05697 
.1174     .04822 
.0952     .03949 

40°o6' 
40  41 
4i  15 
4i  5° 
42  24 

0.75 
.76 

•77 
.78 
•79 

0.68164  9-83355 
.68892   .83817 
.69614   .84269 
.70328   .84713 
•71035   .85147 

0.73169  9.86433 
.72484   .86024 
.71791   .85607 
.71091   .85182 
.70385   .84748 

0.93160  9.96923 

.95045   -97793 
.96967   .98662 
.98926  9.9953  1 
i  .0092   0.00400 

1.0734    0.03077 
.0521     .02207 

.03U     -01338 
I.OIO9     .00469 
0.99084   9.99600 

42°5S' 
4333 
44  07 
44  4i 
45  16 

0.80 
.81 
.82 

•83 
.84 

0.71736  9.85573 
.72429   .85991 
.73115   .86400 
.73793   .86802 
.74464   .87195 

0.69671   9.84305 
.68950   .83853 
.68222   .83393 
.67488   .82922 
.66746   .82443 

1.0296   0.01268 
.0505    .02138 
.07  1  7    .03008 

•0934    -03879 
.1156    .04752 

0.97121   9-98732 

«95T97   -97862 
.93309   .96992 
.91455   .96121 

•89635   -95248 

45°5o' 
46  25 
46  59 
47  33 
48  08 

b 
.87 
.88 
.89 

0.75128  9.87580 
.75784   .87958 
.76433   .88328 
.77074   .88691 
.77707   .89046 

0.65998  9.81953 
.65244   .81454 
.64483   .80944 
.63715   .80424 
.62941   .79894 

1.1383   0.05627 
.1616    .06504 

•'853    -07384 
.2097    .08266 
.2346    .09153 

0.87848  9-94373 
.86091   .93496 
.84365   .92616 
.82668   .91734 
.80998   .90847 

48°42' 

49  16 
49  51 

50  25 
51  oo 

0.90 
.91 
.92 
•93 
•94 

0-78333  9-89394 
.78950   .89735 
.79560   .90070 
.80162   -90397 
.80756   .90717 

0.62161  9.79352 

•6i375   -78799 
.60582   .78234 
.59783   .77658 
.58979   .77070 

1.2602   0.10043 
.2864    -10937 
•3133    ."835 
.3409    .12739 
.3692    .13648 

0-79355  9-89957 
•7773s   .89063 
.76146   .88165 
.74578   .87261 
.73034   .86352 

5i°34' 

52  08 

S2  43 
53  i7 
53  5i 

°$ 

•97 
.98 

•99 

0.81342  9.91031 

•81919   -91339 
.82489   .91639 
.83050   .91934 
.83603   .92222 

0.58168  9.76469 

•57352   .75855 
.56530   .75228 
.55702   .74587 
.54869   .73933 

1.3984   0.14563 
.4284    .15484 
.4592    .16412 
.4910    .17347 
.5237    .18289 

0.71511  9.85437 
.70010   -84516 
.68531   .83588 
.67071   .82653 
.65631   .81711 

54°26'  I 
55  oo 
5535 
5609 

5643 

I.OO 

0.84147  9-92504 

0-54030  9-73264 

1.5574   0.19240 

0.64209  9.80760 

57°i8' 

SMITHSONIAN  TABLES. 


TABLE    14  (continued). 
CIRCULAR  (TRIGONOMETRIC)  FUNCTIONS. 


39 


RADIANS. 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES.  1 

Nat.      Log. 

Nat.     Log. 

Nat.      Log. 

Nat.     Log. 

I.OO 
.01 
.02 

•°3 
.04 

0.84147   9.92504 
.84683    .92780 
.85211    .93049 

•85730    -93313 
.86240    .93571 

0.54030   9.73264 
.53186    .72580 
.52337    .71881 
.51482    .71165 
.50622    .70434 

1.5574   0.19240 
.5922    .2O2OO 
.6281    .21169 
.6652    .22148 
.7036    .23137 

0.64209   9.80760 
.62806   .79800 
.61420   .78831 
.60051    .77852 
.58699   .76863 

57°iS' 

5752 
58  27 
5901 
5935 

I.O5 
.06 
.07 
.08 
.09 

0.86742   9-93823 
.87236    .94069 
.87720    .943!° 
.88196   -94545 
.88663   -94774 

0.49757   9.69686 
.48887    .68920 
.48012    -68135 

•47133    -67332 
.46249    .66510 

1.7433   0.24138 
.7844    .25150 
.8270    .26175 
.8712    .27212 
.9171    .28264 

0-57362   9-75862 
.56040    .74850 

•54734   -73825 
.53441   .72788 
.52162   .71736 

6o°io' 
6044 
61  18 

61  53 
62  27 

1.  10 

.11 

.12 

•13 
.14 

0.89121   9.94998 
.89570   .95216 
.90010   .95429 
.90441   .95637 
•90863   .95839 

0.45360   9.65667 
.44466   .64803 
•43568    .63917 
.42666    .63008 
.41759    .62075 

1.9648   0.29331 
2.0143    -30413 
.0660    -31512 
.1198    .32628 
•1759    .33763 

0.50897  9.70669 
.49644   .69587 
'  .48404   .68488 
.47175   .67372 
•45959   -66237 

63°02' 

6336 
64  10 

6445 
65  19 

wi 

.16 

•17 
.18 
.19 

0.91276  9.96036 
.91680   .96228 
.92075   .96414 
.92461   .96596 
.92837   .96772 

0.40849   9.61118 
•39934   -60134 
.39015   .59123 
.38092   .58084 
.37166   .57015 

2.2345   0.34918 
.2958    .36093 
.3600    .37291 
.4273    .38512 
•4979   -39757 

O-44753  9.65082 
•43558   -63907 
.42373   .62709 
.41199   .61488 
.40034   .60243 

£Si 

67  02 

6737 
68  ii 

i.  20 

.21 

.22 

•23 
.24 

0.93204  9.96943 
.93562   .97110 
.93910   .97271 
.94249   .97428 
•94578   -97579 

0.36236  9.55914 
•35302   .5478o 
•34365   -53611 
.33424   .52406 
.32480   .51161 

2.5722  0.41030 
.6503   .42330 
•7328   .43660 
.8198   .45022 
.9119   .46418 

0.38878  9.58970 
•37731   -57670 
•36593   -56340 
•35463   .54978 
-34341   -53582 

68°45' 

69  20 

69  54 
70  28 
71  03 

k*s 
.26 
.27 
.28 
.29 

0.94898  9.97726 
.95209   .97868 
.95510   .98005 
.95802   -98137 
.96084   .98265 

o-3r532  949875 
.30582   .48546 
.29628   -47170 
.28672   .45745 
.27712   .44267 

3.0096  0.47850 
•"33   -49322 
.2236   .50835 
.3413   -52392 
•4672   .53998 

0-33227  9-52150 
.35121   .50678 
.31021   .49165 
.29928   .47608 
.28842   .46002 

7i°37' 

72  12 
72  46 

73  20 
7355 

i.3o 

•31 
•32 
•33 
•34 

0.96356  9.98388 
.96618   .98506 
.96872   .98620 
.97115   .98729 
.97348   .98833 

0.26750  9.42732 
.25785   .41137 
.24818   .39476 
.23848   -37744 
•22875   -35937 

3.6021  0.55656 
•7471   -57369 
•9°33   -59M4 
4.0723   .60984 
.2556   .62896 

0.27762  9-44344 
.26687   .42631 
.25619   .40856 
•24556   -39OI6 
•23498   -37104 

74°29' 
7503 
753» 

76  12 
7647 

•3 

s 

•39 

0-97572  9-98933 
.97786   .99028 
.97991   .99119 
.98185   .99205 
.98370   .99286 

0.21901  9.34046 
.20924   .32064 
.19945   .29983 
.18964   -27793 
.17981   .25482 

4.4552  0.64887 
.6734   .66964 
•9131   -69135 
5.1774   .71411 
4707   -73804 

0.22446  9-35"3 
•21398   -33036 
-20354   -30865 
.19315   .28589 
.18279   .26196 

77°2i' 
77  55 
7830 
79  04 
7938 

1.40 
.41 
.42 
•43 
44 

0-98545  9-99363 
.98710   .99436 
.98865   .99504 
.99010   .99568 
.99146   .99627 

0.16997  9.23036 
.16010   .20440 
.15023   .17674 
.14033   .14716 
.13042   .11536 

5-7979  0.76327 
6.1654   .78996 
6.5811   .81830 

7-0555   -84853 
7.6018   .88092 

0.17248  9.23673 
.16220   .21004 
.15195   .18170 
.14173   .15147 
.13155   .11908 

8o°i3' 
8047 

8l  22 

81  56 

82  30 

i-45 
.46 

•47 
.48 
.49 

0.99271  9.99682 

•99387   -99733 
.99492   .99779 
.99588   .99821 
.99674   .99858 

0.12050  9.08100 
.11057   .04364 
.10063   .00271 
.09067  8.95747 
.0807  1   .90692 

8.2381  0.91583 
8.9886   -95369 
9.8874   .99508 
10.983   1.04074 
12.350    .09166 

0.12139  9.08417 
.11125   .04631 
.10114   .00492 
.09105  8.95926 
.08097   .90834 

83°o5' 
8339 
84  13 
8448 

85  22 

1.50 

0-99749  9-99891 

0.07074  8.84965 

14.101   1.14926 

0.07091  8.85074 

85°57' 

SMITHSONIAN  TABLES. 


40 


TABLES    14  (continued)   AND    15. 

CIRCULAR  FUNCTIONS  AND  FACTORIALS. 

TABLE  14  (continued}.  —  Circular  (Trigonometric)  Functions. 


Q 

SINES. 

COSINES. 

TANGENTS. 

COTANGENTS. 

DEGREES. 

Nat.            Log 

Nat.             Log 

Nat.             Log. 

Nat.             Log. 

1.50 

•51 

•52 
•53 
•54 

0.99749     9.99891 
.99815        .99920 
.99871        .99944 
.99917        .99964 
•99953        '99979 

0.07074     8.84965 
.06076       .78361 
.05077        .70565 
.04079       .61050 
.03079       .48843 

I4.IOI      1.14926 
16.428        -21559 
19.670        .29379 
24.498        .38914 
32.461        .51136 

0.07091      8.85074 
.06087        -78441 
.05084        .70621 
.04082        .61086 
.03081        .48864 

ff57' 

8631 
87  05 
87  40 
88  14 

'3 

% 

•59 

0.99978     9.99991 
0.99994     9-99997 
I  .OOOOO      O.OOOOO 

0.99996  9.99998 
0.99982  9.99992 

0.02079     8.31796 
.01080     8.03327 
.00080     6.90109 
-.00920     7.9639611 
-.01920     8.2833611 

48.078      1.68195 
92.621      1.96671 

I255-8        3.09891 
108.65      2.03603 
52.067     1.71656 

0.02080     8.31805 
.01080     8.03329 
.00080     6.90109 
—.00920     7.9639711 
-.01921     8.28344n 

88°49' 
89  23 

89  57 
9032 
91  06 

1.60 

0.99957    9.99981 

-0.02920    8-46538n 

34.233     1-53444 

-0.02921    8.46556n 

9i°4o' 

90°=  i.  570  7963  radians. 


TABLE  15. -Logarithmic  Factorials. 
Logarithms  of  the  products  1.2.3 «,  n  from  I  to  100. 

See  Table  17  for  Factorials  i  to  20. 
See  Table  31  for  log.  r  (n.  +  i),  values  of  n  between  i  and  2. 


«. 

log  («/) 

». 

log  («.') 

m. 

log  («/) 

n. 

log  («/) 

1 

o.ooopoo 

26 

26.605619 

51 

66.190645 

76 

111.275425 

2 

0.301030 

27 

28.036983 

52 

67.906648 

77 

113.161916 

3 
4 

0.778151 

1.380211 

28 
29 

29.484141 
30.946539 

53 
54 

69.630924 
71.363318 

78 
79 

115.054011 
116.951638 

5 

2.079181 

30 

32-423660 

55 

73.103681 

80 

118.854728 

6 

2.857332 

31 

33.915022 

56 

74.851869 

81 

120.763213 

7 

3.702431 

32 

35.420172 

57 

76.607744 

82 

I22.6/7O27 

8 

4.605521 

33 

36.938686 

58 

78.371172 

83 

124.596105 

9 

5-559763 

34 

38.470165 

59 

80.142024 

84 

126.520384 

10 

6.559763 

35 

40.014233 

60 

81.920175 

85 

128.449803 

11 

7.601156 

36 

4L570535 

61 

83-705505 

86 

130.384301 

12 

8.680337 

37 

43-!38737 

62 

85.497896 

87 

132.323821 

T3 
14 

9.794280 

10.940408 

38 
39 

44.718520 
46.309585 

63 
64 

87.297237 
89,103417 

88 
89 

-  134-268303 
136.217693 

15 

12.116500 

40 

47.911645 

65 

90.916330 

90 

I38.I7I936 

16 

13.320620 

41 

49.524429 

66 

92.735874 

91 

140.130977 

18 

14.551069 
15.806341 

42 
43 

51.147678 
52.781147 

67 
68 

94.561949 
96.394458 

92 
93 

142:094765 
144.063248 

i9 

17.085095 

44 

54424599 

69 

98.233307 

94 

146.036376 

20 

18.386125 

45 

56.077812 

70 

100.078405 

95 

148.014099 

21 

19.708344 

46 

57.740570 

71 

101.929663 

96 

149.996371 

22 

21.050767 

47 

59.412668 

72 

103.786996 

97 

151.983142 

23 

22.412494 

48 

61.093909 

73 

105.650319 

98 

1  53-974368 

24 

23.792706 

49 

62.784105 

74 

107.519550 

99 

155.970004 

25 

25.190646 

50 

64.483075 

75 

109.394612 

100 

157.970004 

SMITHSONIAN  TABLES. 


TABLE  16. 
HYPERBOLIC  FUNCTIONS. 


u 

sinh.  u 

cosh,  u 

tauh.  u 

coth.  u 

gd  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

0.00 
.01 
.02 

•03 
.04 

O.OOOOO    —  00 

.01000  8.00001 
.02000   .30106 
.03000  .47719 
.04001   .60218 

I.OOOOO   O.OOOOO 

.00005   .00002 

.00020    .00009 

.00045   .00020 
.00080   .00035 

O.OOOOO   —  00 

.01000  7-99999 

.02000   8.30097 

.02999  -47699 
.03998  .60183 

00         00 
IOO.OO3    2.OOOOI 
50.007    1.69903 

33-343   1-52301 
25.013   1.39817 

oo°oo' 
o  34 
i  09 

1  43 
2  17 

0.05 
.06 
.07 
.08 
.09 

0.05002  8.69915 
.06004   .77841 
.07006   -84545 

.08009  .90355 
.09012  .95483 

1.00125  0.00054 
.00180   .00078 
.00245   .00106 
.00320  .00139 
.00405   .00176 

0.04996  8.69861 

.05993  .77763 

.06989   .84439 
.07983   .90216 

.08976  .95307 

20.017   I-3°i39 
16.687   -22237 
14.309   -15561 
12.527   .09784 
11.141   .04693 

2  52 
3  26 

4  oo 
4  35 
5  09 

O.IO 

.11 

.12 

•J3 
.14 

0.10017  9.00072 

.11022    .04227 

.12029   .08022 
•i3°37   -us1? 

.14046  .14755 

1.00500  0.00217 
.00606  .00262 
.00721   .00312 
.00846   .00366 
.00982   .00424 

0.09967  8.99856 
.10956  9-03965 
.11943  .07710 

.12927   .11151 

.13909  .14330 

10.0333  1.00144 
9.1275  0.96035 

8-3733   .9229° 
7.7356   .88849 
7.1895   .85670 

5  43 
6  17 

652 
7  26 
8  oo 

o.i<5 
.16 

•I? 
.18 
.19 

0.15056  9.17772 
.16068   .20597 

.17082  .23254 
.18097  .25762 

.19115   .28136 

1.01127  0.00487 

.01283  .00554 

.01448   .00625 
.01624   .00700 
.01810   .00779 

0.14889  9.17285 
.15865   .20044 

.16838  .22629 

.17808   .25062 

•18775  -27357 

6.7166  0.82715 
6.3032   .79956 
5-9389   -77371 
5.6154   .74938 
5.3263   .72643 

8  34 
9  08 
9  42 
10  15 
10  49 

O.2O 
.21 

.22 

•23 
.24 

0.20134  9.30392 
.21155  .32541 
.22178  .34592 
•23203  .36555 
.24231  .38437 

1  .02007  0.00863 
.02213   .00951 
.02430  .01043 
.02657   .01139 
.02894   .01239 

0.19738  9.29529 
.20697  .31590 
.21652  .33549 
.22603  .35416 
.23550  -37198 

5.0665  0.70471 
4.8317   .68410 
4.6186   .66451 
4.4242   .64584 
4.2464   .62802 

ii  23 
ii  57 

12  30 
13  °4 

13  37 

0.25 

.26 

2 

.29 

0.25261  9.40245 
.26294   .41986 

.27329  .43663 

.28367   .45282 
.29408   .46847 

1.03141  0.01343 
•03399  -01452 

.03667   .01564 
.03946  .01681 
.04235   .01801 

0.24492  9.38902 
•25430  -40534 

.26362   .42099 
.27291  .43601 
.28213  .45046 

4.0830  0.61098 
3-9324   .59466 
3-7933   .57901 
3.6643   .56399 

3-5444   -54954 

14  ii 
14  44 
IS  i? 
15  5° 
16  23 

0.30 
•31 
•32 
•33 
•34 

0.30452  9.48362 
.31499  .4983° 
.32549  .51254 
.33602  .52637 
•34659  -53981 

1.04534  0.01926 
.04844  .02054 

.05164   .02187 
•05495   -°2323 

.05836  .02463 

0.29131  9.46436 

.30044  .47775 
.30951  .49067 
.31852  .50314 
.32748  .51518 

34327  0.53564 
.3285   .52225 

-2309   -50933 
.1395   .49686 
.0536   .48482 

16  56 
17  29 
18  02 
18  34 
19  07 

o-35 
•36 

3 

•39 

0-35719  9-55290 
.36783  .56564 
.37850  .57807 
.38921  .59019 

.39996   .60202 

1.  06188  0.02607 

.06550  .02755 
.06923  .02907 
.07307  .03063 

.07702   .03222 

0.33638  9.52682 

-34521  .53809 

•35399   -54899 
•36271   .55956 
.37136   .56980 

2.9729  0.47318 
.8968   .46191 
.8249   .45101 
.7570   .44044 
.6928   .43020 

19  39 

2O  12 

20  44 
21  16 

21  48 

0.40 
.41 
.42 
43 
•44 

0.41075  9.61358 

.42158  .62488 
.43246  .63594 
.44337  .64677 
.45434  .65738 

1.08107  0.03385 

•08523  -03552 

.08950   .03723 

.09388  .03897 
.09837  .04075 

0-37995  9-57973 
.38847   .58936 

•39693   -59871 
.40532   .60780 
.41364   .61663 

2.6319  0.42027 
.5742   .41064 
.5193   .40129 
.4672   .39220 
•4175   -38337 

22  2O 
22  52 
23  23 

23  55 
24  26 

0-45 
.46 

•47 
.48 

•49 

0.46534  9.66777 
.47640  .67797 
.48750  .68797 
.49865  .69779 
.50984  .70744 

1.102970  .04256 
.10768  .04441 

.11250   .04630 

.11743  .04822 

.12247   .05018 

0.42190  9.62521 
.43008   .63355 
.43820   .64167 
.44624   .64957 
.45422   .65726 

2.3702  0.37479 
.3251   .36645 
.2821   .35833 
.2409   .35043 
.2016   .34274 

24  57 

25  28 

25  59 
26  30 
27  01 

0.50 

0.52110  9.71692 
f 

1.12763  0.05217 

0.46212  9.66475 

2.1640  0.33525 

27  3' 

SMITHSONIAN  TABLES. 


TABLE    1  6   (continued). 
HYBERBOLIC  FUNCTIONS. 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth.  u 

gd  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

I  0.50 

•51 

•52 
•53 
•54 

0.52110  9.71692 
.53240   .72624 

•54375   -73540 
.55516   .74442 
•56663   .75330 

1.12763  0.05217 
.13289   .05419 
.13827   .05625 

•14377   -05834 
.14938   .06046 

0.46212  9.66475 
•46995   -67205 
.47770   .67916 
.48538   .68608 
.49299   .69284 

2.1640   0.33525 
.1279    .32795 
.0934    .32084 
.0602    .31392 
.0284    .30716 

__O-.T  ' 

27  31 

28  02 

28  32 

29  02 

29  32 

°:P 
9 

•59 

0.57815  9.76204 
•58973   -77065 
.60137   -779H 
.61307   .78751 
.62483   .79576 

1.15510  0.06262 
.16094   .06481 
.16690   .06703 
.17297   .06929 
.17916   .07157 

0.50052  9.69942 
.50798   .70584 
.51536   -7I2II 
.52267   .71822 
.52990   .72419 

1.9079   0.30058 
.9686    .29416 
.9404    .28789 
.9133    .28178 
.8872    .27581 

30  02 
30  32 

31  oi 

31  31 
32  oo 

0.60 
.61 
.62 

63 
.64 

0.63665  9.80390 
.64854   .81194 
.66049   -81987 
.67251   .82770 
•68459   -83543 

1.18547  0.07389 
.19189   .07624 
.19844   .07861 
.20510   .08102 
.21189   .08346 

0.53705  9-73001 
•54413   -73570 
.55113   .74125 
•55805   .74667 
.56490   .75197 

1.8620   0.26999 
.8378    .26430 
•8145    -25875 
•7919    -25333 
.7702    .24803 

32  29 

32  58 
33  27 
33  55 
34  24 

0.615 
.66 
.67 
.68 
.69 

0.69675  9.84308 
.70897   .85063 
.72126   .85809 
.73363   -86548 
.74607   .87278 

1.21879  °-°8593 
.22582   .08843 
.23297   .09095 
.24025   .09351 
.24765   .09609 

0.57167  975715 
•57836   .76220 
.58498   .76714 
.59152   .77197 
•59798   .77669 

1.7493   0.24285 
.7290    .23780 
.7095    .23286 
.6906    .22803 
.6723    .22331 

34  52 
35  20 
35  48 
36  16 
36  44 

0.70 

•7i 

.72 

•73 
•74 

0.75858  9.88000 
.77117   .88715 
.78384   .89423 
.79659   -90123 
.80941   .90817 

1.25517  0.09870 
.26282   .10134 
.27059   .10401 
.27849   .10670 
.28652   .10942 

0.60437  9.78130 
.61068   .78581 
.61691    .79022 
•62307   .79453 
.62915   .79875 

1.6546   0.21870 
.6375    .21419 
.6210    .20978 
.6050    -20547 
.5895    .20125 

37  ii 
37  38  ! 
38  05 
38  32 
38  59 

°tt 
% 

•79 

0.82232  9.91504 
•8353°   -92185 
.84838   .92859 

•86153   -93527 
.87478   .94190 

1.29468  o.i  1216 
.30297   .11493 
.31139   .11773 
.31994   .12055 
.32862   .12340 

0.63515  9.80288 
.64108   .80691 
.64693   .81086 
.65271    .81472 
.65841    .81850 

1.5744   O.I97I2 

•5599   -19309 
.5458   .18914 
.5321    .18528 
.5188   .18150 

39  26 
39  52 
40  19 
40  45 
41  ii 

0.80 
.81 

.82 

•83 
.84 

0.88811  9.94846 
.90152   .95498 

•91503   -96144 
.92863   .96784 
•94233   -97420 

1-33743  0.12627 
.34638   .12917 

-35547   -i32°9 
.36468   .13503 
.37404   .13800 

0.66404  9.82219 
.66959   .82581 
.67507    -82935 
.68048   .83281 
.68581    .83620 

1.5059   0.17781 

•4935   -'7419 
.4813   .17065 
.4696   .16719 
.4581    .16380 

4i  37 

42  02 
42  28 

42  5<>   l 

43  18 

0.85 
.86 

•87 
.88 
.89 

0.95612  9.98051 
.97000   .98677 
.98398   .99299 
.99806   .99916 
1.01224  0.00528 

1.38353  0.14099 
.39316   .14400 
.40293   .14704 
.41284   .15009 
.42289   .15317 

0.69107  9.83952 
.69626   .842/7 
.70137    .84595 
.70642   .84906 
.71139   .85211 

1.4470   0.16048 
.4362   .15723 
.4258   .15405 
.4156   .15094 
•4057    ^4789 

43  43 
44  08 
44  32  I 
44  57 
45  21 

0.90 
.91 
.92 
•93 
•94 

1.02652  0.01137 
.04090   .01741 
•05539   -02341 
.06998   .02937 
.08468   .03530 

1.43309  0.15627 
•44342   .15939 
.45390   .16254 
•46453   -l657o 
.47530   .16888 

0.71630  9.85509 
.72113   .85801 
.72590   .86088 
.73059   .86368 
.73522   .86642 

1.3961   0.14491 
.3867    .14199 
.3776   .13912 
.3687    .13632 
.3601    .13358 

45  45 
46  09 

4633 
46  56 
47  20 

o-95 
.96 

•97 
.98 

•99 

1.09948  0.04119 
.11440   .04704 
.12943   .05286 
.14457   .os864 
.15983   .06439 

1.48623  0.17208 

•49729   -I7531 
•50831   .17855 
.51988   .18181 
.53141   .18509 

0.73978  9.86910 
.74428   .87173 
.74870   .87431 
.75307   .87683 
.75736   .87930 

1.3517   0.13090 
.3436   .12827 
•3356   -12569 
.3279   .12317 
.3204   .12070 

47  43 
48  06 
48  29 
48  51 
49  '4 

T.OO 

1.17520  0.07011 

1.54308  0.18839 

0.76159  9.88172 

1.3130   0.11828 

49  36 

SMITHSONIAN  TABLES. 


TABLE    1  6  (continued). 
HYPERBOLIC  FUNCTIONS. 


43 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth  u 

gd  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

I.OO 
.01 

.02 

•°3 
.04 

1.17520  0.07011 
.19069   .07580 
.20630   .08146 
.22203   .08708 
.23788   .09268 

1.54308  0.18839 
.55491    .19171 
.56689   .19504 
.57904   .19839 
.59134   .20176 

0.76159  9.88172 
.76576   .88409 
.76987   .88642 
.77391   -88869 
.77789   .89092 

1.3130   0.11828 
.3059    .11591 

•2989    ."358 
.2921    .11131 
.2855    .10908 

49°36' 
49  S8 

5O  21 
50  42 

51  04 

'•°l 
.06 

.07 
.08 
.09 

1.25386  0.09825 
.26996   .10379 
.28619   .10930 
.30254   .11479 
.31903   .12025 

1.60379  0.20515 
.61641   .20855 
.62919   .21197 
.64214   .21541 
.65525   .21886 

0.78181  9.89310 
.78566   .89524 
.78946   .89733 
.79320   -89938 
.79688   .90139 

1.2791   0.10690 
.2728    .10476 
.2667    .10267 
.2607    .10062 
.2549    .09861 

51  26 

52  08 
52  29 
52  50 

1.  10 

.11 

.12 

•13 
.14 

1.33565  0.12569 
.35240   .13111 
.36929   .13649 
.38631   .14186 
.40347   .14720 

1.66852  0.22233 
.68196   .22582 
.69557   .22931 
.70934   .23283 
.72329   .23636 

0.80050  9-90336 
.80406   .90529 
.80757   .90718 
.8lI02   .90903 
.81441   .91085 

1.2492   0.09664 
.2437    .09471 
.2383    .09282 
.2330    .09097 
.2279    .08915 

53  « 
53  3i 
53  52 
54  12 
54  32 

"i 

.16 

.17 
.18 
.19 

1.42078  0.15253 
.43822   .15783 
.45581   .16311 
•47355   -l6836 
•49M3   •I736° 

I.7374I   0.23990 
.75171    .24346 
.76618   -24703 
.78083   .25062 

•79565   .25422 

0.81775  9.91262 
.82104   .91436 
.82427   .91607 
.82745   .91774 
.83058   .91938 

1.2229   0.08738 
.2180    .08564 
.2132    .08393 
.2085    .08226 
.2040    .08062 

54  52 
55  " 
55  3i 
55  50 
56  09 

i.  20 

.21 
.22 

•23 
.24 

1.50946  0.17882 
.52764   .18402 
.54598   .18920 
.56447   .19437 
.58311   .19951 

i  .8  1066  0.25784 
.82584   .26146 
.84121   .26510 
.85676   .26876 
.87250   .27242 

0.83365  9.92099 
.83668   .92256 
.83965   .92410 
.84258   .92561 
.84546   .92709 

1.1995   0.07901 
.1952    .07744 
.1910    .07590 
.1868    .07439 
.1828    .07291 

56  29 

56  47 
57  06 
57  25 
57  43 

3 

.27 
.28 
.29 

1.60192  0.20464 
.62088   .20975 
.64001   .21485 
.65930   .21993 
.67876   .22499 

1.88842  0.27610 
.90454   .27979 
.92084   .28349 
•93734   .28721 
.95403   .29093 

0.84828  9.92854 
.85106   .92996 
.85380   .93135 
.85648   .93272 

•859I3   -934°6 

1.1789   0.07146 
.1750    .07004 
.1712    .06865 
.1676    .06728 
.1640    .06594 

58  02 
58  20 
5838 
58  55 
59  13 

i   1-3° 

•31 
•32 
•33 
•34 

1.69838  0.23004 
.71818   .23507 
.73814   .24009 
.75828   .24509 
.77860   .25008 

1.97091  0.29467 
.98800   .29842 
2.00528   -30217 
.02276   .30594 
.04044   .30972 

0.86172  9-93537 
.86428   .93665 
.86678   .93791 
.86925   .93914 
.87167   .94035 

1.1605   0.06463 
.1570    .06335 
•J537   -06209 
.1504   .06086 
.1472   .05965 

59  3i 

59  48 
60  05 

60  22 

60  39 

hs 

3 

•39 

1.79909  0.25505 
.81977   .26002 
.84062   .26496 
.86166   .26990 

.88289   .27482 

2.05833  0.31352 
.07643   .31732 
.09473   .32113 
.11324   .32495 
.13196   .32878 

0.87405  9.94154 
.87639   .94270 
.87869   .94384 
.88095   -94495 
.88317   .94604 

1.1441   0.05846 
.1410   -05730 
.1381   .05616 
-I351   -05505 
-1323   -05396 

60  56 
61  13 
61  29 
61  45 
62  02 

1.40 
.41 

.42 
•43 
•44 

1.90430  0.27974 
.92591   .28464 
.94770   .28952 
.96970   .29440 
.99188   .29926 

2.15090  0.33262 
.17005   .33647 
.18942   .34033 
.20900   .34420 
.22881   .34807 

0.88535  9.94712 
.88749   -94817 
.88960   .94919 
.89167   .95020 
•89370   -95M9 

1.1295  0.05288 
.1268   .05183 
.1241   .05081 
.1215   .04980 
.1189   .04881 

62  18 

6234 
62  49 
63  05 

63  20 

•i 

:44£ 

.49 

2.01427  0.30412 
.03686   .30896 

•05965   -3!379 
.08265   .31862 
.10586   .32343 

2.24884  0.35196 
.26910   .35585 
•28958   .35976 
.31029   .36367 
.33123   .36759 

0.89569  9.95216 
•8976;   -95311 
.89958   .95404 
.90147   .95495 
•90332   .95584 

1.1165  0.04784 
.1140   .04689 
.1116   .04596 
.1093   -04505 
.1070   .04416 

6336 
63  51 
64  06 
64  21 
6436 

1  1-50 

2.12928  0.32823 

2.35241  0.37151 

0-905!  5  9-95672 

1.1048   0.04328 

64  51 

SMITHSONIAN   TABLES. 


44 


TABLE    16   (contimtea). 
HYPERBOLIC    FUNCTIONS. 


u 

sinh.  u 

cosh.  u 

tanh.  u 

coth.  u 

gd.  u 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

1.50 

•51 
•52 
•53 
•54 

2.12928  0.32823 

•I529I   -33303 
.17676   .33781 
.20082   .34258 
•22510   .34735 

2.35241  0.37151 
•37382   .37545 
•39547   -37939 
.41736   .38334 

•43949   -38730 

0.90515  9-95672 
.90694   .95758 
.90870   .95842 
.91042   .95924 
.91212   .96005 

1.1048   0.04328 
.1026    .04242 
.1005    .04158 
.0984    .040/6 
•0963    .03995 

64°  SI' 

65  05 
65   20 

65  34 
65  48 

!-55 
•56 

:§ 

•59 

2.24961  0.35211 
.27434   -35686 
.29930   .36160 
.32449   .36633 

•34991   -37105 

2.46186  0.39126 
.48448   .39524 

•50735   -39921 
.53047   .40320 
.55384   .40719 

0.91379  996084 
.91542   .96162 
.91703   .96238 
.91860   .96313 
.92015   .96386 

1.0943   0.03916 
.0924    .03838 
.0905    .03762 
.0886    .03687 
.0868    .03614 

66  02 
66  16 

66  30 

g  43 

66  57 

1.60 
.61 
.62 

•63 
.64 

2-37557  0.37577 
40146   .38048 
.42760   .38518 
•45397   -38987 
•48059   .39456 

2.57746  0.41119 
.60135   .41520 
.62549   .41921 
.64990   .42323 
.67457   .42725 

0.92167  9.96457 
.92316   .96528 
.92462   .96597 
.92606   .96664 
.92747   .96730 

1.0850   0.03543 
.0832    .03472 
.0815    .03403 
.0798    .03336 
.0782    .03270 

67  10 
67  24 
67  37 
67  50 
68  03 

1.65 
.66 
.67 
.68 
.69 

2.50746  0.39923 
.53459   .40391 
.56196   .40857 
.58959   .41323 
.61748   .41788 

2.69951  0.43129 
.72472   43532 
.75021   .43937 
.77596   -44341 
.80200   .44747 

0.92886  9.96795 
.93022   .96858 

•93r55   -96921 
.93286   .96982 
.93415   -9/042 

1.0766   0.03205 
.0750    .03142 

•°735    .03079 
.0720    .03018 
.0705    .02958 

68  15 
68  28 
68  41 
68  53 
69  05 

1.70 

•7i 

.72 

•73 
•74 

2.64563  0.42253 
.67405   .42717 
.70273   43T8o 
.73168   43643 
.76091   .44105 

2.82832  0.45153 

•85491   -45559 
.88180   .45966 
.90897   .46374 
.93643   .46782 

o.9354i  9-97ioo 
•93665   -97  IS8 
.93786   .97214 
.93906   .97269 
•94023   .97323 

1.0691   0.02900 
.0676    .02842 
.0663   .02786 
.0649   .02731 
.0636   .02677 

69  18 

69  30 
69  42 

69  54 

70  05 

'3 

•77 
.78 

•79 

2.79041  0.44567 
.82020   .45028 
.85026   .45488 
.88061   .45948 
.91125   .46408 

2.96419  0.47191 
.99224   .47600 
3.02059   .48009 
.04925   .48419 
.07821   .48830 

0.94138  9.97376 
.94250   .97428 
.94361   -97479 
.94470   .97529 
.94576   .97578 

1.0623   0.02624 
.0610   .02572 
.0598   .02521 
.0585   .02471 
.0574   .02422 

70  17 
70  29 
70  40 
70  51 
7i  03 

i.  80 
.81 
.82 

•83 
.84 

2.94217  0.46867 
•97340   47325 
3.00492   .47783 
.03674   .48241 
.06886   .48698 

3.10747  0.49241 
.13705   .49652 
.16694   .50064 
.19715   .50476 
.22768   .50889 

0.94681  9.97626 
•94783   -97673 
.94884   .97719 
.94983   .97764 
.95080   .97809 

1.0562   0.02374 
.0550   .02327 
.0539   .02281 
.0528   .02236 
.0518   .02191 

7i  M 
7i  25 

71  36  ! 
71  46 

7i  57 

1.85 
.86 

•87 
.88 
.89 

3.10129  0.49154 
.13403   .49610 
.16709   .50066 
.20046   .50521 
•234i5   -50976 

3.25853  0.51302 
.28970   .51716 
.32121   .52130 

•35305   .52544 
.38522   .52959 

0.95175  9-97852 
.95268   .97895 
•95359   -97936 
•95449   -97977 
•95537   -98017 

1.0507   0.02148 
.0497   .02105 
.0487    .02064 
.0477    .02023 
.0467    .01983 

72  08 
72  18 
72  29 
72  39 
72  49 

1.90 
.91 
.92 
•93 
•94 

3.26816  0.51430 
.30250   .51884 
•337i8   .52338 
.37218   .52791 
•40752   -53244 

3.41773  0.53374 

•45058   -53789 
.48378   .54205 
.51733   .5462! 
«55I23   -55038 

0.95624  9.98057 
.95709   .98095 
.95792   .98133 
.95873   .98170 
•95953   -98206 

1.0458   0.01943 
.0448   .01905 
.0439   .01867 
.0430   .01830 
.0422    .01794 

72  59 
73  09 
73  19 
73  29 
73  39  , 

1.95 
.96 

•97 
.98 

•99 

3.44321  0.53696 
•47923   -54148 
.51561   .54600 

•55234   -55051 
.58942   .55502 

3.58548  0.55455 
.62009   -55872 
•65507   .5629o 
.69041   .56707 
.72611   .57126 

0.96032  9.98242 
.96109   .98276 
.96185   .98311 
.96259   .98344 
.96331   .98377 

1.0413   0.01758 
.0405    .01724 
.0397    .01689 
.0389   .01656 
.0381    .01623 

73  48 

73  58 
74  07 
74  17 
74  26  I 

2.00 

3.62686  0.55953 

3.76220  0.57544 

0.96403  9-98409 

1.0373   0.01591 

74  35 

SMITHSONIAN  TABLES. 


TABLE    1  6  (continued). 
HYPERBOLIC  FUNCTIONS. 


45 


sinh.  u 

cosh.  u 

tanh.  u 

coth.  u. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.    Log. 

gd.  u 

|  2.00 
.OI 

.02 

•03 
.04 

3.62686  0.55953 
.66466   .56403 
.70283   .56853 
.74138   .57303 
.78029   .57753 

3.76220  0.57544 
.79865   .57963 
•83549   -58382 
.87271   .58802 
.91032   .59221 

0.96403  9.98409 
.96473   .98440 
.96541   .98471 
.96609   .98502 
.96675   .98531 

I-°373   0.01591 
.0366    .01560 
•0358    -01529 
.0351    .01498 
.0344    .01469 

74°35' 
74  44 
74  53 
75  02 
75  " 

2.O5 
.06 
.07 
.08 
.09 

3.81958  0.58202 
.85926   .58650 
•89932   ^9099 
•93977   -59547 
.98061   .59995 

3.94832  0.59641 
.98671   .60061 
4.02550   .60482 
.06470   .60903 
.10430   .61324 

0.96740  9.98560 
.96803   .98589 
.96865   .98617 
.96926   .98644 
.96986   .98671 

I-°337   0.01440 
.0330   .01411 
.0324   .01383 
.0317   .01356 
.0311    .01329 

75  20 

75  28 
75  37 
75  45 
75  54 

2.IO 
.11 
.12 

•!3 

.14 

4.02186  0.60443 
.06350   .60890 
•10555   -61337 
.14801   .61784 
.19089   .62231 

4.14431  0.61745 
.18474   .62167 
.22558   .62589 
.26685   -63011 
.30855   .63433 

0.97045  9.98697 
.97103   .98723 
.97159   .98748 
.97215   .98773 
.97269   .98798 

1.0304  0.01303 
.0298  .01277 
.0292  .01252 
.0286  .01227 
.0281  .01202 

76  02 
76  10 
76  19 
76  27 

7635 

2-'5 
.16 

.18 
'  -i9 

4.23419  0.62677 
.27791   .63123 
.32205   .63569 
.36663   .64015 
.41165   .64460 

4.35067  0.63856 
.39323   .64278 
.43623   .64701 
.47967   .65125 
.52356   .65548 

0-97323  9-9882I 
-97375   -98845 
.97426   .98868 
•97477   -98890 
.97526   .98912 

1.0275  0.01179 
.0270  -01155 
.0264  .01132 
.0259  .01110 
.0254  .01088 

76  43 
76  51 
7658 
77  06 

77  14 

2.  2O 
.21 
.22 

•23 
.24 

4.45711  0.64905 
.50301   .65350 

•54936   -65795 
.59617   .66240 
.64344   .66684 

4.56791  0.65972 
.61271   .66396 
.65797   .66820 
.70370   .67244 
.74989   .67668 

0-97574  9-98934 
.97622   .98955 
.97668   .98975 
.97714   .98996 
•97759   -99016 

1.0249  0.01066 
.0244  .01045 
.0239  .01025 
.0234  .01004 
.0229  .00984 

77  21 

77  29 
77  36 
77  44 
77  Si 

2.25 
.26 

3 

.29 

4.69117  0.67128 

•73937   -67572 
.78804   .68016 
.83720   -68459 
.88684   -68903 

4.79657  0.68093 
.84372   .68518 
.89136   .68943 
.93948   .69368 
.98810   .69794 

0.97803  9.99035 
•97846   .99054 
.97888   .99073 
.97929   .99091 
.97970   .99109 

1.0225  0.00965 
.0220  .00946 
.0216  .00927 

.0211  .00909 
.0207  .00891 

77  58 
7805 

78  12 
78  I9 
78  26 

2.30 

•31 
•32 
•33 
•34 

4.93696  0.69346 
.98758   .69789 
5.03870   .70232 
.09032   .70675 
.14245   .71117 

5.03722  0.70219 
.08684   .70645 
.13697   .71071 
.18762   .71497 
.23878   .71923 

0.98010  9.99127 
.98049   .99144 
.98087   .99161 
.98124   .99178 
.98161   .99194 

1.0203  0.00873 
.0199  .00856 
.0195  .00839 
.0191  .00822 
.0187  .00806 

7833 
78  40 

78  46 

78  53 
79  oo 

'$ 

9 

•39 

5.19510  0.71559 
.24827   .72002 
.30196   .72444 
.35618   .72885 
•41093   .73327 

5.29047  0.72349 
.34269   .72776 
•39544   -73203 
•44873   -7363° 
.50256   .74056 

0.98197  9.99210 
•98233   .99226 
.98267   .99241 
.98301   .99256 
•98335   -99271 

1.0184  0.00790 
.Ol8o  .OO774 
.0176  .00759 
.0173  .00744 
.0169  .00729 

79  06 
79  J3 
79  19 
79  25 
79  32 

2.40 
.41 
.42 
•43 
•44 

5.46623  0.73769 
.52207   .74210 
.57847   .74652 
•63542   .75093 
•69294   -75534 

5-S5695  0.74484 
.61189   .74911 
-66739   -75338 
.72346   .75766 
.78010   .76194 

0.98367  9.99285 
.98400   .99299 
.98431   .99313 
.98462   .99327 
.98492   -99340 

I.OI66   0.00715 
.0163     .OO70I 
.0159     .00687 
.0156     .00673 
.0153     .00660 

7938 
79  44 
79  5° 
79  56 

80  02 

2.45 
.46 

•47 
.48 

•49 

5.75103  0.75975 
.80969   .76415 
.86893   .76856 
.92876   .77296 
.98918   .77737 

5.83732  0.76621 
.89512   .77049 

•95352   .77477 
6.01250   .77906 
.07209   .78334 

0.98522  9-99353 
.98551   .99366 

.98579   -99379 
.98607   .99391 
.98635   .99403 

I.OI50   0.00647 
.0147     .00634 
.OI44     .OO62I 
.0141     .00609 
.0138     .00597 

80  08 
80  14 
80  20 
80  26 
80  31 

2.50 

6.05020  0.78177 

6.13229  0.78762 

0.98661  9.99415 

1.0136   0.00585 

80  37 

SMITHSONIAN   TABLES. 


TABLE    1  6  (continuecf). 

HYPERBOLIC   FUNCTIONS. 


u 

sinh.  u 

cosh.  u 

tanh.  u 

coth.  u 

gd.U 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

2.50 
•51 

•52 

•53 
•54 

6.05020  0.78177 
.11183   -78617 
.17407   .79057 
.23692   .79497 
.30040   .79937 

6.13229  0.78762 
.19310   .79191 

•25453   -796l9 
.31658   .80048 
.37927   .80477 

0.98661  9.99415 
.98688   .99426 
.98714   .99438 

•98739   -99449 
.98764   .99460 

1.0136   0.00585 

•0133    .00574 
.0130    .00562 
.0128    .00551 
.0125    .00540 

80°  37' 
80  42 
80  48 
80  53 
80  59 

2.55 
•56 

:P 

•59 

6.36451  0.80377 
.42926   .80816 
a   .81256 
.81695 
•82134 

6.44259  0.80906 
.50656   .81335 
.57118   .81764 
.63646   .82194 
.70240   .82623 

0.98788  9.99470 
.98812   .99481 

•98835   -99491 
.98858   .99501 
.98881   .99511 

1.0123   0.00530 
.OI2O    .00519 
.OIl8    .00509 
.0115    .00499 
.0113    .00489 

81  04 
81  10 
81  15 

8l   20 

81  25 

2.60 
.61 
.62 

:§ 

6.69473  0.82573 
.76276   .83012 
.83146   .83451 
.90085   .83890 
.97092   .84329 

6.76901  0.83052 
.83629   .83482 
.90426   .83912 
.97292   .84341 
7.04228   .84771 

0.98903  9.99521 
.98924   .99530 
.98946   .99540 
.98966   .99549 
•98987   .99558 

i.  oi  1  1   0.00479 

.OIO9    .00470 
.OIO7     .00460 
.0104    .00451 
.OIO2     .00442 

81  30 

81  35 
81  40 

81  45 
81  50 

1 

!69 

7.04169  0.84768 
.11317   .85206 
.18536   .85645 
.25827   .86083 
.33190   .86522 

7.11234  0.85201 
.18312   .85631 
.25461   .86061 
.32683   .86492 
.39978   .86922 

0.99007  9.99566 
.99026   .99575 

•99045   -99583 
.99064   .99592 
.99083   .99600 

i.  oioo  0.00434 
.0098    .00425 
.0096   .00417 
.0094   .00408 
.0093   .00400 

81  55 
82  oo 
82  05 
82  09 
82  14* 

2.70 
•71 

•72 

•73 

•74 

7.40626  0.86960 
•48137   .87398 
.55722   .87836 
.63383   .88274 
.71121   .88712 

7.47347  0.87352 
•54791   -87783 
.62310   .88213 
.69903   .88644 
.77578   .89074 

0.99101  9.99608 
.99118   .99615 
.99136   .99623 

•99!53   -99631 
.99170   .99638 

1.0091   0.00392 
.0089    .00385 

.0087   .00377 

.0085    .00369 
.0084   .00362 

82  19 

82  23 
82  28 
82  32 
82  37 

2.75 
.76 

•77 
.78 

•79 

778935  0.89150 
.86828   .89588 
.94799   .90026 
8.02849   .90463 
.10980   .90901 

7.85328  0.89505 

•93!57   -89936 
8.01065   .90367 

•09053   -90798 
.17122   .91229 

0.99186  9.99645 
.99202   .99652 
.99218   .99659 
.99233   .99666 
.99248   .99672 

1.0082   0.00355 
.0080    .00348 
.0079   .00341 
.0077   .00334 
.0076   .00328 

82  41 

82  45 
82  50 
82  54 
82  58 

2.80 
.81 
.82 

•ll 

8.19192  0.91339 
.27486   .91776 
.35862   .92213 
.44322   .92651 
.52867   .93088 

8.25273  0.91660 
.33506   .92091 
.41823   .92522 
.50224   .92953 
•58710   .93385 

0.99263  9.99679 
.99278   .99685 
.99292   .99691 
.99306   -99698 
.99320   .99704 

1.0074   0.00321 

.0073   .00315 
.0071   .00309 

.0070    .00302 
.0069   .00296 

83   02 
83   07 
83   II 

83   15 
83   19 

11 

•87 
.88 
.89 

8.61497  0.93525 
.70213   .93963 
.79016   .94400 
.87907   .94837 
.96887   .95274 

8.67281  0.93816 
*75940   .94247 
.84686   .94679 
•93520   .95"o 
9.02444   .95542 

0-99333  9-99709 
.99346   .99715 

•99359   -99721 
.99372   .99726 
•99384   -99732 

1.0067   0.00291 
.0066   .00285 
.0065   .00279 
.0063   .00274 
.0062    .00268 

83   23 

83   27 

ii£ 

83  38 

2.90 
.91 
.92 
•93 
•94 

9.05956  0.95711 
.15116   .96148 
.24368   .96584 
•33712   .97021 
.43149   .97458 

9.11458  0.95974 
.20564   .96405 
.29761   .96837 
.39051   .97269 
.48436   .97701 

0.99396  9-99737 
.99408   .99742 
.99420   .99747 
•99531   -99752 
•99443   -99757 

1.0061   0.00263 
.0060   .00258 
.0058   .00253 
.0057   .00248 
.0056   .00243 

83  42 
83  46 
83  50 
83  53 
83  57 

1 

•99 

9.52681  0.97895 
.62308   .98331 
.72031   .98768 
.81851   .99205 
.91770   .99641 

9.57915  0.98133 
.67490   .98565 
.77161   .98997 
.86930   .99429 
.96798   .99861 

0-99454  9-99762 
.99464   .99767 
-99475   -99771 
•99485   -99776 
.99496   .99780 

1.0055   0.00238 
.0054   .00233 
.0053   .00229 
.0052   .00224 

.0051     .00220 

84  oo 
84  04 
84  08 
84  ii 
84  15 

3.00 

10.01787   1.00078 

10.06766  1.00293 

0.99505  9-99785 

1.0050    O.O02I5 

84  18 

SMITHSONIAN   TABLES. 


TABLE  1  6  (continued). 
HYPERBOLIC  FUNCTIONS. 


47 


u 

sinh.  u 

cosh,  u 

tanh.  u 

coth.  u 

gd.  U 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

Nat.     Log. 

3-0 
.1 

.2 

•3 
4 

10.0179  1.00078 
11.0765   .04440 
12.2459   .08799 

!3-5379   -1315$ 
14.9654   .17509 

10.0677  1.00293 
11.1215   .04616 
12.2866   .08943 
I3-5748   .13273 
14.9987   .17605 

0.99505  9-99785 

•99595   -99824 
.99668   .99856 
.99728   .99882 
•99777   -99903 

1.0050   0.00215 
.0041    .00176 
.0033    .00144 
.0027    .00118 
.0022     .00097 

84°  1  8' 

84  50 

85  20 

85  47 
86  ii 

3-5 

2 

•9 

16.5426  1.21860 
18.2855   .26211 
20.2113   .30559 

22.3394   -34907 
24.6911   .39254 

16.5728  1.21940 
18.3128   .26275 
20.2360   .30612 
22.3618   -34951 
24-7113   -39290 

0.99818  9.99921 
.99851   .99935 
-99878   -99947 
.99900   .99957 
.99918   .99964 

I.OOlS    O.OOO79 
.OOI5     .00065 
.0012     .00053 

.0010   .00043 

.0008     .00036 

8632 
86  52 
87  10 
87  26 
87  41 

4.0 
.1 

.2 

•3 

4 

27.2899  1.43600 
30.1619   .47946 
33-3357   -52291 
36.8431   .56636 
40.7193   .60980 

27.3082  1.43629 
30.1784   .47970 

33-3507   -52310 
36.8567   .56652 
40.7316   .60993 

0-99933  9-99971 
•99945   -99976 
•99955   -99980 
•99963   -99984 
•99970   .99987 

I.OOO7    O.OOO29 
.0005     .00024 
.OOO4     .OOO2O 
.OOO4     .OOOl6 
.OOO3     .OOOI3 

87  54 
88  06 
88  17 
88  27 
88  36 

4-5 

'.$ 
•9 

45.0030  1.65324 
49-7371   -69668 
54.9690   .74012 
60.7511   .78355 
67.1412   .82699 

45.0141  1.65335 
49-7472   -69677 
54.9781   .74019 
60.7593   -78361 
67.1486   .82704 

0-99975  9-99989 
.99980   .99991 
.99983   .99993 
.99986   .99994 
.99989   .99995 

1.0002    0.000  1  1 
.OOO2     .OOOO9 
.OOO2     .00007 
.0001     .00006 

.0001    .00005 

88  44 
88  51 
88  57 
8903 
8909 

5-o 

74.2032  1.87042 

74.2099  1.87046 

0.99991  9-99996 

i.oooi   0.00004 

89  14 

Table  17.    Factorials. 

See  table  15  for  logarithms  of  the  products  1.2.3.  •  •  •  «  from  i  to  roo. 
See  table  31  for  log.  («+/)  for  values  of  «  between  i.ooo  and  2.000. 


« 

7 

n  : 

n:  =  i.  2.  3.  4  .  .  .  n 

n 

I 

i. 

i 

I 

2 

0-5 

2 

2 

3 

.16666  66666  66666  66666  66667 

6 

3 

4 

.04166  66666  66666  66666  66667 

24 

4 

5 

•00833  33333  33333  33333  33333 

120 

5 

6 

0.00138  88888  88888  88888  88889 

720 

6 

7 

.00019  84126  98412  69841  26984 

5040 

7 

8 

.00002  48015  87301  58730  15873 

40320 

8 

9 

10 

.00000  27557  31922  39858  90653 
.00000  02755  73192  23985  89065 

3  62880 
36  28800 

9 
10 

ii 

o.ooooo  00250  52108  38544  17188 

399  16800 

ii 

12 

13 

14 
15 

.00000  00020  87675  69878  68099 

.00000  ooooi  60590  43836  82161 
.00000  ooooo  11470  74559  77297 
.00000  ooooo  00764  71637  31820 

4790  01600 
62270  20800 
8  71782  91200 
130  76743  68000 

12 
13 
14 
15 

16 

17 

o.ooooo  ooooo  00047  79477  33239 
.ooooo  ooooo  00002  81145  72543 

2092  27898  88000 
35568  74280  96000 

16 
J7 

18 

.ooooo  ooooo  ooooo  15619  20697 

6  40237  37057  28000 

18 

19 

.ooooo  ooooo  ooooo  00822  06352 

121  64510  04088  32OOO 

19 

:7 

20 

.ooooo  ooooo  ooooo  00041  10318 

2432  9O2OO  81766  4OOOO 

20 

SMITHSONIAN  TABLES. 


48 


TABLE  18. 
EXPONENTIAL  FUNCTION. 


X 

logjo(^)      *x        *~x 

X 

logio(^)      ex        e-x 

0.00 
.01 

.02 

•03 

.04 

O.OOOOO     I.OOOO     I.OOOOOO 

.00434    .0101   0.990050 

.00869      .0202      .980199 

.01303    •°3°5    -970446 
.01737    .0408    .960789 

0.50 

•51 

•52 

•53 
•54 

0.21715    1.6487    0.606531 
.22149     -6653     .600496 
.22583     .6820     .594521 
.23018     .6989     .588605 
.23452     .7160     .582748 

0.05 
.06 

.07 
.08 
.09 

0.02171    I-°5I3   0.951229 
.02606    .0618    .941765 
.03040    .0725    .932394 
.03474    .0833    .923116 
.03909    .0942    .9I3931 

•s 

% 

•59 

0.23886    1.7333    0.576950 
.24320     .7507     .571209 
.24755     -7683     .565525 
.25189     .7860     .559898 
.25623     .8040     .554327 

O.IO 

.11 

.12 

•13 
.14 

0.04343   1.1052   0.904837 
.04777    .1  163    .895834 
.05212    .1275    .886920 
.05646    .1388    .878095 
.06080    .1503    .869358 

0.60 
.61 
.62 

•63 
.64 

0.26058    I.822I    0.548812 

.26492    .8404    .5433  5  1 

.26926   .8589   .537944 
.27361    .8776   .532592 
•27795   -8965   .527292 

°:ll 
:li 

•19 

0.06514   1.1618   0.860708 
.06949    .1735    .852144 
.07383    .1853    .843665 
.07817    .1972    .835270 
.08252    .2092    .826959 

°:I1 
.67 

.68 
•69 

0.28229   1.9155   0.522046 
.28663    .9348    .516851 

.29098   .9542   .511709 

•29532    -9739    .506617 
.29966    .9937    .501576 

0.20 
.21 

.22 

•23 
.24 

0.08686   1.2214   0.818731 
.09120    .2337    .810584 
•°9554    .2461    .802519 
.09989    .2586    -794534 
.10423    .2712    .786628 

0.70 
•71 

•72 
•73 
•74 

0.30401   2.0138   0.496585 
.30835    .0340    49l644 
.31269    .0544    .486752 
•3!703    -0751    .481909 
.32138    .0959    .477H4 

°3 

3 

.29 

0.10857   1.2840   0.778801 
.11292    .2969    .771052 
.11726    .3100    .763379 
.12160    .3231    .755784 
•I2595    -3364    .748264 

*% 

•77 
.78 
•79 

0.32572   2.1170   0.472367 
.33006    .1383    .467666 
.33441    .1598    .463013 
.33875    .1815    .458406 
.34309    .2034    453845 

0.30 
•31 
•32 
•33 

•34 

0.13029   1-3499   0.740818 
.13463    .3634    -733447 
•i3897    -377I    .726149 
.14332    .3910    .718924 
.14766    .4049    .711770 

0.80 
.81 
.82 

•83 

.84 

0.34744   2.2255   0.449329 
.35178    .2479    444858 
.35612    .2705    440432 
.36046    .2933    436049 
.36481    .3164    43I7n 

$ 
P 

•39 

0.15200   1.4191   0.704688 
•T5635    -4333    .697676 
.16069    .4477    .690734 
.16503    .4623    .683861 
.16937    .4770    .677057 

°!I 

:! 
.89 

0.36915   2.3396   0.427415 
•37349    -3632    .423162 
.37784    -3869    418952 
.38218    .4109    .4147^3 
.38652    .4351    .410656 

0.40 
.41 

.42 
•43 
.44 

0.17372   1.4918   0.670320 
.17806    .5068    .663650 
.18240    .5220    .657047 
•J8675    -5373    -650509 
•I9J09    -5527    .644036 

0.90 
.91 
.92 

•93 

.94 

0.39087    2.4596   0.406570 
.39521    .4843    402524 

•39955    -5093    -398519 
.40389.    .5345    .394554 
.40824    .5600    .390628 

0-45 
.46 

•47 
.48 

49 

0-I9543   1-5683   0.637628 
.19978    .5841    .631284 
.20412    .6000    .625002 
.20846    .6161    .618783 
.21280    .6323    .612626 

o-95 
.96 

•97 
.98 

•99 

0.41258   2.5857   0.386741 
.41692    .6117    .382893 
.42127    .6379    .379083 
.42561    .6645    .37  5311 
.42995    .6912    .371577 

0.50 

0.21715   1.6487   0.606531 

1.  00 

0.43429   2.7183   0.367879 

SMITHSONIAN  TABLES. 


TABLE  1  8  (continued). 

EXPONENTIAL   FUNCTION, 


49 


X 

Iog10(£x)     ez        e—x 

X 

logic  (fx  )      ex         e~x 

1.  00 
.OI 
.02 

•03 
.04 

0.43429    2.7183    0.367879 
.43864     .7456     .364219 
.44298     .7732     .360595 
.44732     .8011     .357007 
.45167     .8292     -353455 

1.50 

•51 

.52 
•53 
•54 

0.65144    44817    0.223130 
•65578     -5267     .220910 
.66013     .5722     .218712 
.66447     .6182     .216536 
.66881     .6646     .214381 

'•°5 
.06 
.07 
.08 
.09 

0.45601     2.8577    0.349938 
.46035     .8864     .346456 

.46470    .9154    .343°°9 
.46904    .9447    -339596 
•47338    -9743    -336216 

^55 
•56 

% 

•59 

0-67316    4-7II5    0.212248 
•67750     .7588     .210136 
.68184     .8066     .208045 

.68619    .8550    .205975 
•69053    .9037    .203926 

1.  10 

.11 

.12 

•13 
.14 

0.47772   3.0042   0.332871 
.48207    .0344    .329559 
.48641    .0649    .326280 

•49075    -0957    .323033 
.49510    .1268    .319819 

i.  60 
.61 
.62 

•63 
.64 

0.69487   4.9530   0.201897 
.69921   5.0028    .199888 
•70356    -0531    -197899 
.70790    .1039    .195930 
.71224    .1552    .193980 

':!3 
:,1 

.19 

0.49944   3.1582   0.316637 
.50378    .1899    .313486 
.50812    .2220    .310367 
.51247    .2544    .307279 
.51681    .2871    .304221 

1.65 
.66 

.69 

0.71659   5.2070   0.192050 
•72093    .2593    .190139 
.72527    .3122    .188247 
.72961    .3656    .186374 
•73396    4195    .184520 

1.20 
.21 
.22 

'23 
.24 

0.52115   3.3201   0.301194 
•52550    -3535    .298197 
.52984    .3872    .295230 
.53418    .4212    .292293 
•53853    4556    -289384 

1.70 

.71 

.72 

•73 
•74 

0-73830   5-4739   0.182684 
.74264    .5290    .180866 
.74699    .5845    .179066 
.75133    .6407    .177284 
•75567    .6973    -175520 

.26 
.27 
.28 
.29 

0.54287    3-4903   0.286505 
.54721    .5254    .283654 
.55155    .5609    .280832 
•55590    -5966    .278037 
.56024    .6328    .275271 

•76 

•77 
.78 

•79 

0.76002   5.7546   0.173774 
.76436    .8124    .172045 
.76870    .8709    .170333 
77304    -9299    -168638 
•77739    -9895    .166960 

I.30 
•31 

•32 

•33 
•34 

0.56458   3.6693   0.272332 
•56893    .7062    .269820 

•57327    -7434    -267135 
.57761    .7810    .264477 
.58195    .8190    .261846 

i.  80 
.81 
.82 

•83 

.84 

0.78173   6.0496   0.165299 
.78607    .1104    .163654 
.79042    «I7I9    .162026 
.79476    -2339    -I6of4 
.79910    .2965    .158817 

i-3S 
•36 

% 

•39 

0.58630   3.8574   0.259240 
.59064    .8962    .256661 
.59498    .9354    .254107 

•59933    -9749    -251  579 
.60367   4.0149    .249075 

1.85 
.86 

•87 
.88 
.89 

0.80344   6.3598   0.157237 
.80779    .4237    .155673 
.81213    .4883    .154124 
•81647    -5535    -152590 
.82082    .6194    .151072 

1.40 
.41 

.42 
•43 
•44 

0.60801    4-0552   0.246597 
.61236    .0960    .244143 
.61670    .1371    .241714 
.62104    .1787    .239309 
.62538    .2207    .236928 

1.90 
.91 
.92 
•93 
•94 

0.82516   6.6859   0.149569 
.82950    -7531    .148080 
•83385    -8210    .146607 
.83819    .8895    .i45I48 
•84253    -9588    .143704 

i-45 
.46 

•47 
.48 

•49 

0.62973   4-2631   0.234570 
.63407    .3060    .232236 
.63841    .3492    -229925 
.64276    .3929    .227638 
.64710    .4371    -225373 

'$ 
IS 

•99 

0.84687   7.0287   0.142274 
.85122    .0993    .140858 

.85556    .1707    .139457 
.85990    .2427    .138069 
•86425    .3155    .136695 

1.50 

0.65144   4-4817   0.223130 

2.00 

0.86859   7-3891   0.135335 

SMITHSONIAN  TABLES. 


TABLE  1Q  (continued). 
EXPONENTIAL  FUNCTION 


X 

logio  («*)     «*       «-* 

•*• 

logw  ('*)     <x        e~x 

2.00 
.01 
.02 

•03 
.04 

0.86859  7.3891  0.135335 
.87293   .4633   .133989 
.87727   -5383   -132655 

.88162    .6141    .131336 
.88596    .6906    .130029 

2.50 
•51 
•52 
•53 

•54 

1.08574   I2.I82     0.082085 
.09008     .305      .081268 
.09442     .429      .080460 
.09877     .554      -079659 
.10311     .680      .078866 

2.05 
.06 
.07 
.08 
.09 

0.89030   7-7679   0.128735 
.89465   .8460   .127454 
.89899   .9248   .126186 
•9°333   8.0045    -124930 
.90768    .0849    .123687 

2:ll 
:P 

•59 

1.10745   12.807     0.078082 
.11179     .936      .077305 
.11614   13.066      .076536 
.12048     .197      -075774 
.12482     .330      .075020 

2.10 
.11 
.12 

•13 
.14 

0.91202   8.1662   0.122456 
.91636    .2482    .121238 
.92070    -3311    .120032 
.92505    .4149    .118837 
.92939    .4994    .117655 

2.60 
.61 
.62 

3 

1.12917    13.464     0.074274 

•I335I    -599     .073535 
•I3785    .736     .072803 
.14219    .874     .072078 
.14654   14.013     .071361 

2:ll 
3 

.19 

0-93373   8.5849   0.116484 
.93808    .6711    .115325 
.94242    .7583    .114178 
.94676    .8463    .113042 
•95IJo    .9352    .111917 

^ 

•67 

.68 
.69 

1.15088   14.154    0.070651 
.15522    .296     .069948 
•:5957    -440     .069252 
•16391    .585     -068563 
.16825    .732     .067881 

2.  2O 
.21 

.22 

•23 
.24 

0-95545   9.0250   0.110803 
•95979    -JI57    .109701 
.96413    .2073    .108609 
.96848    .2999    .107528 
.97282    .3933    .106459 

2.70 
•7i 
-72 
•73 
-74 

1.17260   14.880    0.067206 
.17694   15.029     .066537 
.18128    .180     .065875 
•!8562    .333     .065219 
.18997    .487     -064570 

2.1 
2 

.29 

0.97716   9.4877   0.105399 
.98151    .5831    .104350 
.98585    .6794    .103312 
.99019    .7767    .102284 
•99453    -8749    .101266 

2-75 
.76 

•77 
.78 

•79 

1.19431   15.643    0.063928 
.19865    .800     .063292 
.20300    .959     .062662 
.20734   16.119     .062039 
.21168    .281     .061421 

2.30 
•3i 
•32 
•33 

•34 

0.99888   9.9742   0.100259 
1.00322   10.074     .099261 
.00756    .176     .098274 
.01  191    .278     .097296 
.01625    .381     .096328 

2.80 
.81 
.82 

fe 

1.21602   16.445    0.060810 
.22037    .610     .060205 
.22471    .777     .059606 
.22905    .945     .059013 
.23340   17.116     .058426 

Ml 
$ 

•39 

1.02059   10.486    0.095369 
.02493    -591     .094420 
.02928    .697     .093481 
.03362    .805     .092551 
.03796    .913     .091630 

•8 

.87 

.88 
-89 

1-23774   17.288    0.057844 
.24208    .462     .057269 
.24643    .637     .056699 
.25077    .814     .056135 
•2551!    -993     -055576 

2.40 

.41 
.42 
•43 
•44 

1.04231   11.023    0.090718 
.04665    .134     .089815 
.05099    .246     .088922 
•05534    -359     .088037 
.05968    .473     .087161 

2.90 
.91 
.92 
•93 
•94 

1.25945   18.174    0.055023 
.26380    .357     .054476 
.26814    .541     -053934 
.27248    .728     -053397 
.27683    .916     .052866 

2-45 
.46 

$ 

.49 

1.06402   11.588    0.086294 
.06836    .705     .085435 
.07271    .822     .084585 
.07705    .941     .083743 
.08139   12.061     .082910 

2H 

a 

.99 

1.28117   19.106    0.052340 
.28551    .298     .051819 
.28985    .492     .051303 
.29420    .688     -050793 
.29854    .886     .050287 

2.50 

1.08574   12.182    0.082085 

3-oo 

1.30288   20.086    0.049787 

SMITHSONIAN  TABLES. 


TABLE    1  8  (continued). 
EXPONENTIAL  FUNCTION. 


X 

logio(^)      ex        e-x 

X 

logio(^)      «x        e-x 

3.00 

.01 

.02 

•°3 
.04 

1.30288    20.086    0.049787 
.30723      .287     .049292 
.31157      .491     .048801 
.31591      .697     .048316 
.32026      .905     .047835 

3-50 
•51 

•52 

•53 
•54 

1.52003   33«II5   0.030197 

.52437      .448     .029897 
.52872      .784     -029599 

•533°6   34-124    -029305 
.53740     .467    .029013 

3-05 
.06 
.07 
.08 
.09 

1.32460    21.115    0.047359 
.32894      .328     .046888 
•33328      .542     .046421 
•33763      .758     -045959 
•34197     -977    -045502 

3:H 
31 

•59 

I-54I75   34-8i3   0.028725 
.54609   35.163    .028439 
•55043     -5!7    .028156 
•55477     -874    .027876 
.55912   36.234    .027598 

3.10 
.11 

.12 

•13 
.14 

1.34631    22.198   0.045049 
.35066     .421    .044601 
.35500     .646    .044157 
•35934     -874    -043718 
.36368   23.104    .043283 

3.60 
.61 

.62 

4 

1.56346   36.598   0.027324 
.56780     .966    .027052 
•57215   37-338    .026783 
.57649     •7I3    .026516 
.58083   38.092    .026252 

3:!1 
3 

.19 

1.36803   23.336   0.042852 
•37237     -571    .042426 
.37671     .807    .042004 
.38106   24.047    .041586 
.38540     .288    .041172 

^ 

.67 

.68 
.69 

i  -585!  7   38.475   0.025991 
.58952     .861    .025733 
•59386   39.252    .025476 
.59820     .646    .025223 
.60255   40.045    .024972 

3.20 

.21 

.22 

•23 
.24 

1.38974   24.533   0.040762 

•39409     -779    -040357 
.39843   25.028    .039955 
.40277     .280    .039557 
.40711     .534    .039164 

3-70 
-71 

•72 
•73 
•74 

1.60689   40.447   0.024724 
.61123     .854    .024478 
.61558   41.264    .024234 
.61992     .679    .023993 
.62426   42.098    .023754 

3-25 
.20 
.27 
.28 
.29 

1.41146   25.790   0.038774 
.41580   26.050    .038388 
.42014     .311    .038006 
.42449     .576    .037628 
.42883     .843    .037254 

3-75 
.76 

$ 

•79 

1.62860   42.521   0.023518 
•63295     .948    .023284 
•63729   43-38o    -023052 
.64163     .816    .022823 
.64598   44.256    .022596 

3-3° 
•31 

•32 

•33 
•34 

1.43317    27.113   0.036883 
•437  5  i     .385    -036516 
.44186     .660    .036153 
.44620     .938    .035793 
.45054   28.219    .035437 

3-8o 
.81 
.82 

U 

1.65032   44-701   0.022371 
.65466   45.150    .022148 
.65900     .604    .021928 
•66335   46.063    .021710 
.66769     .525    .021494 

^ 
% 

•39 

1.45489   28.503   0.035084 
.45923     .789    .034735 
.46357    29.079    .034390 
.46792     .371    .034047 
.47226     .666    .033709 

3il 

.87 
.88 
.89 

1.67203   46.993   0.021280 
.67638   47-465    .021068 
.68072     .942    .020858 
.68506   48.424    .020651 
.68941     .911    .020445 

3-40 
.41 
.42 
•43 

•44 

1.47660   29.964   0.033373 
.48094   30.265    .033041 
.48529     .569    .032712 
.48963     .877    .032387 
•49397    3I-l87    -032065 

3-90 
.91 
.92 
•93 
•94 

1.69375   49.402   0.020242 
.69809     .899    .020041 
.70243   50.400    .019841 
.70678     .907    .019644 
.71112   51.419    .019448 

3-45 
.46 

•47 
.48 

•49 

1.49832   31.500   0.031746 
.50266     .817    .031430 
.50700   32.137    .031117 
.51134     .460    .030807 
.51569     .786    .030501 

3-95 
.96 

•99 

1.71546   51.935   0.019255 
.71981    52.457    .019063 
.72415     .985    .018873 
.72849   53.517    .018686 
.73283   54-055    .018500 

3-50 

1.52003   33-115   0.030197 

4.00 

I-737I8   54.598   0.018316 

SMITHSONIAN  TABLES. 


TABLE     1  8   (continued. 
EXPONENTIAL    FUNCTION 


X 

logio(^)      **        e-x 

X 

logio(^)      e*         e-x 

4.00 

.01 

.02 

•03 
.04 

1.73718    54.598    0.018316 
.74i52   55-I47    -018133 

.74586   .701   .017953 

.75021   56.261    .017774 

.75455    .826   .017597 

4.50 
•51 

.52 

•53 

•54 

1  -95433   90.017   0.011109 
.95867     .922    .010998 
.96301    91.836    .010889 
•96735   92-759    .010781 
.97170   93.691    .010673 

4-05 
.00 
.07 
.08 
.09 

4.10 
.11 
.12 

•13 
.14 

1.75889   57-397   0.017422 
.76324     .974    .017249 
.76758   58.557    .017077 
.77192   59.145    .016907 
.77626     .740    .016739 

1.78061   60.340   0.016573 
•78495     -947    .016408 
.78929   61.559    .016245 
.79364   62.178    .016083 
.79798     .803    .015923 

4-55 
•56 

% 

•59 

4.60 
.61 
.62 

•63 
.64 

1.97604   94.632   0.010567 
.98038   95.583    .010462 
•98473   96.544    .010358 
.98907   97,514    .010255 
.99341   98.494    .010153 
i 

1  -9977  5   99-484   0.010052 

2.OO2IO    100.48       .009952 
.00644    101-49       .009853 
.01078    IO2.5I       .009755 
.01513    103.54       .009658 

4-15 

:is 

.19 

1.80232    63.434   0.015764 
.80667    64.072    .015608 
.81101     .715    .015452 
•81535    65-366    .015299 
.81969   66.023    .015146 

4-65 
.66 

:§ 

2.OI947    104.58      0.009562 
.02381    105.64       .009466 
.O2§l6    106.70       .009372 
.03250    107.77       .009279  ' 
.03684    108.85       .009187 

4.20 

.21 

.22 

•23 

.24 

1.82404   66.686   0.014996 
.82838   67.357    .014846 
.83272   68.033    .014699 
.83707     .717    .014552 
.84141   69.408    .014408 

4.70 
•71 
•72 

•73 
•74 

2.O4II8    109.95      O.OO9O95 
.04553    HI.05       .009005 
.04987    112.17       .008915 
.05421    II3-3O       .008826 
.05856    114.43       .008739 

4.25 
.26 

-.3 

.29 

I-84575   70-105   0.014264 
.85009     .810    .014122 
.85444   71.522    .013982 
.85878   72.240    .013843 
.86312     .966    .013705 

4-75 
•76 

$ 

•79 

2.06290    115.58      0.008652 
.06724    II6.75       .008566 
.07158    117.92       .008480 
.07593    119.10       .008396 
.08027    120.30       .008312 

4.30 

•31 

•32 
•33 
•34 

1.86747   73-7oo   0.013569 
.87181   74-440    .013434 
.87615   75-l89    .0133°° 
.88050     .944    .013168 
.88484   76.708    .013037 

4.80 
.81 

.82 

•83 

.84 

2.08461    121.51      O.008230 
.08896    122-73       .008148 
.09330    123.97       .008067 
.09764    125.21       .007987 
.10199    126.47       .007907 

4-35 
•36 

i 

•39 

1.88918   77.478   0.012907 
•89352   78-257    .012778 
.89787   79.044    .012651 
.90221   79.838    .012525 
•90655   80.640    .012401 

4-85 
.86 
.87 
.88 
.89 

2.10633    127.74      0.007828 
.11067  '   I29.O2       .OO775O 
.11501    130.32       .007673 
.11936    131.63       -007597 
.12370    132.95       .007521 

4.40 
.41 
.42 
•43 
•44 

1.91090   81.451   0.012277 
.91524   82.269    .012155 
.91958   83.096    .012034 
•92392     -931    .011914 
.92827   84.775    .011796 

4-90 
.91 
.92 
•93 
•94 

2.12804    134.29      0.007447 
.13239    135-64       .007372 

•13673   T37-oo     .007299 
.14107   138.38     .007227 
.14541   139.77     .007155 

4-45 
.46 

•47 
.48 
•49 

1.93261   85.627   0.011679 
•93695   86.488    .01  1  562 
.94130   87.357    .011447 
.94564   88.235    .011333 

.94998     89.121      .011221 

4-95 
.96 

•97 
.98 

•99 

2.14976   141.17    0.007083 
.15410   142.59     .007013 
.15844   144-03     -006943 
.16279   145-47     .006874 
.16713   146.94     .006806 

4-5° 

1  -95433   90-017   0.011109 

S-oo 

2.17147   148.41    0.006738 

SMITHSONIAN  TABLES. 


TABLE  1  8  (continued). 
EXPONENTIAL    FUNCTION. 


53 


X 

logio(^)              ex                 e-x 

X 

Iog10('*)              #*                  e-* 

5.00 

.01 

.02 

-03 
.04 

2.17147          148.41          0.006738 
.17582         149.90           .006671 
.18016         151-41            .006605 
.18450         152.93           -006539 
.18884         15447           .006474 

5-o 

.2 

•3 
•4 

2.17147          148.41          0.006738 
.21490          164.02            .006097 
•25833          181.27            .005517 
.30176          200.34            .004992 
•345*9        221.41          .004517 

5:0°! 

.07 
.08 
.09 

2.19319         156.02         0.006409 
•J9753        '57-59         .006346 
.20187        I59«I7          .006282 
.20622        160.77          .006220 
.21056        162.39         .006158 

1 

.8 
•9 

2.38862        244.69        0.004087 
.43203        270.43          .003698 
.47548        298.87          .003346 
-51891        330-30         .003028 
.56234       365.04         .002739 

5.10 
.11 

.12 

•13 

.14 

2.21490        164.02        0.006097 
.21924        165.67          .006036 
.22359        !67-34          -005976 
.22793        169.02          .005917 
.23227        170.72          .005858 

6.0 
.1 

.2 

•3 
•4 

2.60577        40343       0.002479 
.64920       445.86         .002243 
.69263       492.75         .002029 
.73606       544-57          .001836 
.77948       601.85         .001662 

5-15 
.16 

.19 

2.23662        172.43        0.005799 
.24096        174.16          .005742 
.24530        175.91          .005685 
.24965        177.68          .005628 
•25399        179-47          -005572 

6i 
•I 

•9 

2.82291        665.14       0.001503 
.86634       735.  10         .001360 
.90977        812.41          .001231 
•95320       897.85         .001114 
.99663       992.27         .001008 

5.20 
.21 
.22 

'         -23 

.24 

2.25833        181.27        0.005517 
.26267        183.09          .005462 
.26702        184.93          -005407 
.27136        186.79          -005354 
.27570        188.67          .005300 

7.0 
.1 

.2 

•3 

•4 

3.04006      1096.6         0.000912 

.08349         1  2  1  2.O                .OOO8  2  5 
.12692         1339.4                .000747 

•I7°35      1480.3           .000676 
.21378      1636.0           .000611 

5-25 

.20 
.27 
.28 
.29 

2.28005        190.57        0.005248 
.28439        192.48          .005195 
.28873        19442          .005144 
.29307        196.37          .005092 
.29742        198.34          .005042 

7:l 
% 

•9 

3.25721      1808.0         0.000553 
.30064      1998.2           .000500 
.34407      2208.3           -000453 
.38750      2440.6           .000410 
.43093      2697.3           .000371 

5-30 
•31 
•32 

•33 

•34 

2.30176        200.34        0.004992 
.30610        202.35          .004942 
.31045        204.38          -004893 
.31479        206.44          .004844 
.31913        208.51          .004796 

8.0 
.1 

.2 

•3 
•4 

3.47436      2981.0         0.000335 
•5T779      3294-5           .000304 
.56121      3641.0           .000275 
.60464      4023.9           .000249 
.64807      4447.1            .000225 

*$ 

s 

•39 

2.32348        210.61        0.004748 
.32782        212.72          .004701 
.33216        214.86          .004654 
.33650        217.02          .004608 
.34085        219.20          .004562 

8:i 
3 

•9 

3.69150      4914.8         0.000203 
•73493      543J-7           .000184 
.77836      6002.9           .000167 
.82179      6634.2           .000151 
.86522      7332.0           .000136 

540 
.41 
.42 
•43 
•44 

2.34519        221.41        0.004517 
-34953        223.63         .004472 
.35388        225.88          .004427 
.35822        228.15         -004383 
.36256        230.44         .004339 

9.0 
.1 

.2 

•3 

•4 

3.90865      8103.1          0.000123 

.95208        8955.3                .OOOI  12 

.99551      9897.1            .000101 
4.03894     10938.              .000091 
.08237    12088.            .000083 

5-45 
.46 

•47 
.48 

•49 

2.36690        232.76       0.004296 
•37125        235.10         .004254 
•37559        237.46         .004211 
•37993        239.85          .004169 
.38428        242.26          .004128 

gl 

i 

•9 

4.12580    13360.          0.000073 
.16923     14765.              .000068 
.21266     16318.              .000061 
.25609     18034.              .000055 
.29952     19930.              .000050 

5-50 

2.38862        244.69        0.004087 

10.0 

4.34294   22026.         0.000045 

SMITHSONIAN  TABLES. 


54 


TABLE  1 9. 
EXPONENTIAL  FUNCTIONS. 

Value  of  e^  and  e-**  and  their  logarithms. 


Jf 

*** 

log  X 

,-*' 

log  e~** 

0.1 

I.OIOI 

0.00434 

0.99005 

1.99566 

2 

1.0408 

01737 

96079 

98263 

3 

1.0942 

03909 

9*393 

96091 

4 

I-I73S 

06949 

85214 

93°5! 

5 

1.2840 

10857 

77880 

89M3 

0.6 

'•4333 

O.I5635 

0.69768 

1.84365 

7 

1.6323 

21280 

61263 

78720 

8 

1.8965 

27795 

52729 

72205 

9 

2.2479 

35T78 

44486 

64822 

1.0 

2.7183 

43429 

36788 

56571 

1.1 

2 

3-3535 
4.2207 

0.52550 
62538 

0.29820 
23693 

1.47450 
37462 

3 

5-4I9S 

73396 

18452 

26604 

4 

7.0993 

85122 

14086 

14878 

5 

94877 

97716 

10540 

02284 

1.6 

1.2936  X  10 
1.7993 

1.11179 
255" 

0.77305  X  io-1 

555/6   •« 

I.8882I 
74489 

8 

2-5534  ;; 

40711 

39l64 

59289 

9 

2.0 

54598  •• 

56780 
737i8 

27052   •« 
18316   " 

43220 
26282 

2.1 

8.2269  " 

1.91524 

0.12155   " 

2.08476 

2 

1.2647  X  io2 

2.10199 

79071  X  IO-2 

3.89801 

3 

1.9834  •« 

29742 

50418   " 

70258 

4 

3-1735  " 

5oi54 

315" 

49846 

5 

5.1801  " 

7H34 

19305 

28566 

2.6 

7 

8.6264  " 

1.4656  X  io3 

2.93583 
3.16601 

0.11592   " 

68233  X  10-8 

3-06417 
4-83399 

8 

2.5402   " 

40487 

39367 

595  1  3 

9 

44918   " 

65242 

22263    « 

34758 

3-o 

8.1031   " 

90865 

I234I 

09135 

3.1 

1.4913  X  10* 

4-17357 

0.67055  X  io-4 

5.82643 

2 

2.8001 

44718 

35713 

55282 

3 

5-3637 

72947 

18644   " 

27053 

4 

1.0482  X  io5 

5.02044 

95402  X  io~5 

6-97956 

5 

2.0898   " 

32011 

47851   " 

67989 

3.6 

4.2507 

5.62846 

0.23526   " 

6.37154 

I 

8.8205 
1.8673  X  icfi 

94549 
6.27121 

H337   " 
53553  X  io-« 

_0545' 
7.72879 

9 

4.0329 

60562 

24796 

39438 

4.0 

8.8861 

94871 

11254   « 

05129 

4-1 

1.9975  X  io7 

7.30049 

0.50062  X  io—  7 

5.69951 

2 

3 

1.0718  X  io8 

66095 
8.03010 

21830   « 

93303  X  IO-8 

33905 
9.96990 

4 

2.5582   « 

40794 

39089  " 

59206 

5 

6.2296   « 

79446 

16052 

20554 

4.6 

1.5476  X  io9 

9.18967 

0.64614  X  io-* 

10.81033 

i 

3.9225   " 
1.0142  X  io10 

59357 
10.00614 

25494  " 

98595  X  io~10 

40643 
11.99386 

9 

2.6755   " 

42741 

37376   " 

57259 

5-o 

7.2005   « 

85736 

13888   " 

14264 

SMITHSONIAN  TABLES. 


TABLE  20. 
EXPONENTIAL   FUNCTIONS. 

n;  v 

Values  ol  6**  and B     *   and  their  logarithms. 


55 


X 

»r 

e** 

log  e** 

r-* 

logtf     ** 

1 

2-1933 

0.34109 

0-45594 

1.65891 

2 

4.8105 

.68219 

.20788 

.31781 

3 

1.0551  X  10 

1.02328 

.94780  X  io-1 

2.97672 

4 

2.3141 

-36438 

.43214 

.63562 

5 

5-0754     ' 

-70547 

.19703 

•29453 

6 

1.1132  X  io2 

2.04656 

0.89833  X  I0~2 

3-95344 

7 

2.4415     " 

.38766 

.40958 

.61234 

8 

5-3549       " 

•72875 

.18674          " 

.27125 

9 

1.1745  X  io* 

3.06985 

.85144  X  io~3 

4-93015 

10 

2.5760       « 

.41094 

.38820       " 

.58906 

11 

5.6498       " 

3-75203 

0.17700       " 

4.24797 

12 

1.2392  X  io4 

4-093  *  3 

.80700  X  io-4 

5.90687 

13 

2.7178       " 

.43422 

.36794       " 

•56578 

14 

5.9610       " 

•77532 

.16776 

.22468 

IS 

i.  3074  X  io5 

5.11641 

.76487  X  I0~5 

6.88359 

16 

'7 

2.8675       " 
6.2893       " 

.79860 

0.34873          " 
.15900          " 

6.54249 
.20140 

18 

1.3794  X  io6 

6.13969 

.72495  X  I  O-6 

7.86031 

1    19 

3.0254       « 

.48079 

•33°53 

.51921 

20 

6.6356       " 

.82188 

.15070 

.17812 

TABLE  21 . 
EXPONENTIAL  FUNCTIONS. 

V*;  _VS; 

Values  ol  6  *  *  and  6     *  *  and  their  logarithms. 


X 

** 

log  e  *  * 

r* 

_VTTB 

1 

1.5576 

0.19244 

0.64203 

L80756 

2 

2.4260 

.38488 

.41221 

.61512 

3 

37786 

•57733 

.26465 

.42267 

4 
5 

$8 

.76977 
.96221 

.16992 
.10909 

.23023 
•03779 

6 

14.277 

1-15465 

0.070041 

2.84535 

j 

22.238 

•34709 

.044968 

.65291 

9 

34.636 
53.948 

•53953 
•73198 

.028871 
.018536 

.46047 
.26802 

10 

84.027 

.92442 

.011901 

•07558 

11 

130.88 

2.11686 

0.0076408 

3.88314 

12 

203.85 
317-5° 

.3093° 
E4 

.0049057 
.0031496 

.69070 
.49826 

14 

494.52 

s 

.OO2O222 

•30582 

15 

770.24 

3 

.0012983 

•JI337 

16 

1199.7 

3.07907 

0.00083355 

4-92093 

I7 

1868.6 

.27151 

•00053517 

.72849 

18 

19 

20 

2910.4 

4533-1 
7060.5 

•46395 
•65639 
.84883 

.00034360 
.00022060 
.00014163 

.53605 
.34361 

SMITHSONIAN  TABLES. 


56     TABLES  22  AND  23.    EXPONENTIAL  FUNCTIONS  AND  LEAST  SQUARES. 

TABLE  22.  —Exponential  Functions. 
Value  of  e?  and  e~*  and  their  logarithms. 


X 

e* 

log^ 

e~* 

X 

e* 

log  e* 

e~x 

1/64 

1/32 

1.0157 
•0317 

0.00679 
•oi357 

0.98450 
.96923 

'/3 

1/2 

!-3956 
.6487 

0.14476 
.21715 

0.71653 
.60653 

1/16 

.0645 

.02714 

•93941 

3/4 

2.1170 

•32572 

•47237 

I/IO 

.1052 

•04343 

.90484 

i 

•7183 

.43429 

.36788 

i/9 

•1175 

.04825 

.89484 

5/4 

3-4903 

-54287 

.28650 

1/8 

i-I33I 

0.05429 

0.88250 

3/2 

4.4817 

0.65144 

0.22313 

i/7 

•1536 

.06204 

.86688 

7/4 

5-7546 

.76002 

•17377 

1/6 

.1814 

.07238 

.84648 

2 

7-3891 

.86859 

•'3534 

i/S 

.2214 

.08686 

.81873 

9/4 

9.4877 

.97716 

.10540 

i/4 

.2840 

.10857 

.77880 

5/2 

12.1825 

1.08574 

.08208 

TABLE  23.  -  Least  Squares. 
Values  of  P  =  -^f0  hx  tr-^*  d  (hx). 

This  table  gives  the  value  of  P,  the  probability  of  an  observational  error  having  a  value  posi- 
tive or  negative  equal  to  or  less  than  x  when  k  is  the  measure  of  precision,  P  =  ~C  *  f<hx^ 
d(hx).  For  values  of  the  inverse  function  see  the  table  on  Diffusion. 


hx 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

0.0 

.01128 

.02256 

•03384 

.04511 

•05637 

.06762 

.07886 

.09008 

.10128 

.1 

.11246 

.12362 

•13476 

•14587 

•15695 

.16800 

.17901 

.18999 

.20094 

.21184 

.2 

.22270 

•23352 

.24430 

.25502 

.26570 

•27633 

.28690 

.29742 

.30788 

.31828 

•3 

•4 

•32863 
.42839 

••33891 
•43797 

•34913 
•44747 

•35928 
.45689 

•36936 
.46623 

•3793s 
•47548 

.38933 
.48466 

.39921 
•49375 

.40901 
•50275 

.41874 
.51167 

0.5 

.6 

!6o3856 

.52924 
.61168 

•53790 
.61941 

•54646 
.62705 

•55494 
.63459 

•56332 
.64203 

.57162 
•64938 

.57982 
•65663 

.58792 
.66378 

•59594 
.67084 

•7 

.67780 

.68467 

.69143 

.69810 

.70468 

.71116 

•71754 

.72382 

.73001 

.73610 

.8 

.74210 

.74800 

•7538i 

•75952 

•76514 

.77067 

.77610 

.78144 

.78669 

.79184 

•9 

.79691 

.80188 

.80677 

.81156 

.81627 

.82089 

.82542 

.82987 

•83423 

.83851 

1.0 

.84270 

.84681 

.85084 

.85478 

•85865 

.86244 

.86614 

.86977 

•87333 

.87680 

.1 

.88021 

.88353 

.88679 

.88997 

.89308 

.89612 

.89910 

.90200 

.90484 

.90761 

.2 

.91031 

.91296 

•91553 

.91805 

.92051 

.92290 

•92524 

•92751 

.92973 

.93190 

•3 

•93401 

.93606 

•93807 

.94002 

.94191 

.94376 

•94556 

•947  3  1 

.94902 

.95067 

•4 

•95229 

•95385 

•95538 

•95686 

•95830 

•95970 

.96105 

.96237 

•96365 

.96490 

1.5 

.96611 

.96728 

.96841 

•96952 

•97059 

.97162 

•97263 

•9736o 

•97455 

•97546 

.6 

•97635 

.97721 

.97804 

.97884 

.97962 

.98038 

.98110 

.98181 

.98249 

•983,15 

.7 

•98379 

.98441 

.98500 

•98558 

.98613 

.98667 

.98719 

.98769 

.98817 

.98864 

.8 

.98909 

-98952 

•98994 

•99035 

.99074 

.99111 

.99147 

.99182 

.99216 

.99248 

•9 

.99279 

.99309 

•99338 

.99366 

.99392 

.99418 

•99443 

.99466 

.99489 

•995II 

2.0 

•99532 

-99552 

•99572 

•99591 

.99609 

.99626 

.99642 

.996# 

.99673 

.99688 

.1 

.99702 

•99715 

.99728 

.99741 

•99753 

.99764 

•99775 

•99785 

•99795 

.99805 

.2 

.99814 

.99822 

.99831 

.99839 

.99846 

•99854 

.99861 

.99867 

•99874 

.99880 

•3 

.99886 

.99891 

•99897 

.99902 

.99906 

.99911 

•999  i  5 

.99920 

.99924 

.99928 

•4 

-9993  i 

•99935 

.99938 

•99941 

•99944 

•99947 

.99950 

•99952 

•99955 

•99957 

2.5 

•99959 

.99961 

•99963 

.99965 

•99967 

•99969 

.99971 

•99972 

•99974 

•99975 

.6 

•99976 

•99979 

.99980 

.99981 

.99982 

•99983 

.99984 

•99985 

.99986 

•7 

.99987 

.99987 

.99988 

.99989 

.99989 

•99990 

.99991 

.99991 

•99992 

•99992 

.8 

•99992 

•99993 

•99993 

•99994 

•99994 

•99994 

•99995 

•99995 

•99995 

•99996 

•9 

•99996 

.99996 

•99996 

•99997 

•99997 

•99997 

.99997 

•99997 

•99997 

.99998 

3.0 

.99998 

•99999 

•99999 

1.  00000 

Taken  from  a  paper  by  Dr.  James  Burgess  'on  the  Definite  Integral  -^J Q  e~t!t  dt,  with  Ex. 
tended  Tables  of  Values.'    Trans.  Roy.  Soc.  of  Edinburgh,  vol.  xxxix,  1900,  p.  257. 


SMITHSONIAN  TABLES. 


TABLE  24. 


57 


LEAST  SQUARES. 

This  table  gives  the  values  of  the  probability  P,  as  defined  in  last  table,  corresponding  to  different  values  of 
xl  r  where  r  is  the  "  probable  error."    The  probable  error  r  is  equal  to  0.47694;  h. 


as 
r 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0.0 

O.I 
0.2 

o-3 

.00000 

•05378 
.10731 
.16035 

.00538 
.05914 
.11264 
.16562 

.01076 
.06451 
.11796 
.17088 

.01614 
.06987 
.12328 
.17614 

.02152 

•07523 
.12860 
.18138 

.02690 
.08059 

I339I 
.18662 

.03228 
•08594 
.13921 
.19185 

.03766 
.09129 

•I4451 
.19707 

•04303 
.09663 
.14980 
.20229 

.04840 
.10197 
•15508 
.20749 

0.4 

.21268 

.21787 

.22304 

.22821 

.23336 

.23851 

•24364 

.24876 

•25388 

.25898 

0.5 

.26407 

.26915 

.27421 

.27927 

.28431 

.28934 

•29436 

.29936 

.30435 

•30933 

0.6 

•3*43° 

•31925 

.32419 

.32911 

.33402 

.33892 

.34380 

.34866 

•35352 

0 

•35835 

0.7 

•3631  7 

.36798 

.37277 

•37755 

•38231 

•38705 

•39178 

.39649 

.40118 

.40586 

0.8 
0.9 

.41052 
.45618 

•4i5I7 
.46064 

.41979 
.46509 

.42440 
.46952 

.42899 
•47393 

•43357 
.47832 

.43813 
.48270 

.44267 
.48705 

.44719 
•49139 

.45169 
•49570 

1.0 

.50000 

.50428 

•50853 

•5I277 

.51699 

.52119 

•52537 

.52952 

.53366 

•53778 

i.i 

1.2 

i-3 

t"  188 
171 
942 

•54595 
•58558 
.62308 

.55001 
.58942 
.62671 

.55404 
•59325 
.63032 

.55806 
•59705 
•63391 

•56205 
.60083 
•63747 

.56602 
.60460 
.64102 

.56998 
.60833 
.64454 

•57391 
.61205 
.64804 

•57782 

-6i575 
.65152 

1.4 

.65498 

.65841 

.66182 

.66521 

.66858 

•67193 

.67526 

•67856 

.68184 

.68510 

1.5 

.68833 

•69155 

.69474 

.69791 

.70106 

.70419 

.70729 

.71038 

•71344 

.71648 

1.6 

.71949 

.72249 

.72546 

.72841 

•73134 

•73425 

•73714 

.74000 

.74285 

•74567 

i-7 

.74847 

•75124 

•75400 

•75674 

•75945 

.76214 

.76481 

.76746 

.77009 

.77270 

1.8 

.77528 

•77785 

.78039 

.78291 

.78542 

.78790 

•79036 

.79280 

.79522 

f 

.79761 

1.9 

•79999 

.80235 

.80469 

.80700 

.80930 

.81158 

.81383 

.81607 

.81828 

.82048 

2.0 

2.1 

2.2 
2-3 

.82266 

•84335 
.86216 
.87918 

.82481 

•84531 
•86394 
.88078 

.82695 
.84726 
•86570 
•?8237 

.82907 
.84919 
.86745 
.88395 

.83117 
.85109 
.8691  7 
.88550 

.83324 
.85298 
.87088 
.88705 

•8353° 
.85486 
.87258 
.88857 

.83734 
•85671 
.87425 
.89008 

.83936 

•85854 
.87591 

•89157 

•84137 
.86036 

•87755 
•89304 

2.4 

.89450 

•89595 

.89738 

.89879 

.90019 

•90157 

•90293 

.90428 

.90562 

.90694 

2.5 

.90825 

.90954 

.91082 

.91208 

•91332 

.91456 

•91578 

.91698 

.91817 

•9*935 

2.6 

.92051 

.92166 

.92280 

.92392 

•92503 

.92613 

.92721 

.92828 

.92934 

•93038 

2.7 

•93141 

•93243 

•93344 

•93443 

•93541 

•93638 

•93734 

.93828 

.93922 

.94014 

2.8 

.94105 

•94195 

.94284 

•94371 

.94458 

•94543 

.94627 

.94711 

•94793 

•94874 

2.9 

•94954 

•95°33 

.95111 

•95l87 

•95263 

•95338 

.95412 

.95484 

•95557 

.95628 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

3 

.95698 

.96346 

.96910 

•97397 

.97817 

.98176 

.98482 

•98743 

.98962 

.99147 

4 

.99302 

•99431 

•99539 

99627 

.99700 

.99760 

.99808 

.99848 

•99879 

.99905 

5 

.99926 

•99943 

.99956 

.99966 

•99974 

.99980 

.99985 

.99988 

.99991 

•99993 

TABLE  25. 
LEAST  SQUARES. 

Values  ol  the  factor  0.6745-1/^1. 

This  factor  occurs  in  the  equation  re  =  0.6745-%/^i   for  the  probable  error  of  a  single  observation,  and  other 

similar  equations. 


n    = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

IO 

0.2248 

0.2133 

0.6745 
.2034 

0.4769 
.1947 

0.3894 
.1871 

0.3372 
.1803 

0.3016 
.1742 

0.2754 
.1686 

0.2549 
.1636 

0.2385 
.1590 

20 

•1547 

.1508 

.1472 

.1438 

.1406 

.1377 

•!349 

•1323 

.1298 

•1275 

30 

.1252 

.1231 

.1211 

.1192 

.1174 

•"57 

.1140 

.1124 

.1109 

.1094 

40 

.1080 

.1066 

•l°S3 

.1041 

.1029 

.1017 

.1005 

.0994 

.0984 

.0974 

50 

60 

0.0964 

.0878 

0.0954 
.0871 

0.0944 
.0864 

0.0935 
.0857 

0.0926 
.0850 

0.0918 
.0843 

0.0909 
.0837 

0.0901 
.0830 

0.0893 
.0824 

0.0886 
.0818 

70 

.0812 

.0806 

.0800 

•0795 

.0789 

.0784 

.0779 

.0774 

.0769 

.0764 

80 
90 

•0759 
.0715 

•0754 
.0711 

.0749 
.0707 

.0745 
.0703 

.0740 
.0699 

.0736 
.0696 

.07  T> 
.0692 

.0727 
.0688 

.0723 
.0685 

.0719 
.0681 

SMITHSONIAN  TABLES. 


TABLE  26. -LEAST  SQUARES. 

Values  ol  the  factor  0.6745-^ n(J' 


This  factor  occurs  in  the  equation  r0=o-(>74S\l    ,V_\  for  the  probable  error  of  the  arithmetic  mean. 


n  = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

0.4769 

0.2754 

0.1947 

0.1508 

0.1231 

0.1041 

0.0901 

0.0795 

IO 

0.0711 

0.0643 

.0587 

.0540 

.0500 

.0465 

•°435 

.0409 

.0386 

•0365 

20 

.0346 

.0329 

.0314 

.0300 

.0287 

.0275 

.0265 

.0255 

.0245 

.0237 

3° 

.0229 

.0221 

.0214 

.0208 

.0201 

.0196 

.0190 

.0185 

.0180 

•0175 

40 

.0171 

.0167 

.0163 

.0159 

•0155 

.0152 

.0148 

.0145 

.0142 

.0139 

50 

0.0136 

0.0134 

0.0131 

0.0128 

0.0126 

0.0124 

O.OI22 

0.0119 

0.0117 

0.0115 

60 

.0113 

.01  1  1 

.0110 

.0108 

.OIO6 

.0105 

.OIO3 

.OIOI 

.0100 

.0098 

70 
80 

.0097 
.0085 

.0096 
.0084 

.0094 
.0083 

.0093 
.0082 

.0092 
.008I 

.0091 
.0080 

.0089 
.0079 

.0088 

.0078 

.0087 
.0077 

.0076 

90 

.0075 

.0075 

.0074 

.0073 

.OO72 

.0071 

.OO7I 

.0070 

.0069 

.0068 

TABLE  27. -LEAST  SQUARES. 

Values  of  the  factor  0.8453- 


iV 

This  factor  occurs  in  the  approximate  equation  r  =0.8453  . —  for  the  probable  error  of  a  single  observation. 

Y  n  (n — /  ) 


n  = 

1 

2 

3 

4 

5 

6 

7 

8 

9 

00 

10 

0.0891 

0.0806 

0.5978 
.0736 

0.3451 
.0677 

0.2440 
.0627 

0.1890 
•0583 

0.1543 
.0546 

0.1304 
•0513 

0.1130 
.0483 

0.0996 
•0457 

20 

•0434 

.0412 

•0393 

.0376 

.0360 

•0345 

•0332 

.0319 

.0307 

.0297 

30 

.0287 

.0277 

.0268 

.0260 

.0252 

.0245 

.0238 

.0232 

.0225 

.0220 

40 

.0214 

.0209 

.0204 

.0199 

.0194 

.0190 

.0186 

.0182 

.0178 

.0174 

50 

0.0171 

0.0167 

0.0164 

0.0161 

0.0158 

0.0155 

0.0152 

0.0150 

0.0147 

0.0145 

60 

.0142 

.0140 

•0137 

•0135 

•0133 

.0131 

.0129 

.0127 

.0125 

.OI23 

g 

.0122 
.0106 

.0120 
.0105 

.0118 
.0104 

.0117 
.0102 

.0115 

.OIOI 

.0113 

.0100 

.0112 
.0099 

.Ol  1  1 

.0109 
.0097 

.OIO8 
.0096 

90 

.0094 

.0093 

.0092 

.0091 

.0090 

.0089 

.0089 

.0088 

.0087 

.0086 

TABLE  28. -LEAST  SQUARES. 

Values  of  0.8453 —         • 
n\n — 1 

This  factor  occurs  in  the  approximate  equation  7-0—0.8453 — , for  the  probable  error  of  the  arithmetical  mean. 


n  = 

1 

2 

3 

4 

6 

6 

7 

8 

9 

00 

0.4227 

0.1993 

O.I  22O 

0.0845 

0.0630 

0.0493 

0.0399 

0.0332 

10 

0.0282 

0.0243 

.0212 

.0188 

.0167 

.0151 

.0136 

.0124 

.0114 

.0105 

20 

.0097 

.0090 

.0084 

.0078 

.0073 

.0069 

.0065 

.0061 

.0058 

•0055 

30 

.0052 

.0050 

.0047 

.0045 

,.0043 

.0041 

.0040 

.0038 

.0037 

•0035 

40 

.0034 

•0033 

.0031 

.0030 

.0029 

.0028 

.0027 

.0027 

.0026 

.0025 

50 

0.0024 

0.0027 

0.0023 

0.0022 

O.OO22 

O.OO2I 

0.0020 

0.0020 

0.0019 

0.0019 

60 

.0018 

.00l8 

.0017 

.OOI7 

.OOI7 

.OOl6 

.OOl6 

.0016 

.0015 

.0015 

7° 

.0015 

.OOI4 

.0014 

.OOI4 

.0013 

.0013 

.OOI3 

.OOI3 

.0012 

.0012 

80 

.0012 

.OOI2 

.0011 

.OO  1  1 

.0011 

.0011 

.OOI  I 

.OOIO 

.OOIO 

.OOIO 

90 

.0010 

.OOIO 

.OOIO 

.0009 

.0009 

.0009 

.0009 

.0009 

.0009 

.0009 

SMITHSONIAN  TABLES. 


TABLE  29. 
LEAST  SQUARES. 


Observation  equations  : 

aizi  +  biz<j  +  •  •  .   II.ZQ  =  MI,  weight 
.  .  .  I2zq  =  M2.  weight 


anzi  +  bnZg  +  •  •  •    InZq  =  Mn,  weight  pn. 

Auxiliary  equations  : 

[paa]     =pia?      +p2ai      +  .  .  .  Pna2. 
[pab]    =  piaify  +  p2a2b2  +  .  .  .  pnanbn. 

[paM]  =  piaiMi  +  p2a2M2  +  .  .  .  pnanMn. 

Normal  equations  : 

fpaaUi  +  rpablz,  +  .  .  .  [pal]zq  =  [paM] 
[pabjzi  +  [pbbjza  +  .  .  .  [pbl]zq  =  [pbM] 

[pla]zi  +  [plbjzg    +'...'  [plljzq  =  [plM]. 

Solution  of  normal  equations  in  the  form, 

Zl  =  A^paM]  +  Bi[pbM]  +  .  .  .  L^plM] 
z2  =  A2[paM]  +  B2[pbM]  +  .  .  .  LgtplMJ 

zq=An[paM]+Bn[pbMJ+  ,'.  .  Ln[plM], 
gives  : 

weight  of  zi  =  pzl  =  (Ai)-1  ;  probable  error  of  zi  =  —  ^—~ 


weight  of  za  =  pz2  =  (B-j)-1  ;  probable  error  of  z2  =  - 


weight  of  zq  =  pZ(]  =  (Ln)"1;  probable  error  of  zq  = — — _ 
wherein 


VR. 


r  =  probable  error  of  observation  of  weight  unity 
=  0.6745  -%/  —  HX_  .  (q  unknowns.) 


Arithmetical  mean,  n  observations:  _ 


r  =  0.6745  \j  —  —  =         53  (approx.)  =probable  error  of  pb- 

\/n(n— i)'  servation  of  weight  unity. 


,          /    Sv2     _  0.8453  S  v       / 

r0  =  o.6745-i/  — j^n: —      (approx.)  =  probable  error 

\  n  (n—  i )         nVn— i  of  mean. 

Weighted  mean,  n  observations: 

/Spv2  r  /    Spv2 

r  =  0.6745  "Y  ~n~T;  r°  =^7^=a6745  \(n-i)Sp 

Probable  error  (R)  of  a  function  (Z)  of  several  observed  quantities  zi,  za,  .  .  .  whose 
probable  errors  are  respectively,  rlf  r2,  .  .  .  . 

Z   =  f  (Zl,  z2,  .  .  .) 


Examples  : 

Z  =  zi  ±  z2  +  .  .  .  R2  =  r\  +  r\  +  . 


Z  =  AZl  ±  Az2  ±  .  .  .  R2  =A2  r 

Z  =  zi  z2.  R2  ^zi  r*  +  za  rj 


SMITHSONIAN  TABLES. 


6o 


TABLE  30. 
DIFFUSION. 

Inverse  *  values  oiv/c=i—  -^  j 

log  x  =  log  (zq)  +  \og\/kt.     t  expressed  in  seconds. 
=  log  5  +  \og\Ski.    t  expressed  in  days. 
=  log  7  +  log  \/kt.  "        "  years. 

f    k  =  coefficient  of  diffusion,  t 
c  =  initial  concentration. 
v  =  concentration  at  distance  x,  time  t. 


w/e 

lOg  2? 

zq 

log  8 

& 

log  7 

y 

0.00 

+  00 

+  00 

+  00 

+  00 

00 

00 

.01 

0.56143 

3.6428 

3.02970 

1070.78 

4-3*098 

20463. 

.02 

•5*7*9 

3.2900 

2.98545 

967.04 

.26674 

18481. 

•03 

.48699 

3.0690 

•95525 

902.90 

.23654 

17240. 

.04 

.46306 

2.9044 

•93*32 

853-73 

.21261 

16316. 

0.05 

0.44276 

2.7718 

2.91102 

814.74 

4.19231 

15571. 

.06 

.42486 

2.6598 

.89311 

781.83 

.17440 

14942. 

.07 

.40865 

2.5624 

.87691 

753-20 

.15820 

14395- 

.08 

.39372 

2.4758 

.86198 

727.75 

•*4327 

13908. 

.09 

•37979 

2-3977 

.84804 

704.76 

•12933 

13469. 

0.10 

.11 

0.36664 
•354*4 

2.3262 
2.2602 

2.83490 
.82240 

683.75 
664.36 

4.11619 

.10369 

13067. 
12697. 

.12 

.34218 

2.1988 

.81044 

646.31 

.09173 

12352. 

•13 

•33067 

2.1413 

•79893 

629.40 

.08022 

12029. 

.14 

•3*954 

2.0871 

.78780 

6i347 

.06909 

11724. 

0.15 

0.30874 

2.0358 

2.77699 

598.40 

4.05828 

11436. 

.16 

.29821 

1.9871 

•76647 

584.08 

.04776 

11162. 

•17 

.28793 

.75619 

570.4* 

.03748 

10901. 

.18 

.27786 

1.8961 

.74612 

557-34 

.02741 

10652. 

.19 

.26798 

1.8534 

.73624 

544-8o 

.01753 

10412. 

0.20 

0.25825 

1.8124 

2.72651 

532.73 

4.00780 

10181. 

.21 

.24866 

1.7728 

.71692 

521.10 

3.99821 

9958.9 

.22 

.239*9 

I.7346 

509.86 

.98874 

9744.1 

•23 

.22983 

1.6976 

.69808 

498.98 

•97937 

9536.2 

.24 

.22055 

1.6617 

.68880 

488.43 

.97010 

9334-6 

0.25 

0.21134 

1.6268 

2.67960 

478.19 

3.96089 

9138.9 

.26 

.20220 

*-5930 

.67046 

468.23 

•95*75 

8948.5 

•27 

.19312 

1.5600 

.66137 

458.53 

.94266 

8763.2 

.28 

.18407 

1.5278 

•65232 

449.08 

.93361 

8582.5 

.29 

•17505 

1.4964 

•6433* 

439-85 

.92460 

8406.2 

0.30 

0.16606 

1-4657 

2.6343* 

430.84 

3.91560 

8233-9 

.31 

.15708 

1-4357 

.62533 

422.02 

.90662 

8065.4 

•32 

.14810 

1.4064 

.61636 

4*3-39 

.89765 

7900.4 

•33 

.13912 

1.3776 

.60738 

404.93 

.88867 

7738.8 

•34 

.13014 

1.3494 

.59840 

396.64 

.87969 

7580-3 

0.35 

0.12114 

1.3217 

2.58939 

388.50 

3.87068 

7424.8 

.36 

.11211 

1.2945 

•58037 

380.51 

.86166 

7272.0 

•37 

•I0305 

1.2678 

•57*3* 

372.66 

.85260 

7122.0 

•38 

•09396 

1.2415 

.56222 

364-93 

•8435* 

6974.4 

•39 

.08482 

1.2157 

•55308 

357-34 

.83437 

6829.2 

0.40 

0.07563 

1.1902 

2.54389 

349-86 

3.82518 

6686.2 

.41 

.06639 

1.1652 

.53464 

342.49 

.81593 

6545-4 

.42 

.05708 

1.1405 

•52533 

335-22 

.80662 

6406.6 

•43 

•04770 

i.n6i 

•5*595 

328.06 

.79724 

6269.7 

•44 

.03824 

1.0920 

.50650 

320.99 

•78779 

6134.6 

0.45 

0.02870 

1.0683 

2.49696 

314.02 

3-77825 

6001.3 

.46 

.01907 

1.0449 

48733 

307-13 

.76862 

5869-7 

•47 

.00934 

1.0217 

•47760 

300.33 

.75889 

5739-7 

.48 

9-9995* 

0.99886 

•46776 

293.60 

•74905 

5611.2 

•49 

0.97624 

•45782 

286.96 

•739** 

5484.1 

0.50 

9-97949 

0.95387 

2.44775 

280.38 

3.72904 

5358.4 

•Kelvin,  Mathematical  and  Physical  Papers,  vol.  III.  p.  428  ;  Becker,  Am.  Jour. 
of  Sci.  vol.  III.  1897,  p.  280.  t  For  direct  values  see  table  23. 

SMITHSONIAN  TABLES. 


TABLE  30  (continued). 
DIFFUSION. 


61 


./. 

log  2? 

* 

^ 

S 

logy 

V 

0.50 

9-97949 

0.95387 

2.44775 

280.38 

3.72904 

5358.4 

.51 

.96929 

•93T74 

•43755 

273.87 

.71884 

5234-1 

•52 
•53 

.95896 
.94848 

.90983 
.88813 

.42722 
.41674 

267.43 
261.06 

•70851 
.69803 

5111.0 
4989.1 

•54 

.93784 

.86665 

.40610 

25474 

•68739 

4868.4 

0.55 

9.92704 

0.84536 

2.39530 

248.48 

3-67659 

4748.9 

1    -56 

.91607 
§490 

.82426 
•80335 

.38432 
.373i6 

242.28 
236.13 

.66561 
•65445 

4630.3 
4512.8 

.58 

354 

,  .78260 

.36180 

230.04 

.64309 

4396.3 

•59 

197 

'  -76203 

•35023 

223.99 

.63152 

4280.7 

0.60 

9.87018 

0.74161 

2-33843 

217.99 

3-6I973 

4166.1 

.61 

.85815 

•72135 

.32640 

212.03 

.60770 

4052.2 

.62 

.84587 

.70124 

.31412 

206.12 

•59541 

3939-2 

•63 

.83332 

.68126 

«3OI57 

200.25 

.58286 

3827.0 

.64 

.82048 

.66143 

.28874 

194.42 

.57003 

37I5-6 

0.65 

9.80734 

0.64172 

2.27560 

188.63 

3-55689 

3604.9 

.66 
.67 
.68 

.79388 
.78008 
•76590 

.62213 
.60266 
•58331 

.26214 

•24833 
.23416 

182.87 

177.15 
171.46 

•54343 
.52962 

3494-9 
3385.4 
3276.8 

.69 

•75133 

•56407 

•21959 

165.80 

.50088 

3168.7 

0.70 

•71 

9-73634 

.72089 

0-54493 

.52588 

2.20459 
.18915 

160.17 
154.58 

3.48588 
.47044 

3061.1 

2954.2 

.72 

.70495 

.50694 

.17321 

149.01 

-4545° 

2847-7 

•73 

.68849 

.48808 

•15675 

143-47 

.43804 

2741.8 

•74 

.67146 

.46931 

.13972 

137-95 

.42101 

2636.4 

0.75 

9.65381 

0.45062 

2.12207 

132.46 

3-40336 

253r-4 

.76 

•63550 

.43202 

.10376 

126.99 

•38505 

2426.9 

•77 

.61646 

.41348 

.08471 

121.54 

.36600 

2322.7 

.78 
•79 

.59662 
.57590 

•39502 
.37662 

.06487 
.04416 

ii6.n 
110.70 

.34616 

•32545 

2219.0 
2115.7 

0.80 

9-55423 

0.35829 

2.02249 

105-31 

3-30378 

2012.7 

.81 

.82 

.53150 

•50758 

•34001 
.32180 

.97584 

99-943 
94-589 

.28104 
•25713 

1910.0 
1807.7 

•83 
.84 

•48235 
45564 

•30363 

•28552 

-95061 
.92389 

89.250 
83.926 

.23190 
.20518 

1705-7 
1603.9 

0.85 

9.42725 

0.26745 

1.89551 

78.615 

3.17680 

1502.4 

.86 

•39695 

.24943 

.86521 

73-3'7 

.14650 

1401.2 

.87 

-36445 

.23145 

.83271 

68.032 

.11400 

1300.2 

.88 

.32940 

.21350 

.79766 

62.757 

.07895 

1199.4 

.89 

•29135 

•19559 

.7596i 

57-492 

3.04090 

1098.7 

0.90 

.91 

9.24972 
•20374 

0.17771 
.15986 

1.71797 
.67200 

52.236 
46.989 

2.99926 
•95329 

8H'o3 

.92 

.15239 

.14203 

.62065 

41-750 

.90194 

797-89 

•93 
•94 

.09423 
9.02714 

.12423 
.10645 

.56249 
•49539 

36-516 
31.289 

.84378 
.77668 

697.88 
597-98 

0.95 

8.94783 

0.08868 

1.41609 

26.067 

2.69738 

498.17 

.96 

.85082 

•07093 

.31907 

20.848 

.60036 

398.44 

•97 

.72580 

•05319 

.19406 

I5-633 

•47535 

298.78 

.98 

.54965 

.03545 

.01791 

10.421 

.29920 

199.16 

•99 

.24859 

.01773 

9.71684 

5.21007 

1.99813 

99-571 

1.00 

—  oo 

o.ooooo 

—  00 

o.ooooo 

—  00 

0.000 

SMITHSONIAN  TABLES. 


62 


TABLE  31 . 
GAMMA  FUNCTION 


Value  of  log 


r*ac*-ldx  + 10. 


r 

JQ 


Values  of  the  logarithms  + 10  of  the  "  Second  Eulerian  Integral "  (Gamma  function)    I     e-*x!*^dx  or  log  T(«)-f-io 

%/o 

for  values  of  n  between  i  and  2.    When  n  has  values  not  lying  between  i  and  2  the  value  of  the  function  can  be 
readily  calculated  from  the  equation  T(«+i)  =  nT(n)  =  n(n— i)  .  .  .  («— r)r(«— r). 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.00 

I.OI 

9-99  

75287 

97497 
72855 

95001 
70430 

925*2 
68011 

90030 
65600 

63196 

85087 
60798 

82627 
58408 

80173 
56025 

77727 
53648 

1.02 

48916 

46561 

44212 

41870 

39535 

37207 

34886 

§72 

30265 

1.03 
1.04 

27964 
°5334 

25671 
03108 

23384 
00889 

21104 
98677 

18831 
96471 

16564 
94273 

Poi 

"052 
89895 

06 
..*6 

07567 
85544 

1.05 

9-9883379 

81220 

79068 

76922 

74783 

72651 

70525 

68406 

66294 

64188 

i.  06 

62089 

59996 

579*0 

55830 

51690 

49630 

47577 

4553° 

43489 

1.07 

4*455 

39428 

37407 

35392 

3*382 

29387 

27398 

254*5 

23439 

1.08 
1.09 

21469 
02123 

19506 
00223 

98329 

*5599 
96442 

1*7*7 
92686 

iy 

07860 
88956 

0594* 
87100 

04029 
85^50 

1.10 

.11 

9.9783407 
653*3 

81570 
63538 

7973s 
61768 

779*4 
60005 

76095 
58248 

74283 
56497 

72476 

54753 

70676 
530*4 

68882 
51281 

67095 
49555 

.12 

47834 

46120 

444** 

42709 

4*013 

39323 

37638 

35960 

34288 

32622 

•r3 

29308 

27659 

26017 

24381 

22751 

21126 

19508 

17896 

16289 

.14 

14689 

13094 

1*505 

09922 

08345 

06774 

05209 

03650 

02096 

00549 

1.15 

9.9699007 

9747  i 

95941 

944*7 

92898 

91386 

89879 

88378 

86883 

85393 

.16 

83910 

82432 

80960 

79493 

78033 

76578 

75*29 

73686 

72248 

70816 

•17 

69390 

67969 

66554 

63742 

62344 

60952 

59566 

58*85 

56810 

.18 

55440 

54076 

52718 

5*366 

50019 

48677 

4734* 

46011 

44687 

43368 

•*9 

42054 

40746 

39444 

38i47 

36856 

35570 

34290 

33016 

3*747 

30483 

1.20 

9.9629225 

27973 

26725 

25484 

24248 

23017 

21792 

20573 

19358 

18150 

.21 

16946 

15748 

H556 

13369 

12188 

i  ion 

09841 

08675 

07515 

06361 

.22 

05212 

04068 

02930 

01796 

00669 

99546 

98430 

973^8 

96212 

95*i* 

•23 

594oi  5 

92925 

91840 

90760 

89685 

88616 

87553 

86494 

8544* 

84393 

.24 

83350 

823*3 

81280 

80253 

79232 

78215 

77204 

76198 

75*97 

74201 

1.25 

9-9573211 

72226 

71246 

70271 

69301 

68337 

67377 

66423 

65474 

6453° 

.26 
.27 

63592 

54487 

62658 
53604 

61730 

52727 

60806 

59888 
50988 

58975 
50126 

58067 
49268 

48416 

56267 
47570 

55374 
46728 

.28 

4589* 

45059 

44232 

434*° 

42593 

41782 

40975 

40173 

39376 

38585 

.29 

37798 

37016 

36239 

35467 

34700 

33938 

33*8* 

32429 

31682 

30940 

1.30 

9-9530203 

29470 

28743 

28021 

27303 

26590 

25883 

25180 

24482 

23789 

•31 

23100 

22417 

21739 

21065 

20396 

19732 

19073 

18419 

17770 

17125 

•32 

16485 

I585° 

15220 

J4595 

*3975 

*3359 

12748 

12142 

11541 

10944 

•33 

I0353 

09766 

09184 

08606 

08034 

07466 

06903 

06344 

0579* 

05242 

•34 

04698 

04158 

03624 

03094 

02568 

02048 

01532 

OIO2I 

00514 

OOOI2 

1.35 

9-94995*5 

99023 

98535 

98052 

97573 

97100 

96630 

96l66 

95706 

95251 

1.36 

94800 

94355 

939*3 

93477 

92617 

92*94 

9*776 

91362 

90953 

•37 

90549 

90149 

89754 

89363 

88977 

88595 

88218 

87846 

87478 

87II5 

•38 
•39 

86756 
834*7 

86402 
83108 

86052 
82803 

85707 
82503 

85366 
82208 

85030 
81916 

84698 
81630 

84371 
81348 

84049 
81070 

83731 
80797 

1.40 

•4* 

9.9480528 
78084 

80263 
77864 

80003 
77648 

79748 

77437 

79497 
77230 

79250 

77027 

79008 
76829 

78770 
76636 

76446 

78308 
76261 

.42 

76081 

75905 

75733 

75565 

75402 

75243 

75089 

74939 

74793 

74652 

•43 

745*5 

74382 

74254 

74*30 

74010 

73894 

73783 

73676 

73574 

73476 

1.44 

73382 

73292 

73207 

73*25 

73049 

72976 

72908 

72844 

72784 

72728 

*  Legendre's  "Exercises  de  Calcul  Integral,"  tome  ii. 


SMITHSONIAN  TABLES. 


TABLE  31  (.continued'). 

GAMMA   FUNCTION. 


n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.45 

9.9472677 

72630 

72587 

72549 

725H 

72484 

72459 

72437 

72419 

72406 

1.46 

72397 

72393 

72392 

72396 

72404 

72416 

72432 

72452 

72477 

72506 

1.47 

72539 

72576 

72617 

72662 

72712 

72766 

72824 

72886 

72952 

73022 

1.48 

73097 

73175 

73258 

73345 

73436 

73531 

73630 

73734 

73841 

73953 

1.49 

74068 

74188 

743  !  2 

74440 

74572 

74708 

74848 

74992 

75293 

1.50 

9-9475449 

75610 

75774 

75943 

76116 

76292 

76473 

76658 

76847 

77040 

if  i 

77237 

774  -n 

77642 

77851 

78064 

78281 

78502 

78727 

78956 

79189 

1.52 

79426 

79667 

79912 

80161 

80414 

80671 

80932 

81196 

81465 

81738 

82015 

82295 

82580 

82868 

83161 

83457 

83758 

84062 

84370 

84682 

i-54 

84998 

85642 

85970 

86302 

86638 

86977 

87321 

87668 

88019 

1.55 

9.9488374 

88733 

89096 

89463 

89834 

90208 

90587 

90969 

91355 

9!745 

1.56 

92139 

92537 

92938 

93344 

93753 

94166 

94583 

95004 

95429 

95857 

1-57 

96289 

96725 

97165 

97609 

98056 

98508 

98963 

99422 

99885 

00351 

1.58 

500822 

01296 

01774 

02255 

02741 

03230 

03723 

04220 

04720 

05225 

1.59 

05733 

06245 

06760 

07280 

07803 

08330 

08860 

09395 

09933 

10475 

1.60 

9.9511020 

11569 

I2I22 

12679 

13240 

13804 

H372 

14943 

I55I9 

16098 

1.61 

16680 

17267 

17857 

18451 

19048 

19649 

20254 

20862 

2H75 

22O9I 

1.62 

22710 

23333 

23960 

24591 

25225 

25863 

26504 

27149 

27798 

28451 

1.63 

29107 

29766 

30430 

31097 

31767 

32442 

33120 

33801 

34486 

35*75 

1.64 

35867 

36563 

37263 

37966 

38673 

39383 

40097 

40815 

41536 

42260 

1.65 

9.9542989 

43721 

44456 

45195 

45938 

46684 

47434 

48187 

48944 

49704 

1.66 

50468 
58303 

51236 
59106 

52007 
59913 

52782 
60723 

61536 

54342 
62353 

55I27 
63174 

63998 

56708 
64825 

65656 

1.68 

66491 

67329 

68170 

69015 

69864 

70716 

7243° 

73293 

74159 

1.69 

75028 

75901 

76777 

77657 

78540 

79427 

80317 

81211 

82I08 

83008 

1.70 

9.9583912 

84820 

85731 

86645 

87563 

88484 

89409 

90337 

21268 

92203 

1.71 

93  HI 

94083 

95028 

95977 

96929 

97884 

98843 

99805 

00771 

01740 

1.72 

602712 

03688 

04667 

06636 

07625 

08618 

09614 

IO6I3 

11616 

12622 

13632 

H645 

1  5661 

16681 

17704 

18730 

19760 

20793 

21830 

1.74 

22869 

23912 

24959 

26009 

27062 

28118 

29178 

30241 

31308 

32377 

1.75 

9-9633451 

34527 

35607 

36690 

37776 

38866 

39959 

41055 

42155 

43258 

1.76 
1.77 
1.78 

44364 
55606 
67176 

§473 
749 

46586 
57894 
69529 

47702 

59043 
70710 

48821 

60195 
71895 

49944 
61350 
73082 

51070 
62509 
74274 

52I99 
63671 
75468 

53331 
64836 
76665 

lit 
77866 

1.79 

79070 

80277 

81488 

82701 

83918 

85138 

86361 

87588 

888l8 

90051 

1.80 

9.9691287 

92526 

93768 

95°H 

96263 

97515 

98770 

00029 

OI29I 

02555 

1.81 

703823 

05095 

06369 

07646 

08927 

I02II 

11498 

12788 

I4082 

15378 

1.82 

16678 

17981 

I9287 

20596 

21908 

23224 

24542 

25864 

27189 

28517 

1.83 

29848 

31182 

32520 

33860 

35204 

36551 

37900 

39254 

4O6lO 

41969 

1.84 

4333  i 

44697 

46065 

47437 

48812 

50190 

5T57i 

52955 

54342 

55733 

1.85 

1.86 

9.9757126 
71230 

58522 
72657 

59922 
74087 

61325 

75521 

62730 
76957 

64139 
78397 

65551 
79839 

66966 
81285 

68384 
82734 

69805 
84186 

1.87 

85640 

87098 

88559 

90023 

91490 

92960 

94433 

95909 

97389 

98871 

1.88 
1.89 

800356 
J5374 

01844 
16893 

03335 
18414 

04830 
J9939 

06327 
21466 

07827 
22996 

0933  i 
24530 

10837 
26066 

12346 
27606 

13859 
29148 

1.90 

1.91 

I  I-92 

9.9830693 
46311 
62226 

32242 
47890 
63834 

33793 
49471 
65445 

35348 

5I055 
67058 

36905 
52642 

68675 

38465 
54232 
70294 

40028 

55825 
71917 

41595 
5742i 
73542 

43l64 
59020 

44736 
60621 
76802 

J-93 

78436 

80073 

81713 

83356 

85002 

86651 

88302 

§99-57 

91614 

•^-x—  

9J57J 

1.94 

94938 

96605 

98274 

99946 

01621 

03299 

04980 

06663 

08350 

10039 

1.95 

9.9911732 

13427 

i5I25 

16826 

18530 

20237 

21947 

23659 

25375 

27093 

1.96 
1.97 
1.98 
1.99 

28815 
46185 
63840 
81779 

30539 
47937 
65621 
83588 

32266 
49693 
67405 
85401 

33995 

69192 
87216 

35728 

532J3 
70982 

89034 

37464 

54977 
72774 

90854 

39202 
56744 
74570 
92678 

40943 
58513 
76368 
945°4 

60286 
78169 
96333 

44435 
62062 

9® 

SMITHSONIAN  TABLES. 


64 


TABLE  32. 
ZONAL  SPHERICAL  HARMONICS. 


Degrees 

Pi 

P2 

PS 

P. 

p. 

Pe 

PT 

0 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

+  I.OOOO 

I 

.9998 

•9995 

.9991 

.9985 

•9977 

.9968 

•9957 

2 

•9994 

.9982 

•9963 

•9939 

.9909 

.9872 

.9830 

3 

.9986 

•9959 

.9863 

•9795 

•97  i  4 

.9620 

4 

.9976 

.9927 

•9854 

.9758 

.9638 

•9495 

•9329 

5 

+  0.9962 

+  0.9886 

+  0.9773 

+  0.9623 

+  0.9437 

+  0.9216 

+  0.8962 

6 

•9945 

•9836 

.9674 

•9459 

.9194 

.8881 

.8522 

7 

•9925 

•9777 

•9557 

.9267 

.8911 

.8492 

.8016 

8 

•9903 

.9709 

•9423 

.9048 

.8589 

.8054 

•7449 

9 

.9877 

•9633 

•9273 

.8803 

.8232 

•7570 

.6830 

10 

+  0.9848 

+  0.9548 

+  0.9106 

+  0.8532 

+  0.7840 

+  0.7045 

+  0.6164 

ii 

.9816 

•9454 

•8923 

.8238 

.7417 

.6483 

.5462 

12 

•978i 

•9352 

.8724 

.7920 

.6966 

.5891 

•4731 

13 

•9744 

.9241 

.8511 

•7582 

.6489 

•5273 

.3980 

14 

•9703 

.9122 

.8283 

.7224 

•5990 

•4635 

.3218 

I5 

+  0.9659 

+  0.8995 

+  0.8042 

+  0.6847 

+  0.5471 

+  0.3983 

+  0.2455 

16 

.9613 

.8860 

.7787 

•6454 

•4937 

•3323 

+  .1700 

17 

.9563 

.8718 

•75*9 

.6046 

•4391 

.2661 

+  .0961 

18 

.8568 

.7240 

.5624 

•3836 

.2002 

+  .0248 

19 

•9455 

.8410 

.6950 

.5192 

.3276 

•1353 

—  -°433 

20 
21 

H-o-9397 
•9336 

+  0.8245 
.8074 

+  0.6649 
•6338 

+  0.4750 
.4300 

+  0.2715 
.2156 

+  0.0719 
+  .0106 

—  0.1072 
.1664 

22 

.9272 

•7895 

.6019 

•3845 

.1602 

—  .0481 

.2202 

23 

•9205 

.7710 

.5692 

•3386 

.1057 

—  -1038 

.2680 

24 

•9135 

•7518 

•5357 

.2926 

.0525 

—  .1558 

•3°94 

25 

+  0.9063 

+  0.7321 

+  0.5016 

+  0.2465 

+  0.0009 

—  0.2040 

—  0.3441 

26 

.8988 

.7117 

.4670 

.2007 

—  .0489 

.2478 

•3717 

27 

.8910 

.6908 

•4319 

•J553 

—  .0964 

.2869 

.3922 

28 

.8829 

.6694 

•3964 

.1105 

—  -1415 

.3212 

•4053 

29 

.8746 

.6474 

.3607 

.0665 

-  .1839 

•3502 

•41  i3 

30 

+  0.8660 

.8572 

+  0.6250 
.6021 

+  0.3248 
.2887 

+  0.0234 
—  .0185 

—  0.2233 
•2595 

—  0.3740 
•3924 

—  0.4102 
.4022 

32 

.8480 

.5788 

•2527 

—  .0591 

.2923 

•4053 

•3877 

33 

.8387 

•5551 

.2167 

—  .0982 

.3216 

.4127 

.3671 

34 

.8290 

•5310 

.1809 

—  -1357 

•3473 

.4147 

•3409 

35 

+  0.8192 

+  0.5065 

+  0.1454 

—  0.1714 

—  0.3691 

—  0.4II4 

—  0.3096  I 

36 

.8090 

o/* 

.4818 

.1102 

.2052 

•3871 

.4031 

.2738 

37 

.7986 

•4567 

•°755 

.2370 

.4011 

.3898 

•2343 

38 

.7880 

•43  J  4 

.0413 

.2666 

.4112 

•3719 

.1918 

39 

.7771 

.4059 

.0077 

.2940 

.4174 

•3497 

.1470 

40 

+  0.7660 

+  0.3802 

0.0252 

—  0.3190 

—  0.4197 

—  0.3236 

—  0.1006 

41 

•7547 

•3544 

•0574 

.3416 

.4181 

•2939 

—  -0535 

42 

•7431 

.3284 

.0887 

.3616 

.4128 

.2610 

—  .0064 

43 

•73*4 

•3023 

.1191 

•3791 

.4038 

•2255 

+  -0398 

44 

•7193 

.2762 

.1485 

•3940 

•39H 

.1878 

+  .0846 

45 

+  0.7071 

+  0.2500 

—  0.1768 

—  0.4063 

—  0.3757 

—  0.1484 

+  0.1271 

46 

.6947 

.2238 

.2O4O 

.4158 

.3568 

—  .1078 

.1667 

47 

.6820 

•1977 

.2300 

.4227 

•335° 

—  .0665 

.2028 

48 

•6691 

.1716 

•2547 

.4270 

•3I05 

—  .0251 

•235° 

49 

•6561 

.1456 

.2781 

.4286 

.2836 

+  .0161 

50 

+  0.6428 

+  0.1198 

O.3OO2 

—  0.4275 

—  0.2545 

+  0.0564 

+  0.2854 

SMITHSONIAN  TABLES. 


*  Calculated  by  Mr.  C.  E.  Van  Orstrand  for  this  publication. 


TABLE  32  (continued). 
ZONAL   SPHERICAL    HARMONICS. 


!  Degrees 

Pi 

P2 

PS 

p* 

P5 

p« 

PT 

50 
51 

+  0.6428 
.6293 

+  0.1198 
.0941 

^o/- 

—  0.3002 
•3209 

—  0.4275 
4239 

—  0.2545 
•2235 

+  0.0564 
•0954 

+  0.2854 

•3031 

52 

•6157 

.0686 

.3401 

.4178 

.1910 

.7164, 

53 

.6018 

•0433 

•3578 

4093 

•1571 

.1677 

O   Or 

.3221 

54 

.5878 

.0182 

•3740 

.3984 

.1223 

.2002 

•3234 

9 

+  0-5736 
•5592 

—  0.0065 
.0310 

—  0.3886 
.4016 

—0.3852 
.3698 

—  0.0868 
—  .0509 

+  0.2297 
.2560 

+  0.3191 

•3°95 

57 

•5446 

.055! 

4I31 

•3524 

—  .0150 

.2787 

•2947 

58 

•5299 

.0788 

.4229 

•3331 

+  .0206 

.2976 

.2752 

59 

-S1S° 

.1021 

.4310 

•3119 

+  -0557 

•3I25 

.2512 

60 
61 

+  0.5000 
.4848 

—  0.1250 
.1474 

—  04375 
4423 

—  0.2891 

.2647 

+  0.0898 
.1229 

4  0.3232 
.3298 

+  0.2231 
.1916 

62 

4695 

.1694 

4455 

.2390 

•1545 

•3321 

•1572 

63 

.   4540 

.1908 

•447  i 

.2121 

.1844 

•3302 

.1203 

64 

4384 

.2117 

4470 

.1841 

.2123 

.3240 

.0818 

66 

+  0.4226 
.4067 

—  0.2321 
.2518 

—  0.4452 
.4419 

—  0.1552 
.1256 

+  0.2381 
.2615 

+  0.3138 
.2997 

+  0.0422 
+  .OO22 

67 

•3907 

.2710 

4370 

•0955 

.2824 

.2819 

—  -°375 

68 

•3746 

•2895 

4305 

.0651 

.3005 

.2606 

*Jf  J 

—  -0763 

69 

•3584 

•3074 

.4225 

•0344 

•3158 

.2362 

—  -"35 

1 
70 

+  0.3420 

—  0.3245 

—  04130 

—  0.0038 

+  0.3281 

+  0.2089 

—  0.1483 

71 

•3256 

.3410 

.4021 

+  .0267 

•3373 

.1791 

.1808 

72 

.3090 

•3568 

.3898 

.0568 

•3434 

.1472 

.2099 

73 

.2924 

.3718 

.3761 

.0864 

•3463 

.1136 

.2352 

74 

.2756 

.3860 

.3611 

•"53 

*J  •  «-/ 

.3461 

.0788 

•2563 

75 
76 

+  0.2588 
.2419 

—  0-3995 

.4122 

—  0.3449 

•3275 

+  0.1434 

•1705 

+  0.3427 
•3362 

+  0.0431 
+  .0070 

—  0.2730 
.2850 

77 

.2250 

.4241 

.3090 

.1964 

.3267 

—  .0290 

.2921 

78 

.2079 

4352 

.2894 

.2211 

•3H3 

—  .0644 

.2942 

79 

.1908 

4454 

.2688 

•2443 

.2990 

—  .0990 

.2913 

80 
81 

+  0.1736 
.1564 

—  0.4548 
4633 

—  0.2474 
•2251 

+  0.2659 
.2859 

+  0.2810 
.2606 

—  0.1321 
•l635 

—  0.2835 
.2708 

82 

.1392 

.4709 

.2020 

.3040 

.2378 

.1927 

•2536 

83 

.1219 

4777 

•1783 

.3203 

.2129 

.2193 

.2321 

84 

.1045 

.4836 

•1539 

•3345 

.1861 

.2431 

.2067 

85 

+  0.0872 

—  0.4886 

—  O.I29I 

+  0.3468 

+  0.1577 

—  0.2638 

—  0.1778 

86 

.0698 

4927 

.1038 

.3569 

.1278 

.2810 

.1460 

87 

•0523 

.0781 

.3648 

.0969 

.2947 

.1117 

88 
89 

•0349 
•0175 

4995 

.0522 
.0262 

•3704 
•3739 

.0651 
.0327 

•3045 
•3*05 

•07J5 

.0381 

90 

+  0.0000 

—  0.5000 

—  0.0000 

+  0.3750 

+  o.oooo 

—  0.3125 

—  0.0000 

SMITHSONIAN  TABLES. 


66 


TABLE  33. 
ELLIPTIC   INTEGRALS, 

Values  ot  \  '( 1-  sin2  e  sin2  $)**  d* 
Jo 


* 


This  table  gives  the  values  of  the  integrals  between  o  and  IT  /z  of  the  function  (i—  sin2  0  sin2  ^)      </<£  for  different  val- 
ues  of  the  modulus  corresponding  to  each  degree  of  6  between  o  and  90. 


e 

fl     d* 

c* 

\  *(i—  sin2»sin2A)W 

Jo 

e 

Xs      dj> 

f'x  suvtfsin   fc 
i 

Jo   (i  —  sin2  6  sin2  ^>)' 

(i—  sin20sm2#)i 

Number. 

Log. 

Number. 

Log. 

Number. 

Log. 

Number. 

Log. 

0° 

1.5708 

0.196120 

1.5708 

0.196120 

45° 

1.8541 

0.268127 

1.3506 

0.130541 

I 

5709 

I96I53 

5707 

196087 

6 

8691 

271644 

3418 

127690 

2 

5713 

196252 

5703 

195988 

7 

8848 

275267 

3329 

124788 

3 

5719 

196418 

5697 

195822 

8 

9OII 

279001 

3238 

121836 

4 

.5727 

196649 

5689 

I9559I 

9 

9180 

282848 

3M7 

118836 

5° 

L5738 

0.196947 

1.5678 

0.195293 

50° 

1.9356 

0.286811 

'•3PS5 

0.115790 

6 

5751 

I973I2 

5665 

194930 

i 

9539 

290895 

2963 

112698 

7 

197743 

5649 

194500 

2 

9729 

295101 

2870 

109563 

8 

5785 

198241 

5632 

194004 

3 

9927 

299435 

2776 

106386 

9 

5805 

198806 

5611 

193442 

4 

2.0133 

303901 

2681 

103169 

10° 

1.5828 

0.199438 

1.5589 

0.192815 

55° 

2.0347 

0.308504 

1.2587 

0.099915 

i 

5f54 

200137 

5564 

192121 

6 

0571 

313247 

2492 

096626 

2 

5882 

200904 

5537 

191362 

7 

0804 

318138 

2397 

093303 

3 

5913 

201740 

5507 

190537 

8 

1047 

323182 

2301 

089950 

4 

5946 

202643 

5476 

189646 

9 

1300 

328384 

2206 

086569 

15° 

6 

1.5981 
6020 

0.203615 
204657 

1.5442 
5405 

0.188690 
187668 

60° 
i 

2.1565 
1842 

0.333753 
339295 

1.  21  11 

2015 

0.083164 
079738 

9 

6061 
6105 
6151 

205768 
206948 
208200 

5367 
5326 
5283 

186581 
185428 
184210 

2 

3 
4 

2132 
2435 
2754 

345020 
350936 
357053 

1920 
1826 
1732 

076293 
072834 
069364 

20° 

i 

1.6200 
6252 

0.209522 
210916 

1-5238 

0.182928 
181580 

65° 

6 

2.3088 
3439 

0.363384 
369940 

1.1638 

1545 

0.065889 
062412 

2 

6307 

212382 

5141 

180168 

7 

3809 

376736 

J453 

058937 

3 

6365 

213921 

5090 

178691 

8 

4198 

383787 

1362 

055472 

4 

6426 

215533 

5037 

177150 

9 

4610 

39III2 

1272 

052020 

25° 

1.6490 

0.217219 

1.4981 

0.175545 

70° 

2.5046 

0.398730 

1.1184 

0.048589 

6 

6557 

218981 

4924 

173876 

i 

5507 

406665 

1096 

045  l  83 

7 

6627 

2208l8 

4864 

172144 

2 

5998 

414943 

ion 

041812 

8 

6701 

222732 

4803 

170348 

3 

6521 

4235Q6 

0927 

038481 

9 

6777 

224723 

4740 

168489 

4 

7081 

432660 

0844 

035200 

30° 

1.6858 

0.226793 

1.4675 

0.166567 

75° 

2.7681 

0.442176 

1.0764 

0.031976 

i 

6941 

228943 

4608 

164583 

6 

8327 

452196 

0686 

028819 

2 

7028 

231173 

4539 

162537 

7 

9026 

462782 

0611 

025740 

3 

7119 

233485 

4469 

160429 

8 

9786 

474008 

0538 

022749 

4 

7214 

235880 

4397 

158261 

9 

3.0617 

485967 

0468 

019858 

35° 

I.73I2 

0.238359 

14323 

0.156031 

80° 

3«I534 

0.498777 

1.0401 

0.017081 

6 

7415 

240923 

4248 

153742 

i 

2553 

512591 

0338 

014432 

7 

7522 

243575 

4171 

I5I393 

2 

3699 

527613 

0278 

011927 

8 

7633 

246315 

4092 

148985 

3 

5004 

544120 

0223 

009584 

9 

7748 

249146 

4013 

146519 

4 

6519 

562514 

0172 

007422 

40° 

1.7868 
7992 

0.252068 
255085 

i.393i 
3849 

0.143995 
141414 

85° 

6 

3.8317 
4.0528 

0.583396 
607751 

1.0127 
0086 

0.005465 
003740 

2 

8122 

258197 

3765 

138778 

7 

3387 

637355 

0053 

002278 

3 

8256 

261406 

3680 

136086 

8 

7427 

676027 

0026 

OOII2I 

4 

8396 

264716 

3594 

1  33  340 

9 

5-4349 

735192 

0008 

000326 

45° 

1.8541 

0.268127 

1.3506 

0.130541 

90° 

oo 

oo 

1.  0000 



SMITHSONIAN  TABLES. 


TABLE  34.  £* 

MOMENTS  OF  INERTIA,  RADII  OF  GYRATION,  AND  WEIGHTS. 

In  each  case  the  axis  is  supposed  to  traverse  the  centre  of  gravity  of  the  body.    The  axis  is 
one  of  symmetry.     The  mass  of  a  unit  of  volume  is  w. 


Body. 

Axis. 

Weight. 

Moment  of  Inertia  Io. 

Square  of  Ra- 
dius of  Gyra- 
tion p2. 

8 

Sirwr^ 

2^2 

Sphere  of  radius  r 

Diameter 

{^.fttVT 

T 

3 

15 

Spheroid  of  revolution,  po- 
lar axis  2a,  equatorial  di- 

Polar axis 

4*war* 

Sinvar* 

2f2 

ameter  2r 

3 

15 

Ellipsoid,  axes  20,  2<5,  2c 

Axis  2a 

Qirwabc 
3 

4vwabc(bz-\-c^  ) 

^24-f2 

'5 

5 

Spherical  shell,  external  ra- 
dius r,  internal  r1 

Diameter 

4TrW(r*  —  r'9) 

Sirwir5  —  r'5) 

2(^6  —  r'5) 

3 

IS 

5(^—^8) 

Ditto,  insensibly   thin,  ra- 
dius r,  thickness  dr 

Diameter 

^•Kwr^dr 

%Tnvr*dr 

2r2 

3 

3 

Circular  cylinder,  length  2a, 

Longitudinal 

2irwar* 

irwar^ 

r2 

radius  r 

axis  20, 

2 

Elliptic  cylinder,  length  2a, 

Longitudinal 

Trwabc^+c*) 

P+c* 

transverse  axes  2b,  2c 

axis  20. 

2 

4 

Hollow    circular    cylinder, 
length    2a,  external    ra- 
dius r,  internal  r1 

Longitudinal 

axis  20. 

-*^ 

™M 

r^-\-r^ 

2 

Ditto,  insensibly  thin,  thick- 
ness dr 

Longitudinal 
axis  20. 

tpnuardr 

«rwar*dr 

r* 

Circular  cylinder,  length  2a, 
radius  r 

Transverse 
diameter 

2irwarz 

flWrtr2(3r24-4«2) 

r-     + 
4^3 

.     6 

Elliptic  cylinder,  length  20, 
transverse  axes  20,  2b 

Transverse 
axis  2b 

2irwabc 

invafc(y*+4a?) 

*++ 

4^3 

6 

Hollow   circular    cylinder, 
length    2a,  external    ra- 

Transverse 
diameter 

2*wa(r*-r>*} 

irwa  ]  -5(r*  —  r'*) 

r*+r*      a* 

G    ^    -|~4£9(r2    r**)  C 

\  ' 

dius  r,  internal  r1 

4          3 

Ditto,  insensibly  thin,  thick- 
ness dr 

Transverse 
diameter 

qmuardr 

3 

¥  +  1 

Rectangular  prism,  dimen- 
sions 2a,  2&t  2C 

Axis  20. 

Swafc 

^wabc(b^-\-cz) 

^-f.^ 

3 

3 

Rhombic  prism,  length  20, 
diagonals  2bt  2c 

Axis  20, 

^wabc 

2wabc(b^cz) 

^-ff2 

3 

6 

Ditto 

Diagonal  2b 

qwabc 

2ivabc(ci-\-2ai} 

*     a* 

3 

6  +  3 

(Taken  from  Rankine.) 


SMITHSONIAN  TABLES. 


68  TABLE  35. 

STRENGTH  OF  MATERIALS. 

The  strength  of  most  materials  varies  so  that  the  following  figures  serve  only  as  a  rough  indication  of  the  strength  of  a 

particular  sample. 


TABLE  35  (a). -Metals. 


Name  of  Metal. 

Tensile  strength  in 
pounds  per  sq.  in. 

Aluminum  wire 

3OOOO-4OOOO 

Brass  wire 

50000-150000 

Bronze  wire,  phosphor,  hard- 

drawn 

IIOOOO-I4OOOO 

Bronze    wire,    silicon,   hard- 

drawn 

95000-II5000 

Bronze  :  Cu,  58.54  parts  ;  Zn, 

38.70;   Al,  0.21  ;  with  2.55 

parts  of  the  alloy,  Sn,  29.03, 

wrought  iron,  58.06,  ferro- 

manganese,  12.91 
Copper  wire,  hard-drawn 
Gold  wire 

60000-75000 
6OOOO-7OOOO 
2OOOO 

Iron,  cast 

I3000-33000 

"     wire,  hard-drawn 

8OOOO-I2OOOO 

"        "      annealed 

5OOOO-6OOOO 

Lead,  cast  or  drawn 

2600-3300 

Palladium  * 

39000 

Platinum  *  wire 

50000 

Silver  *  wire 

42000 

Steel 

80000-330000 

"  wire,                   maximum 

460000 

"  Specially  treated  nickel- 

steel,  approx.  comp.  0.40 

C;    3.25   Ni;    treatment 

secret 

250000 

"  piano     wire,     0.033     "*• 

cliatn. 

357000-390000 

"  piano  wire,  0.051  in.  diam. 

325000-337000 

Tin,  cast  or  drawn 

4OOO-5OOO 

Zinc,  cast 

7000-13000 

"     drawn 

220OO-3OOOO 

According  to   Boys,  quartz  fibres  have  a 

tensile  strength  of  between  116000  and  167000 

pounds  per  square  inch. 

TABLE  35  (b).  —  Stones.* 


Material. 

Size  of  test 

Resistance  to 
crushing  in 

pds.  per  sq.  in. 

Marble 

4  in.  cubes 

7600-20700 

Tufa 

2    "         " 

7700-11600 

Brownstone 
Sandstone 

4  in.  cubes 

7300-23600 
2400-29300 

Granite 

4  '<       - 

9700-34000 

Limestone 

4  «      « 

6000-25000 

*  Data  furnished  by  the  U.  S.  Geological  Survey. 


TABLE  35(c). -Brick.* 


Kind  of  Brick. 

Resistance  to  crushing  in  pds. 
per  sq.  in. 

Tested 
flatwise. 

Tested 
on  edge. 

Soft  burned 
Medium  burned 
Hard  burned 
Vitrified 
Sand-lime 

1800-4000 
4000-6000 
6000-8500 
8500-25000 
1800-4000 

I  600-3000 
3000-4500 
4500-6500 
6500-20000 

Brick  piers  laid  up  in  I  part  Portland 
cement,  3  of  sand,  have  from  20  to  40  per 
cent  the  crushing  strength  of  the  brick. 

Authority  of  Wertheim. 


*  Data  furnished  by  the  U.  S.  Geological  Survey. 


TABLE  35  (d).  —  Concretes.* 


Coarse 
Aggregate. 

Proportions  by  volume. 
Cement  :  sand  :  aggregate. 

Size  of  test  piece. 

Resistance  to 
crushing  in  pds. 
per  sq.  in. 

Sandstone 
Cinders 
Limestone 
Conglomerate 
Trap 

I  :  5  :  14   to       :  I  :  5 
1:3:6      «        :i:3 
1:4:8      «       :  2  :  4 
I  :6  :  12    "        12:4 
1:2:9      "        :  2  :  4 

12  in.  cube 

12    "         " 
12    "         " 
12   "        " 
12   "        " 

1550-3860 
790-2050 
1200-2840 
1080-3830 
820-2960 

*  Data  furnished  by  the  U.  S.  Geological  Survey. 
SMITHSONIAN  TABLES. 


TABLE  36. 
STRENGTH  OF  MATERIALS. 

Average  Results  ol  Timber  Tests. 

The  test  pieces  were  SMALL  and  SELECTED.  Endwise  compression  tests  of 
some  of  the  first  lot,  made  when  green  and  containing  over  40  per  cent  moisture, 
showed  a  diminishing  in  strength  of  50  to  75  per  cent. 

See  also  Table  37.  A  particular  sample  may  vary  greatly  from  these  data, 
which  can  indicate  only  in  a  general  way  the  relative  values  of  a  kind  of  timber. 
Note  that  the  data  below  are  from  selected  samples  and  therefore  probably  high. 

The  upper  lot  are  from  the  U.  S.  Forestry  circular  No.  15 ;  the  lower  from  the 
tests  made  for  the  roth  U.  S.  Census. 


69 


NAME  OF  SPECIES. 

TRANSVERSE 
TESTS. 

COMPRESSION. 

SHEAR- 
ING. 

Modulus 
f  rupture, 
b./sq.  in. 

Modulus  of 
elasticity, 
bs./sq.  in. 

to  grain, 
bs./sq.  in. 

.  to  grain, 
bs./sq.  in. 

Along  the 
grain, 
bs./sq.  in. 

Long-leaf  pine 

1  2,6OO 

2,O7O,OOO 

8,000 

1260 

835 

Cuban  pine 

13,600 

2,370,000 

8,700 

I2OO  ' 

770 

Short-leaf  pine 

IO,IOO 

1,680,000 

6,500 

1050 

770 

Loblolly  pine 

11,300 

2,050,000 

7.400 

1150 

800 

White  pine 

7.900 

1,390,000 

5,400 

700 

4OO 

Red  pine 

9,100 

1  ,62O,OOO 

6,700 

IOOO 

500 

Spruce  pine 

10,000 

1,640,000 

7,300 

I2OO 

800 

Bald  cypress 

7,900 

1,  290^000 

6,000 

800 

500 

White  cedar 

6,300 

9IO,OOO 

5,200 

700 

400 

Douglass  spruce 

7,900 

I,68o,OOO 

5.700 

800 

500 

White  oak 

13,100 

2,090,000 

8,500 

22OO 

IOOO 

Overcup  oak 

11,300 

1,620,000 

7.300 

1900 

IOOO 

Post  oak 

12,300 

2,030,000 

7,100 

3000 

IIOO 

Cow  oak 

11,500 

I,6lO,OOO 

7,400 

I9OO 

900 

Red  oak 

11,400 

1,970,000 

7,200 

2300 

IIOO 

Texan  oak 

13,100 

1,860,000 

8,100 

2000 

900 

Yellow  oak 

10,800 

I,74O,OOO 

7.3oo 

1800 

IIOO 

Water  oak 

12,400 

2,OOO,OOO 

7,800 

2OOO 

IIOO 

Willow  oak 

10,400 

1,750,000 

7,200 

I6OO 

900 

Spanish  oak 

12,000 

1,930,000 

7,700 

1800 

900 

Shagbark  hickory 

16,000 

2,390,000 

9,500 

2700 

IIOO 

Mockernut  hickory 

1  5,200 

2,32O,OOO 

10,100 

3100 

IIOO 

Water  hickory 

12,500 

2,o8o,OOO 

8,400 

24OO 

IOOO 

Bitternut  hickory 

15,000 

2,280,000 

9,600 

22OO 

IOOO 

Nutmeg  hickory 
Pecan  hickory 

12,500 

15.300 

1,940,000 
2,530,000 

8,800 

9,100 

2700 
2800 

IIOO 

I2OO 

Pignut  hickory 

18,700 

2,730,000 

10,900 

3200 

I2OO 

White  elm 

10,300 

I,54O,OOO 

6,500 

I2OO 

800 

Cedar  elm 
White  ash 

13.500 

10,800 

1,700,000 
1,640,000 

8,000 
7,200 

2IOO 
I9OO 

1300 

IIOO 

Green  ash 

11,600 

2,050,000 

8,000 

I7OO 

IOOO 

Sweet  gum 

9,500 

I,7OO,OOO 

7,100 

1400 

800 

Poplar 

9,400 

1,330,000 

5,000 

1  1  2O 

Basswood 

8,340 

1,172,000 

5,190 

880 

Ironwood 

7,540 

1,158,000 

5,275 

2OOO 

Sugar  maple 
White  maple 

16,500 

14,640 

2,250,000 
I,8oO,OOO 

6^850 

3600 
2580 

Box  elder 

7,580 

873,000 

4,580 

1580 

Black  walnut 

11,900 

1,560,000 

8,000 

2680 

Sycamore 

7,000 

790,000 

6,400 

27OO 

Hemlock 

9,480 

1,138,000 

5.400 

IIOO 

Red  fir 

13,270 

1,870,000 

7,780 

1750 

Tamarack 

I3.1  5° 

1,917,000 

7,400 

1480 

Red  cedar 

1  1,  800 

938,000 

6,300 

2000 

Cottonwood 

10,440 

1,450,000 

5,000 

IIOO 

Beech 

16,200 

1,730,000 

6,770 

2840 

SMITHSONIAN  TABLES. 


70  TABLE  37. 

UNIT   STRESSES   FOR    STRUCTURAL   TIMBER 
POUNDS  PER  SQUARE  INCH. 


EXPRESSED    IN 


Recommended  by  the  Committee  on  Wooden  Bridges  and  Trestles,  American  Railway 
Engineering  Association,  1909. 


BENDING. 

SHEARING. 

KIND  OF  TIMBER. 

Extreme  fibre 
stress. 

Modulus  of 
elasticity. 

Parallel  to  grain. 

Longitudinal 
shear  in  beams. 

Average 
ultimate. 

Safe 
stress. 

Average. 

Average 
ultimate  . 

Safe 

stress. 

Average 
ultimate. 

Safe 

stress. 

Douglass  fir 

6lOO 

I2OO 

,510,000 

690 

170 

270 

no 

Long-leaf  pine 

6500 

1300 

,6lO,OOO 

720 

1  80 

300 

120 

Short-leaf  pine 

5600 

IIOO 

,480,000 

710 

170 

330 

130 

White  pine 

4400 

9OO 

,130,000 

400 

100 

1  80 

70 

Spruce 

4800 

1000 

,310,000 

600 

I5O 

170 

70 

Norway  pine 

42OO 

800 

,190,000 

590 

130 

250 

100 

Tamarack 

4600 

900 

,220,000 

670 

170 

260 

IOO 

Western  hemlock 

5800 

IIOO 

I,48o,OOO 

630 

160 

270* 

100 

Redwood 

5000 

900 

800,000 

300 

80 

- 

Bald  cypress 

4800 

900 

1,150,000 

500 

120 

— 

_ 

Red  cedar 

4200 

800 

860,000 

— 

_ 

_ 

White  oak 

5700 

IIOO    . 

1,150,000 

840 

210 

270 

no 

COMPRESSION 

0  JS 

KIND  OF  TIMBER. 

Perpendicular 
to  grain. 

Parallel  to  grain. 

lie 

Formulas  for  safe 

If'O 

53  o 

stress  in  long 

"o  v 

d-n; 

columns  over  15 

Elastic 

Safe 

Average 

Safe 

diameters.f 

limit. 

stress. 

ultimate. 

stress. 

3 

Douglass  fir 
Long-leaf  pine 
Short-leaf  pine 

630 
520 
340 

3JO 

200 
170 

3600 
3800 
3400 

1200 
I3OO 
IIOO 

900 

980 

8^0 

I200(l-L/6o.D) 

i30o(i-L/6o.D) 
iioo(i-L/6o.D) 

10 
10 
IO 

White  pine 

290 

ISO 

3000 

1000 

75° 

iooo(i-L/6o.D) 

IO 

Spruce 

370 

180 

3200 

IIOO 

8^0 

iioo(i-L/6o.D) 

_ 

Norway  pine 

I5° 

2600* 

800 

600 

8oo(i-L/6o.D) 

_ 

Tamarack 

— 

220 

3200* 

1000 

75° 

iooo(i-L/6o.D) 

_ 

Western  hemlock 

440 

220 

35°° 

I2OO 

900 

i2oo(i-L/6o.D) 

_ 

Redwood 

400 

I5O 

33°° 

900 

680 

9oo(i-L/6o.D) 

- 

Bald  cypress 

340 

170 

IIOO 

830 

iioo(i-L/6o.D) 

— 

Red  cedar 

470 

230 

2800 

900 

680 

90o(i-L/6o.D) 

_ 

White  oak 

920 

450 

35°° 

1300 

980 

i30o(i-L/6o.D) 

12 

These  unit  stresses  are  for  a  green  condition  of  the  timber  and  are  to  be  used  without  increasing  the  live- 
load  stresses  for  impact. 
*  Partially  air-dry. 
t  L = length  in  inches.    D  =  least  side  in  inches. 

SMITHSONIAN  TABLES. 


TABLES  38-39.  ji 

ELASTIC  MODULI. 

TABLE  38.  —Rigidity  Modulus. 

If  to  the  four  consecutive  faces  of  a  cube  a  tangential  stress  is  applied,  opposite  in  direction  on 
adjacent  sides,  the  modulus  of  rigidity  is  obtained  by  dividing  the  numerical  value  of  the  tangential 
stress  per  unit  area  (kg.  per  sq.  mm.)  by  the  number  representing  the  change  of  angles  on  the 
non-stressed  faces,  measured  in  radians. 


Substance. 

Rigidity 
Modulus. 

Refer- 
ence. 

Substance. 

Rigidity 
Modulus. 

Refer- 
ence. 

Aluminum  

3350 
2580 

3550 
3715 
3700 
1240 
4060 
2450 
4780 
4213 
445° 
4664 
2850 

3950 
5210 
6706 

7975 
6940 
8108 

7505 
1710 
7820 
4359 

14 

5 

10 

ii 

5 
5 
5 
5 

10 
19 
5 
14 
5 
15 

10 

,76 

H 

5 
5 
ii 

Quartz  fibre    . 

2888 
2380 
2960 
2650 

2816 
8290 

7458 
8070 
7872 
173° 

$o3 

3820 

6630 

6220 

2350 
2730 
1770 
1280 
1190 
2290 

20 
21 

5 
10 
16 
ii 
16 
15 
5 
ii 

5 
19 

5 

!9 

16 

22 

23 
23 
23 
23 

«         « 

Brass      

Silver     

M 

"      cast,  6oCu+  i2Sn    . 
Bismuth,  slowly  cooled    .     . 
Bronze,  cast,  88  Cu  -{-  12  Sn  . 

tt 

"      hard-drawn   .... 
Steel  

"    cast 

Copper,  cast   .    .    .    .    . 

"    cast,  coarse  gr.    .    .    . 

« 

Tin  cast 

« 

M 

Gold  

Zinc  .     . 

tt 

Platinum 

« 

Glass      . 

Clay  rock   

Granite  

Magnesium,  cast      .... 
Nickel    

Marble  

Slate 

Phosphor  bronze     .... 

References  1-16,  see  Table  48.                              21  Boys,  Philos.  Mag.  (5)  30,  1890. 
17  Gratz,  Wied.  Ann.  28,  1886.                              22  Thomson,  Lord  Kelvin. 
18  Savart,  Pogg.  Ann.  16,  1829.                             23  Gray  and  Milne. 
19  Kiewiet,  Diss.  Gottingen,  1886.                       24  Adams-Coker,  Carnegie  Publ.  No.  46, 
20  Threlfall,  Philos.  Mag.  (5)  30,  1890.                          1906. 

TABLE  39.  —Variation  of  the  Rigidity  Modulus  with  the  Temperature. 

nt  =  n0  (i  —  at  —  0f2  —  7/3),  where  t  =  temperature  Centigrade. 


Substance. 

n0 

aio6 

0108 

yi6» 

Authority. 

Brass    .    .         .    . 

2652 
3200 
3972 
3900 
8108 
6940 
6632 
2566 
8290 

2158 

455 
2716 

572 
206 

483 
in 

387 
187 

48 
36 

-a 

19 

12 

50 
38 

59 

32 

47 
—II 

—8 
ii 
—9 

Pisati,  Nuovo  Cimento,  5,  34,  1879. 
Kohlrausch-Loomis,  Pogg.  Ann.  141. 
Pisati,  loc.  cit. 
K  and  L,  loc.  cit. 
Pisati,  loc.  cit. 
K  and  L,  loc.  cit. 

Pisati,  loc.  cit. 
«        «     <« 

«        «     « 

M 

« 

«< 

Silver    

Steel      

nt*  =  n\&  [i  —  a  (t  —  15)];  Horton,  Philos.  Trans 

.204  A,  1905. 

Copper 
Copper  (com- 
mercial) 
Iron 

Steel 

4-37* 

3-8o 
8.26 
8-45 

o  =.00039 

.00038 
.00029 
.00026 

Platinum 
Gold 
Silver 
Aluminum 

6.46* 

2.45 
2.67 

2-55 

a  =  .00012 
.00031 
.00048 
.00148 

Tin  i. 
Lead  o. 
Cadmium  2. 
Quartz  3. 

50*  a  =.00416 
80           .00164 
31            .0058 

00               .00012 

SMITHSONIAN  TABLES. 


*  Modulus  of  rigidity  in  10"  dynes  per  sq.  cm. 


72  TABLE  40. 

ELASTIC  MODULI. 

Young's  Modulus. 

Intensity  of  longitudinal  stress  (kg.  per  sq.  mm.) 
Young's  Modulus  —  Elongation  per  unit  length 


Substance. 

Toe£P- 

fi 

W 

§•8 

>% 

£8 

<U    £ 
&   V 

I 

2 

3 
3 
4 

3 
3 

4 
9 
i 

10 

3 
3 

2 

3 
3 
7 

9 
3 
7 
ii 

10 

9 
4 
u 

9 
5 

12 
II 
2 

Substance. 

T££P- 

Young's 
Modulus. 

Ii 

£  u 

13 
13 

3 
ii 

3 
3 

2 
I 

3 
3 
3 
3 
3 
3 
4 
4 
9 
U 
13 

!3 

5 
3 
3 

!3 

24 
24 
24 

Aluminum       .... 
«( 

Lead,  drawn  .... 
"     annealed     .    .    . 

20 
12.3 
15 
15 

15 
*5 

0 

15.6 

20 

*s 

15 
12.9 

'5 
15 
o 
20 
'9-5 
15 
o 

20 
»-S 

7200 
7462 
1803 
1727 
9194 

-jo-jo 

11697 
20869 
20794 
20310 
21740 
11713 
15750 

!93«5 
28°?3i 

8630 
12450 
10520 
12140 
12550 
13220 

8543 
9810 

10220 

9930 
10450 
12094 

"550 
i33°° 
20300 
22790 
23950 
21680 

Nickel-steel,  5!%  ni.     . 
"     ,     "      25%  ••      . 
Palladium,  annealed    . 
Phosphor-bronze     .     . 
Platinum,  drawn 
"         annealed 

15 

15 
15 
13.2 

10 

15 
15 
15 
15 
15 
15 

J5-5 

*5 
15 

19900 
18600 
9709 

I20IO 
17044 
I55I8 
I6O2O 
15989 

7357 
7140 
18810 
17280 

!9550 
19560 
21136 

2III2 

2I7OO 
20705 
2O9IO 
2O6OO 
3190 

8734 
4I48 
1700 
(6000 

to 

f  8000 
(1500 

)      ^ 

(2500 

6316 

5r59 
8985 

Cadmium    

Delta  metal     ;    .     .    . 
Iron,  drawn     .... 
"     annealed    .     .    .- 
« 

"         drawn 
Silver,  drawn,  .... 
"       annealed       .     . 
Steel  wire,  drawn     .     . 
"      annealed    . 
Steel,  cast,  drawn    .     . 
"        "     annealed    . 
Bessemer  .     .     . 
puddle  .... 
mild  

« 

"       soft     

"     drawn    .... 
"     drawn    .     .     .     , 
Gold,  drawn    .... 
"     annealed     .     .     . 
"     drawn    .... 
Copper,  drawn    .     .     . 
"        annealed     .     . 
"       drawn    .     .    . 
"        drawn    .     .     . 
"        electr.  h'd  d'n 

Brass,  drawn  .... 
(i 

very  soft    .     .     . 
half  soft     .     .     . 
"      hard      .... 
Bismuth      

Zinc,  drawn    .... 
Tin,  drawn      .... 
"    cast    

Glass      

"      drawn  .... 
it 

Carbon  

u 

German  silver     .    .     . 

h'd  d'n 
«          « 

Nickel    ...... 

Marbles  

Granites      

Basic  intrusives  .     .     . 
Rocks  :    See  Nagaoka, 
Philos.  Mag.  1900. 

"      hard  drawn  .     . 
« 

i  Slotte,  Acta  Soc.  Fenn.  26,  1899;  29,  1906*.      10  Baumeister,  Wied.  Ann.  18,  1883. 
2  Meyer,  Wied.  Ann.  59,  1896.                                n  Searle,  Philos.  Mag.  (5)  49,  1900. 
3  Wertheim,  Ann.  chim.  phys.  (3    12,  1844.         12  Cantone,  Wied.  Beibl.  14,  1890. 
4  Pscheidl,  Wien.  Ber.  II,  79,  1879.                       r3  Mercadier,  C.  R.  113,  1891. 
5  Voigt,  Wied.  Ann.  48,  1893.                                 r4  Katzenelsohn,  Diss.  Berlin,  1887. 
6  Amagat,  C.  R.  108,  1889.                                      15  Wertheim,  Pogg.  Ann.  78,  1849. 
7  Kohlrausch,  Loomis,  Pogg.  Ann.  141,  1871.      16  Pisati,  Nuovo  Cimento,  5,  34,  1879. 
8  Thomas,  Drude  Ann.  i,  1900.                            References  17-19,866  Table  47. 
9  Gray,  etc.,  Proc.  Roy.  Soc.  67,  1900. 

Compiled  partly  from  Landolt-Bornstein's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  41-44. 
COMPRESSIBILITY,  HARDNESS,  CONTRACTION  OF  ELEMENTS. 

TABLE  41.  —  Compressibility  of  the  More  Important  Solid  Elements. 


73 


Arranged  in  order  of  the  increasing  atomic  weights.     The  numbers  give  the  mean  elastic  change 
of  volume  for  one  megabar  (0.987  atm.)  between  100  and  500  megabars,  multiplied  by  io5. 


Lithium                     8.8 

Potassium        31.5 

Selenium         n.8 

Iodine               13. 

Carbon                      0.5 

Calcium             5.5 

Bromine           51.8 

Caesium           61. 

Sodium                    15.4 

Chromium         0.7 

Rubidium        40. 

Platinum            0.21 

Magnesium               2.7 

Manganese        0.7 

Molybdium       0.26 

Gold                  0.47 

Aluminum                 1.3 

Iron                    0.40 

Palladium          0.38 

Mercury             3.71 

Silicon                        0.16 

Nickel                0.27 

Silver                 0.84 

Thallium           2.6 

Red  phosphorus       9.0 

Copper               0.54 

Cadmium           i  9 

Lead                  2.2 

Sulphur                    12.5 

Zinc                    1.5 

Tin                      1.6 

Bismuth            2.8 

Chlorine                  95. 

Arsenic              4.3 

Antimony           2.2 

Stull,  Zeitschr.  Phys   Chem  61,  1907. 
TABLE  42.  -  Hardness. 


Agate                7. 

Brass                3-4. 

Iridosmium                 7. 

Sulphur             !  -5-2.5 

Alabaster          1.7 

Calimine              5. 

Iron                         4-5. 

Stibnite                    2. 

Alum             2-2.5 

Calcite                 3. 

Kaolin                           I. 

Serpentine           3-4. 

Aluminum        2, 

Copper          2.5-3. 

Loess  (o°)                   0.3 

Silver                2.5-3. 

Amber          2-2.5 

Corundum           9. 

Magnetite                   6. 

Steel                     5-8.5 

Andalusite       7.5 

Diamond            io. 

Marble                    3-4. 

Talc                          i. 

Anthracite        2.2 

Dolomite      3.5-4- 

Meerschaum          2-3. 

Tin                           1.5 

Antimony         3.3 
Apatite              5. 

Feldspar              6. 
Flint                      7. 

Mica                           2.8 
Opal                        4-6. 

Topaz                     8. 
Tourmaline             7.3 

Aragonite         3.5 

Fluorite               4. 

Orthoclase                  6. 

Wax  (o°)                 0.2 

Arsenic             3.5 

Galena                 2.5 

Palladium                   4.8 

Wood's  metal        3. 

Asbestos           5. 

Garnet                 7. 

Phosphorbronze        4. 

Asphalt         1-2. 

Glass             4.5-6.5 

Platinum                     4.3 

Augite               6. 

Gold              2.5-3. 

Plat-iridium                6.5 

Barite                3.3 
Beryl                 7.8 

Graphite       0.5-1. 
Gypsum        1.6-2. 

Pyrite                          6.3 
Quartz                          7. 

Bell-metal         4. 

Hematite             6. 

Rock-salt                    2. 

Bismuth            2.5 

Hornblende         5.5 

Ross'  metal          2.5-3.0 

Boric  acid         3. 

Iridium                6. 

Silver  chloride            1.3 

From  Landolt-Bbrnstein-Meyerhoffer  Tables  :  Auerbachs,  Winklemann,  Handb.  der  Phys.  1891. 
TABLE  43.  —  Relative  Hardness  of  the  Elements. 


c 

10.0 

Ru 

6-5 

Cu 

3-° 

Au 

2-5 

Sn 

.8 

Li 

0.6 

B 

95 

Mn 

5-° 

Sb 

3-° 

Te 

2-3 

Sr 

.8 

P 

o-5 

Cr 

9.0 

Pd 

4.8 

Al 

2.9 

Cd 

2.0 

Ca 

•5 

K 

0.5 

Os 

7.0 

Fe 

4-5 

Ag 

2.7 

S 

2.0 

Ga 

•5 

Na 

0.4 

Si 

7.0 

Pt 

43 

Bi 

2.5 

Se 

2.0 

Pb 

•5 

Rb 

o-3 

Ir 

6.5 

As 

3-5 

Zn 

2-5 

Mg 

2.O 

In 

.2 

Cs 

0.2 

Rydberg,  Zeitschr.  Phys  Chem  33,  1900 
TABLE  44.  —  Ratio,  p,  ol  Transverse  Contraction  to  Longitudinal  Extension  under  Tensile  Stress. 

(Poisson's  Ratio.) 


Metal 

Pb 

Au 

Pd 

Pt 

Ag 

Cu 

Al 

Bi 

Sn 

Ni 

Cd 

Fe 

P 

0-45 

0.42 

o-39 

0-39 

0.38 

o-35 

0-34 

°-33 

0-33 

0.31 

0.30 

0.28 

From  data  from  Physikalisch-Technischen  Reichsanstalt,  1907. 
p  for:  marbles,  0.27  ;  granites,  0.24 ;  basic-intrusives,  0.36 ;  glass,  0.23.    Adams-Coker,  1906. 
SMITHSONIAN  TABLES. 


74  TABLE  45. 

'  ELASTICITY   OF   CRYSTALS.* 

The  formulas  were  deduced  from  experiments  made  on  rectangular  prismatic  bars  cut  from  the  crystal.  These  bars 
were  subjected  to  cross  bending  and  twisting  and  the  corresponding  Elastic  Moduli  deduced.  The  symbols 
a  ft  y,  at  /3t  Vj  and  a2  /3,  y2  represent  the  direction  cosines  of  the  length,  the  greater. and  the  less  transverse 
dimensions  of  the  prism  with  reference  to  the  principal  axis  of  the  crystal.  E  is  the  modulus  for  extension  or 
compression,  and  T  is  the  modulus  for  torsional  rigidity.  The  moduli  are  in  grams  per  square  centimeter. 


Barite. 

18.51/8*  +  10.427*  +  2(38.79l8V-F  15.217^  +  8.SS«"/8-) 

1  17.66/8*  +[i  16.467*  +  2(20.i6/8V  +  85.297^  +  1 


Beryl  (Emerald). 

l£  =  4.3'S  sin'*  +  4.6.9  co*  +  I3.3'8  rinV  co*  J 

io10  of  the  specimen  make  with  the 

—  =15.00-3.675  cos«fc  —  17.536  cos2^cos29i       [     principal  axis  of  the  crystal. 


Fluorspar. 

i£°  =  13.05-  6.26  (a*  + 

T010 

^  =  58.04  -  50.08  (ft 
Pyrite. 


=  18.60  -  17-95  (0V  +  7-«2  + 
Rock  salt. 


-  =  1  54.58  -  77-28  (  j8  V  +  72«2  +«202) 

Sylvine. 

Ig-0  =  75-1  -48.2  (a*  +  ^  +  74) 

Tnio 

f^p  =  306.0  —  192.8  (/8V  +  72«2  +  a2£2) 

Topaz. 

^°  =  4.34ia4  +  3.46o)84  +  3-77  174  +  2  (3-879/8  V  +  2.8567^  +  2.39a2^) 

Tnio 

^r  =  I4.88a*  +  I6-54/31  +  I6-4574  +  3°^90V  +  40.8972«2  +  43-5i<»202 

Quartz. 

ij0  =  1  2.734  (i  -  72)2  +  16.693  (i  -  7^72  +  9.7057*  -  8.460/87  (3a2  -  0-) 

io10 

—  =  19.665  -f-  9.060732  +  22.9847V  —  16.920  [(7/8!+  £71)  (3001  —  £/8i) 


*  These  formul«e  are  taken  from  Voigt's  papers  (Wied.  Ann.  vols.  31,  34,  and  35). 
SMITHSONIAN  TABLES. 


TABLE  46. 
ELASTICITY   OF  CRYSTALS. 


75 


Some  particular  values  of  the  Elastic  Moduli  are  here  given.  Under  E  are  given  moduli  for  extension  or  compression 
in  the  directions  indicated  by  the  subscripts  and  explained  in  the  notes,  and  under  T  the  moduli  for  torsional 
rigidities  round  the  axes  similarly  indicated.  Moduli  in  grams  per  sq.  cm. 


(a)  ISOMETRIC  SYSTEM.* 


Substance. 


Authority. 


Fluorspar  . 
Pyrite  .  . 
Rock  salt  . 


Sylvine 


Sodium  chlorate 
Potassium  alum  . 
Chromium  alum 
Iron  alum  . 


1473  X  io6 
3530  X  io6 
419  X  io6 
403  X  io6 
401  X  io6 
372  X  io6 
405  X  io6 
181  X  io6 
161  X  io6 
186  X  io6 


1008  X  io6 
2530  X  io6 
349  X  io6 
339  X  io6 
209  X  io6 
196  X  io6 
319  X  io6 
199  X  io6 
177  X  io6 


910  X  io6 
2310  X  io6 

303  X  IO6 


345  X  io6 

1075  X  io6 

I29X  io6 


655  X  io6 


Voigt.f 


Koch.J 
« 

Voigt. 
Koch. 
Beckenkamp.§ 


(6)  ORTHORHOMBIC  SYSTEM.] 


Substance. 


Barite 
Topaz 


620  X  io6 

2304  X  io6 


E2 


Xio6 


959  X  io6 
2652  X  io6 


376  X  io6 
2670  X  io6 


702  X  io6 
2893  X  io6 


740  X  io6 
3180  X  io6 


Authority. 


Voigt. 


Substance. 


Authority. 


Barite 
Topaz 


283  X  io6 
m6x  io6 


293  X  io6 
1353X10' 


121  X  IO6 

1104  X  io6 


Voigt. 


In  the  MONOCLINIC  SYSTEM,  Coromilas  (Zeit.  fur  Kryst.  vol.  i)  gives 
Gvpsum  f  E^  =  887  X  io6  at  21.9°  to  the  principal  axis. 
I  E^u^  313  Xio6  at  75.4°          "          "         " 

Mica       |  Emax  =  2213  X  Io6  in  the  PrinciPal  axis- 

Emin  =  1554  X  io6  at  45°  to  the  principal  axis. 


In  the  HEXAGONAL  SYSTEM,  Voigt  gives  measurements  on  a  beryl  crystal  (emerald). 

The  subscripts  indicate  inclination  in  degrees  of  the  axis  of  stress  to  the  principal  axis  of 

the  crystal. 

E0=2i65Xio«,     £45=1796  Xio6,    E90  =231 2  Xio6, 

TO  =  667  X  io6,      Tgo  =  883  X  io6.      The  smallest  cross  dimension  of  the 

prism  experimented  on  (see  Table  82),  was  in  the  principal  axis  for  this  last  case. 


In  the  RHOMBOHEDRAL  SYSTEM,  Voigt  has  measured  quartz.    The  subscripts  have  the 
same  meaning  as  in  the  hexagonal  system. 

£0=1030  Xio6,     E_  45  =1305  Xio6,    £+45  =  850  Xio6,     £90=785X108, 

To  =  508  X  io8,      T90  =  348  X  io6. 
Baumgarten  H"  gives  for  calcite 

£0  =  501  X  io6,    E_  45  =  441  X  io6,    £+  45  =  772  X  io6,    E9o  =  79°  X  io6. 


*  In  this  system  the  subscript  a  indicates  that  compression  or  extension  takes  place  along  the  crystalline  axis,  and 
distortion  round  the  axis.  The  subscripts  b  and  c  correspond  to  directions  equally  inclined  to  two  and  normal  to  the 
third  and  equally  inclined  to  all  three  axes  respectively. 

T  Voigt,  "  Wied.  Ann."  31,  p.  474,  p.  701,  1*87 ;  34,  P-  981,  1888;  36,  p.  642,  1888. 

%  Koch,  "Wied.  Ann."  18,  p.  325,  1882. 

§  Beckenkamp,  "Zeit.  fur  Kryst."  vol.  io. 

||  The  subscripts  i,  2,  3  indicate  that  the  three  principal  axes  are  the  axes  of  stress;  4,  5,  6  that  the  axes  of  stress 
are  in  the  three  principal  planes  at  angles  of  45°  to  the  corresponding  axes. 

IT  Baumgarten,  "  Pogg.  Ann."  152,  p.  369,  1879. 
SMITHSONIAN   TABLES. 


76 


TABLES  47-49. 
COMPRESSIBILITY  OF  CASES 


TABLE  47.  —Relative  Volumes  at  Various  Pressures  and  Temperatures,  the  volume  at  0°  G  and  at  1  atmo- 
sphere being  taken  as  1 000  000. 


Oxygen. 

Air. 

Nitrogen. 

Hydrogen. 

Atm. 

0° 

99°-S 

>99°.S 

0° 

990.4 

200°.4 

0° 

99°-5 

i99°.6 

0° 

99°-3 

200°.  5 

IOO 

9265 

_ 

973° 

_ 

_ 

9910 

_ 

_ 

_ 

_ 

_ 

200 

300 

4570 
3208 

7000 
4843 

9095 
6283 

7360 

9430 

6622 

3786 

7445 
53oi 

9532 
6715 

5690 
4030 

7567 
5286 

9420 

6520 

4OO 

2629 

4900 

3036 

4170 

5240 

3142 

4265 

5331 

3207 

4147 

5075 

|00 
600 

23I2 
2115 

3244 
2867 

4100 
3570 

2450 

3565 
3180 

4422 

3883 

2780 
2543 

3655 
3258 

3973 

2713 
2387 

3462 
3006 

4210 

3627 

700 

1979 

26lO 

32O2 

2288 

2904 

3502 

2374 

2980 

3589 

2149 

2680 

3212 

800 

1879 

2417 

2929 

2168 

2699 

3219 

2240 

2775 

3300 

1972 

2444 

2900 

900 

I800 

2268 

27l8 

2070 

2544 

3000 

2149 

2616 

3085 

1832 

2244 

2657 

1000 

1735 

2151 

1992 

2415 

2828 

2068 

1720 

2093 

Amagat:  C.  R.  in,  p.  871,  1890;  Ann.  chim.  phys.  (6)  29,  pp.  68  and  505,  1893. 

TABLE  48. -Ethylene. 

pv  at  o°  C  and  i  atm.  =  I. 


Atm. 

0° 

10° 

20° 

30° 

40° 

60° 

80° 

100° 

'«* 

i98°.s 

46 

_ 

0.562 

0.684 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

48 

— 

0.508 

— 

— 

— 

— 

— 

— 

— 

— 

50 

0.176 

O.42O 

O.629 

0.731 

0.814 

0-954 

1.077 

1.192 

1-374 

1.652 

52 

— 

0.240 

0.598 

— 

— 

— 

— 

— 

—  - 

~ 

54 

— 

O.229 

O.56l 

— 

— 

— 

— 

— 

— 

— 

56 

— 

0.227 

0.524 

— 

— 

— 

— 

— 

— 

— 

IOO 

0.310 

0-331 

0.360 

0.403 

0.471 

0.668 

0.847 

1.005 

•247 

1.580 

150 

0.441 

0.459 

0.485 

0.515 

0.551 

0.649 

0.776 

0.924 

.178 

1.540 

200 

0-565 

0.585 

0.610 

0.638 

0.669 

0.744 

0.838 

0.946 

.174 

1.537 

300 

0.806 

0.827 

0.852 

0.878 

0.908 

0.972 

1.048 

1-133 

.310 

1.628 

500 

1000 

1.256 
2.289 

1.280 
2.321 

1.308 
2-354 

'•337 
2.387 

2.422 

M31 
2-493 

1.500 
2.566 

1.578 

2.643 

.721 
2.798 

1.985 

Amagat,  C.  R.  in,  p.  871,  1890;  116,  p.  946,  1893. 
TABLE  49.  —  Ethylene. 


Pressure  in 

Relative  values  of  PV  at  — 

meters  of 

mercury. 

i6°3 

20°.3 

3°°  ' 

4o°.o 

5o°.o 

60°.  o 

7o°.o 

79°-9 

89°.9 

100°  .0 

30 

1950 

2055 

222O 

2410 

2580 

2715 

2865 

2970 

3090 

3225 

60 

810 

900 

1190 

1535 

1875 

2100 

2310 

2500 

2680 

2860 

90 

1065 

TI95 

1510 

I7IO 

1930 

2l6o 

2375 

2565 

1  20 

1325 

1370 

1440 

1540 

1660 

1780 

1950 

2115 

2305 

2470 

150 

!59Q 

1625 

1690 

1785 

1880 

1990 

2125 

2250 

2390 

2540 

1  80 

1855 

1890 

1945 

2035 

2130 

2225 

2340 

2450 

2565 

2700 

210 

2IIO 

2145 

22OO 

2285 

2375 

2470 

2565 

2680 

2790 

2910 

240 

2360 

2395 

2450 

2540 

2625 

272O 

2810 

2910 

3OI5 

3I25 

270 

2610 

2640 

27IO 

2790 

287  S 

2965 

3060 

3150 

3240 

3345 

300 

2860 

2890 

2960 

3040 

3I25 

3215 

3300 

3380 

3470 

3560 

320 

3°35 

3065 

3^5 

3200 

3285 

3375 

3470 

3545 

3625 

3710 

Amagat,  Ann.  chim.  phys.  (5)  22,  p.  353, 


SMITHSONIAN  TABLES. 


TABLES  50-52. 
COMPRESSIBILITY  OF  GASES. 

TABLE  50.  —  Carbon  Dioxide. 


77 


Pressure  in 

Relative  values  of  pv  at  — 

mercury. 

l8°,2 

35° 

.1 

40°.2 

50°.o 

6o°.o 

70°.o 

8o°.o 

90°.o 

100°  .0 

30 

liquid 

2360 

2460 

2590 

2730 

2870 

29 

9S 

3I2O 

3225 

£ 

625 

1725 
750 

1900 

825 

2145 
I2OO 

2330 
1650 

2525 

*975 

2685 
2225 

2845 
2440 

2980 

2635 

no 

825 

93° 

980 

IO9O 

1275 

1550 

1845 

2105 

2325 

140 

1  020 

1120 

1175 

1250 

1360 

1525 

1715 

J95° 

2160 

170 

I2IO 

1310 

1360 

M30 

1520 

1645 

1780 

*975 

2135 

200 

1405 

I5OO 

1550 

1615 

1705 

1810 

1930 

2075 

2215 

230 

J59Q 

i6c 

P 

1730 

I800 

1890 

1990 

2090 

2210 

2340 

260 

1770 

1870 

1920 

1985 

2070 

2166 

2265 

2375 

2490 

290 

J95° 

2060 

2  IOO 

2170 

2260 

2340 

2440 

2550 

2655 

320 

2135 

2240 

2280 

2360 

2440 

2525 

2620 

2725 

2830 

Relative  values  of  PV  ;  pv  at  o°  C.  and  i  atm.  =  i. 

0° 

10° 

20° 

30°            40° 

60° 

80° 

100° 

137°       198°        258° 

50 

0.105 

0.114 

0.680 

0-775       0.750 

0-984 

1.096 

1.  206 

1.380       - 

IOO 

O.2O2 

0.213 

0.229 

0.255       0.309 

0.661 

0.873 

1.030 

1.259     1.582      1.847 

150 

0.295 

0.309 

O.326 

0.346      0.377 

0.485 

0.681 

0.878 

1.159     1.530     1.818 

300 

°-559 

0.578 

0-599 

0.623      0.649 

0.710 

0.790 

0.890 

1.108     M93     1.820 

500 

0.891 

0.913 

0.938 

0.963       0.990 

1.054 

1.124 

I.2OI 

1.362     1.678 

IOOO 

1.656 

1.685 

1.716 

1.748       1.780 

1.848 

I.92I 

1.999 

.      - 

Amagat,  C.  R.  in,  p.  871,  1890;  Ann.  chim.  phys.  (5)  22,  p.  353,  1881;  (6)  29,  pp.  68  and  405*  1893. 


TABLE  51.  -  Compressibility  of  Gases. 


Gas. 

p.v.  (\  atm.) 

i     d(p.v.) 
p.v.       dp 
—  a. 

t 

a 

t  =  O 

Density. 

0  =  32,  o°C 
P  =  76om 

Density. 
Very  small 
pressure. 

povo  (i  atm.). 

02 

1.00038 

—  .00076 

11.2° 

—  .00094 

32. 

32. 

H2 

0-99974 

+  .00052 

10.7 

+  .00053 

2.015  (16°) 

2.0173 

N2 
CO 

I.OOOI5 
1.00026 

—  .00030 
—  .00052 

14.9 
13.8 

—  .00056 

—  .00081 

28.005 
28.000 

28.016 
28.003 

C02 
N2O 

1.00279 
1.00327 

—  .00558 
—  .00654 

15-0 
II.O 

—  .00668 
—  -00747 

44.268 
44.285 

44.014 
43.996 

Air 

I.OOO26 

—  .00046 

II.4 

— 

NH3 

1.00632 

"™ 

" 

Rayleigh,  Zeitschr.  Phys.  Chem.  52,  p.  705,  1905. 
TABLE  52.  -  Compressibility  of  Air  and  Oxygen  between  18°  and  22°  0. 

Pressures  in  metres  of  mercury,  pv,  relative. 


Air 
02 

P 
pv 

24.07 
26968 

34.90 
26908 

45-24 
26791 

55-30 

26789 

64.00 

26778 

72.16 

26792 

84.22 
26840 

101.47 
27041 

214.54 

;  29585 

304.04 
32488 

P 

pv 

24.07 
26843 

34.89 

26614 

- 

55.50 
26185 

64.07 
26050 

72.15 

25858 

84.19 

25745 

101.06 
25639 

214.52 
26536 

303-03 
28756 

Amagat,  C.  R.  1879. 


SMITHSONIAN  TABLES. 


78  TABLES  53-54. 

RELATION    BETWEEN    PRESSURE,   TEMPERATURE    AND 
VOLUME  OF  SULPHUR  DIOXIDE  AND  AMMONIA.* 


TABLE  63.— Sulphur  Dioxide. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experi- 
ments as  indicated  at  the  top  of  the  different  columns. 


Pressure  in  1 
Atmos. 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for 
Experiments  at  Temperature  — 

58°.o 

99°-6 

l83°.2 

58°.o 

99°.6 

l83°.2 

IO 

8560 

9440 

_ 

12 

6360 

7800 

- 

1  0000 

- 

9.60 

- 

14 
rfi 

4040 

6420 

- 

9000 

9.60 

10-35 

- 

18 

_ 

4405 

_ 

8000 

10.40 

11.85 

- 

20 

- 

4030 

- 

7000 

11.55 

I3-05 

- 

24 
28 
32 

- 

3345 
2780 

2305 

3180 

2640 

6000 
5000 

12.30 

14.70 
16.70 

_ 

36 

- 

1935 

2260 

4000 

14.00 

20.15 

- 

40 
CQ 

~ 

1450 

2040 
1640 

35°0 

1440 

23.00 

- 

60 

- 

- 

1375 

3000 

- 

26.40 

29.10 

70 

- 

— 

1130 

2500 

— 

30.15 

33-25 

80 
90 

100 

- 

- 

93° 
790 
680 

2000 
1500 

- 

35-20 
39.60 

40.95 

55-20 

1  20 

- 

- 

545 

IOOO 

- 

- 

76.00 

140 

160 

- 

- 

43° 
325 

500 

~ 

•^ 

117.20 

TABLE  64.— Ammonia. 

Original  volume  100000  under  one  atmosphere  of  pressure  and  the  temperature  of  the  experiments  as 
indicated  at  the  top  of  the  different  columns. 


Pressure  in 
Atmos. 

Corresponding  Volume  for  Ex- 
periments at  Temperature  — 

Volume. 

Pressure  in  Atmospheres  for  Experiments 
at  Temperature  — 

46°.6 

99°-6 

i83°.6 

300.2 

46°.6 

99°.6 

i83°.o 

10 

9500 

_ 

_ 

IOOOO 

8.85 

9-50 

_ 

12-5 

7245 

OfiX 

7635 

- 

9000 

9.60 

10.45 

- 

20 

25 

5000 

6305 
4645 

4875 
3835 

8000 
7OOO 

10.40 
11.05 

11.50 

13.00 

12.00 
13.60 

_ 

30 

- 

2875 

3^5 

6000 

11.80 

1475 

15-55 

- 

35 
40 

45 

- 

2440 
2080 

2680 
2345 
2035 

5000 
4000 

12.00 

16.60 
18.35 

1  8.60 
22.70 

19.50 

24.00 

So 

- 

1490 

1775 

3500 

— 

18.30 

25-40 

27.20 

55 

— 

1250 

!59o 

3000 

— 

— 

29.20 

31.50 

60 

— 

975 

145° 

2500 

- 

- 

34-25 

37-35 

70 
80 

_. 

1245 

II2C 

2000 

- 

- 

41-45 

45-50 

90 

_ 

_ 

I035 

I5OO 

- 

- 

4970 

58.00 

100 

" 

950 

IOOO 

" 

" 

59.65 

93-6o 

From  the  experiments  of  Roth,  "  Wied.  Ann."  vol.  n,  1880. 


SMITHSONIAN  TABLES. 


TABLE  55. 
COMPRESSIBILITY  OF  LIQUIDS, 


79 


If  V\  is  the  volume  under  pressure  p\  atmospheres  at  t°C,  and  V%  is  volume  at  pressure  /2  and  the 
same  temperature,  then  the  compressibility  coefficient  may  be  defined  at  that  temperature  as : 


In  absolute  units  (referred  to  megadynes)  the  coefficient  is 


1.0137 


Substance. 

t. 

Pressures. 

,:* 

li 

Substance. 

'• 

Pressures. 

,.,, 

li 

Acetone 

0 

0.00 

1-500 

82 

i 

Methyl  alcohol 

O 
IOO. 

.8.68-37.3 

221 

3 

" 

o.oo 

500-1000 

59 

" 

«                        it 

18.10 

8 

120 

2 

" 

o.oo 

IOOO-I5OO 

47 

w 

Nitric  acid 

20.3 

1-32 

338 

II 

Benzole 

99-5 
5-95 
17.9 

8.94-36.5 

8 
8 

276 

83 
92 

3 

2 
it 

Oils  :  Almond 
Olive 
Paraffin 

J7- 

14.8 

P 

63 

8 
6 

" 

154 

1-4 

87 

4 

Petroleum 

16.5 

_ 

70 

12 

« 

78.8 

1-4 

126 

Rock 

19.4 

- 

75 

8 

Carbon  bisulphide 

0.00 

1-500 

66 

i 

Rape-seed 

20.3 

- 

60 

<( 

«<              « 

0.00 

500-1000 

53 

" 

Turpentin 

19.7 

— 

79 

** 

<«              it 

o.oo 

1000-1500 

43 

" 

Toluene 

10. 

- 

79 

13 

Chloroform 

49.2 

0. 

1000-1500 

Si 

101 

5 

Xylene 

IOO. 
10. 

™* 

74 

li 

" 

20. 

— 

128 

tt 

H 

IOO. 

— 

132 

" 

M 

40. 

- 

162 

" 

Paraffins:  C6H14 

23- 

O-I 

159 

14 

" 

60. 

— 

204 

u 

C7Hie 

" 

134 

M 

" 

IOO. 

8-9 

211 

3 

CsHjg 

" 

" 

121 

" 

H 

IOO. 

J9~34 

206 

CgH2o 

" 

<« 

"3 

ft 

Collodium 

14.8 

97 

6 

" 

M 

105 

U 

Ethyl  alcohol 

28. 

150-200 

86 

7 

Ci2-H2g 

" 

11 

92 

" 

«           « 

28. 

i  50-400 

81 

" 

C^rigo 

" 

" 

83 

tl 

ft           « 

65. 

150-200 

no 

" 

CieHsi 

tt 

M 

75 

" 

«           it 

65. 

150-400 

IOO 

" 

Water 

0. 

1-25 

52-5 

I 

u           « 

IOO. 

150-200 

168 

" 

M 

10. 

M 

50.0 

tt           tt 

IOO. 

150-400 

132 

" 

" 

20. 

U 

49.1 

tf 

tt           tt 

185. 

150-200 

320 

" 

" 

0. 

25-50 

51.6 

II 

it           tt 

185. 

150-400 

245 

" 

« 

10. 

49.2 

" 

tt           tt 

310. 

150-200 

4200 

" 

* 

20. 

U 

47.6 

" 

u           tt 

310. 

i  50-400 

1530 

M 

" 

0. 

I-IOO 

51'1 

II 

tt                 tt 

0. 

1-50 

96 

I 

" 

10. 

" 

48.3 

tl 

tf          tt 

20. 

1-50 

112 

" 

" 

20. 

" 

46.8 

tl 

tt            tt 

40. 

1-50 

I2>5 

(i 

tt 

50. 

" 

44-9 

tt            tt 

o. 

100-200 

85 

M 

" 

IOO. 

" 

47.8 

11 

tt            tt 

0. 

300-400 

73 

M 

" 

0. 

100-200 

49.2 

" 

tt            tt 

20. 

300-400 

78 

" 

" 

10. 

" 

46.1 

* 

ft            tt 

40. 

3OO-4OO 

87 

M 

" 

20. 

" 

44.2 

* 

tt               tl 

0. 

5OO-6OO 

64 

«' 

« 

5°. 

" 

42-5 

" 

tt               tt 

o. 

20. 

7OO-8OO 
700-800 

i 

M 

M 

IOO. 

o. 

i"soo 

46.§ 
47-5 

"l 

tt          ft 

40. 

700-800 

65 

M 

" 

20.4 

" 

434 

" 

tl            ft 

0. 

9OO-IOOO 

52 

" 

« 

48.85 

M 

41.6 

" 

Ethyl  chloride 

II. 

8.5-34.2 

138 

3 

it 

0. 

500-1000 

41.6 

" 

«          n 

15-2 

8.7-37.2 

" 

tt 

0. 

IOOO-I500 

35-8 

tt 

tt          tt 

61.5 

12.6-34.4 

256 

u 

" 

20.4 

" 

33-8 

" 

tt          tt 

99.0 

12.8-34.5 

495 

" 

" 

48.85 

it 

32.5 

«« 

Glycerine 

20.< 

25 

8 

(I 

0. 

I  5OO-2OOO 

324 

tl 

" 

14.8 

— 

22 

6 

" 

0. 

2OOO-25OO 

29.2 

" 

Mercury 

0. 

- 

3-92 

9 

* 

0. 

2500-3000 

26.1 

" 

" 

0. 

— 

3-90 

10 

" 

48.85 

254 

" 

Methyl  alcohol 

14.7 

8.50-37-I 

104 

3 

For  references  see  page  80. 


SMITHSONIAN  TABLES. 


8o  TABLE  56. 

COMPRESSIBILITY  AND   BULK  MODULI  OF  SOLIDS. 


r 

Solid. 

Compression 
per  unit 
volume  per 
atmo.  X  io6. 

Authority. 

Calculated  values  of  bulk 
modulus  in  — 

Grams  per 
sq.  cm. 

Pounds  per 
sq.  in. 

i-93 

0.747 

1.20 
I.I4 

2.67 
4.20* 

745* 
0.61 
0.113 

0-95 
0.86 

1.02 

2.76 

0.68 
2.2-2.9 

Voigt    .     .     . 

« 
« 
« 
« 
« 
« 
« 

Amagat     .     . 
Buchanan 
Amagat    .     . 

M 

« 
« 

535  X  io6 

906     « 

387      " 
246     " 
138     " 
1694     " 
9140     ' 
1090     ' 
I2O2      " 
1012      " 

374    " 
1518    " 

405    " 

7.61  X  io8 

19.68      " 
12.24      " 
12.89      " 
5.50      « 

3-50  ;; 
1.97  " 
24.11  « 
130.10  " 

15.48  « 
17.10  " 
14.41  " 
5-32  ' 

21.61     " 

5.76  '« 

Beryl  

Fluorspar     .         •     •    •    « 

Sylvine                   .... 

Topaz  
Tourmaline  

Brass  

Lead  

Steel        

Glass  

NOTE:  Winklemann,  Schott,  and  Straulel  (Wied  Ann.  61,  63,  1897; 
others)  for  various  Jena  glasses  in  terms  of  the  volume  decrease  divided 
grams  per  square  millimeter : 
:  for 


)  give  the  following  coefficients  (among 
increase  of  pressure  expressed  in  kilo- 


The  following  values  in  cm2  /  Kg  of  io6  X  Compressibility  are  given  for  the  corresponding  temperatures  by  Griineisen 
Ann.  der  Phys.  33,  p.  65,  1910. 


Al.  —191°,  1.32;  17°,  x.46;  125°,  1.70. 
Cu.  —191°,  0.72;  17°,  0.77;  165°,  0.83. 
Pt.  — 189°,  0.37 ;  17°,  0.39 ;  164°,  0.40. 


Fe.  —  190°,  0.61 ;  18°,  0.63 ;  165°,  0.67. 
Ag.  —  191°,  0.71 ;  16°,  0.76;  166°,  0.86. 
Pb.- 191°, (2.5);  14°,  (3-2) 


No. 

Glass. 

Compres- 
sibility. 

No. 

Glass. 

Compres- 
sibility 

665 

7?2O 

2154 

Kalibleisilicat  

7660 

1299 

Barytborosilicat  

cgoo 

Slo8 

Heaviest  Bleisilicat 

16 

Natronkalkzinksilicat  .... 

Very  Heavy    " 

278 

S  196 

*  Rontgen  and  Schneider  by  piezometric  experiments  obtained  5.0  X  io-6  for  rock  salt,  and  5.6  X  io-8  for  sylvine 
(Wied.  Ann.,  vol.  31). 


References  to  Tables  55  and  56. 


Liquids  (Table  55) : 

1  Amagat,  Ann.  chim.  phys.  (6)  29,  1893. 

2  Rontgen,  Wied.  Ann.  44,  p.  i,  1891. 

3  Amagat,  C.   R.  68,  p.   1170,   1869;  Ann. 

chim.  phys.  (5)  28,    1883. 

4  Pagliani-Palazzo,  Mem.  Acad.  Lin.  (3)  19, 

1883. 

5  Grimaldi,  Zeitschr.  Phys.  Chem.  I,  1887. 

6  de  Metz,  Wied.  Ann.  41,  p.  663, 1890;  47, 

p.  706,  1892. 

7  Barus,  Sill.  Journ.  39,  p.  478, 1890;  41, 1891 ; 

Bull.  U.S.  Geol.  Surv.  1892. 
Solids  (Table  56)  : 
Amagat,  C.  R.  108,  p.  228, 1889;  J.  de  Phys.  (2) 

8,  p.i97,  1889. 


8  Quincke,  Wied.  Ann.  19,  p.  401,  1883. 

9  Amagat,  Ann.  chim.  phys.  (6)  22,  p.  95, 1891. 

10  Aime,  Ann.  chim.  phys.  (3)  8,  p.  268,  1843. 

11  Colladon-Sturm,  Pogg.  Ann.  12,  p.  39,  1828. 

12  Martini. 

13  de  Heen,  Bull.  Acad.  Roy.  Belg.  (3)  9,  1885. 

14  Bartoli,  Rend  Lomb.  (2)  28,  29,  1896. 

15  Protz,  Ann.  der  Phys.  (4)  31,  p.  127,  1910. 
See  also  Bridgman,  Proc.  Ann.  Acad.  48,  p.  309, 

1912  (H2O)  49,  p.  3, 1913  (alcohols,  etc.) ; 
49,  p.  627,  1914  (high  pressure  technique). 

Buchanan,  Proc.  Roy.  Soc.  Edinb.  io,  1880. 
Voigt,   Wied.  Ann.  31,  1887;  34,   1888,  36, 
1888. 


SMITHSONIAN  TABLES. 


TABLE  57.  gj 

SPECIFIC  GRAVITIES  CORRESPONDING  TO  THE  BAUME  SCALE. 

The  specific  gravities  are  for  15.56^  (6o°F)  referred  to  water  at  the  same  temperature  as  unity. 
For  specific  gravities  less  than  unity  the  values  are  calculated  from  the  formula : 


Degrees  Baume 


140 


For  specific  gravities  greater  than  unity  from: 

Degrees  Baume  =  145  — 


Specific  Gravity 
'45 


—130. 


Specific  Gravity 


Specific  Gravities  less  than  i. 

0.00 

O.OI 

0.02 

0.03 

O.O4 

O.O5 

O.o6 

0.07 

0.08 

0.09 

Specific 

Gravity. 

Degrees  Baum6. 

O.6o 
.70 

103.33 

70.00 

99-51 
67.18 

95.81 
64.44 

92.22 
61.78 

88.75 
59-19 

8£38 
56.67 

82.12 
54-21 

78.95 
51.82 

75-88 
4949 

72.90 
47.22 

.80 
.90 

45.00 
2S-56 

42.84 
23^5 

40.73 
22.17 

38.68 
20.54 

36.67 
18.94 

34-71 
17-37 

32.79 
15.83 

30.92 
14.33 

29.09 
12.86 

27.30 
11.41 

I.OO 

IO.OO 

Specific  Gravities  greater  than  i. 

0.00 

O.OI 

O.02 

O.O3 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09 

Specific 

Gravity. 

Degrees  Baume. 

.00 

0.00 

1.44 

2.84 

4-22 

S-58 

6.91 

8.21 

9-49 

10.74 

11.97 

.10 
.20 

13.18 
24.17 

14.37 

25.16 

15-54 
26.15 

16.68 
27.11 

17.81 
28.06 

18.91 
29.00 

20.00 
29.92 

21.07 
30.83 

22.12 
31.72 

23.15 
32.60 

•30 

3346 

34-31 

35-15 

35-98 

36.79 

37-59 

39.16 

39-93 

40.68 

.40 
•50 

4J-43 
48.33 

42.16 
48.97 

42.89 
49.60 

43.60 
50.23 

44-31 
50.84 

45-00 
51-45 

45-68 
52-05 

46.36 
52.64 

47.03 
53.23 

47.68 
53-8o 

.60 
-70 

54.38 

59-7  1 

54-94 
60.20 

5549 
6O.7O 

56.04 

61.18 

56-58 
61.67 

57.12 
62.14 

57.65 
62.61 

58-17 
63.08 

58.69 
63-54 

59-20 
63-99 

.80 

64.44 

64.89 

65-33 

6576 

i  66.20 

66.62 

SMITHSONIAN  TABLES. 


82 


TABLES  58-59. 

REDUCTIONS  OF  WEIGHINGS  IN  AIR  TO  VACUO. 

TABLE  58. 


When  the  weight  M  in  grams  of  a  body  is  determined  in  air,  a  correction  is  necessary  for  the 
buoyancy  of  the  air  equal  to  M  5  (i/d — i/dj)  where  8  =  the  density  (wt.  of  I  ccm  in  grams 
=  0.0012)  of  the  air  during  the  weighing,  d  the  density  of  the  body,  dt  that  of  the  weights. 
5  for  various  barometric  values  and  humidities  may  be  determined  from  Tables  153  to  155.  The 
following  table  is  computed  for  5  =  0.0012.  The  corrected  weight  =  M  +  kM/iooo. 


Density 
of  body 
weighed 
d. 

Correction  factor,  k. 

Density 
of  body 
weighed 
d. 

Correction  factor,  k. 

Pt.  Ir. 

weights 

Brass 
weights 
8.4. 

Quartz  or 

Al.  weights 
2.65. 

Pt.  Ir. 

weights 

Brass 
weights 
8.4. 

Ouartz  or 

AI.  weights 
2.65. 

i 

-7 

+  2.34 

+  1  '94 
+  1.66 

+  2.26 

+  1.86 

+  i-95 
+  i-55 
+  1.26 

1.6 

3 

+  0.69 
+     -65 
+     .62 

+  0.6I 
+    .56 
+     .52 

+  0.30 
+     -25 
+     .21 

•75 

+  !-55 

+  1.46 

+  1-15 

1.9 

+     .58 

+    49 

--     .18 

.80 

+  1.44 

+  1.36 

2.O 

+     -54 

+    46 

~~     •!$ 

.85 
.90 

+  1-36 
+  1.28 

+  1-27 
+  1.19 

^0.96 
.88 

2-5 

+    43 
+    -34 

+    -34 
+    .26 

+     -03 
—     -05 

•95 

+  I.2I 

+  I.I2 

+     .8! 

4.0 

+    .24 

+    .16 

.00 

.1 

+  1-04 

+  1.06 

6.0 

8.0 

+    -H 
+    -09 

+    .06 

+     .01 

—     -30 

.2 

•3 

4 

+  0.94 

+   -87 
+   .80 

+     78 

+   -55 
+   47 
+    40 

1  0.0 

15.0 

20.0 

+    .06 
+    -03 
+    .004 

—     .02 
—     .06 
—     .08 

—   -33 
~   -37 
~   -39 

•5 

+   -75 

+   .66 

+   -35 

22.0 

—   .001 

—     .09 

—   .40 

TABLE  59.  —  Reductions  of  Densities  in  Air  to  Vacno. 

(This  correction  may  be  accomplished  through  the  use  of  the  above  table  for  each  separate 
weighing.) 

If  s  is  the  density  of  the  substance  as  calculated  from  the  uncorrected  weights,  S  its  true  den- 
sity, and  L  the  true  density  of  the  liquid  used,  then  the  vacuum  correction  to  be  applied  to  the 
uncorrected  density,  s,  is  0.0012  (i  — s/L). 

Let  Ws  =  uncorrected  weight  of  substance,  Wi  =  uncorrected  weight  of  the  liquid  displaced 
by  the  substance,  then  by  definition,  s  =  LWS  /Wj.  Assuming  D  to  be  the  density  of  the 
balance  of  weights,  Ws  {i  +0.0012  (r/S  —  i/D)}and  Wi  {i  +0.0012  (i/L  — i/D)}are  the 
true  weights  of  the  substance  and  liquid  respectively  (assuming  that  the  weighings  are  made 
under  normal  atmospheric  corrections,  so  that  the  weight  of  i  cc.  of  air  is  0.0012  gram). 

Ws{i  +  0.0012  (i/S  —  i 
Then  the  true  density 


But  from  above  Ws/Wi 


Wi  {i  +  0.0012  (i/L—  i/D) } 

s/L,  and  since  L  is  always  large  compared  with  0.0012, 
S  —  s  =  0.0012  (i — s/L). 
The  values  of  0.0012  (i — s/L)  for  densities  up  to  20  and  for  liquids  of  density  i  (water), 
0.852  (xylene)  and  13.55  (mercury)  follow : 

(See  reference  below  for  discussion  of  density  determinations). 


Density  of 
substance 
s. 

Corrections. 

Density  of 
substance 

s 

Corrections. 

L=i 

Water. 

L~  0.852 
Xylene. 

L=  '3-55 
Mercury. 

L=i 
Water. 

L=  13-55 
Mercury. 

0.8 

+  O.OOO24 

II. 

—  O.OI2O 

+  O.OOO2 

0.9 

+    .OOOI2 

- 

_ 

12. 

—    .0132 

+     .OOOI 

i. 

o.oooo 

—  O.OOO2 

+  O.OOII 

13. 

—    .0144 

0.0000 

2. 

—   .0012 

—    .OOl6 

+     .0010 

14. 

—    .0156 

0.0000 

3- 
4- 

—  .0024 
—  .0036 

—    .0030 
—    .0044 

+  .0009 
+  .0008 

\l 

—     .0168 
—    .0180 

—     .OOOI 
—     .OOO2 

i: 

—  .0048 

—   .0060 

—    .0058 
—    .0073 

+  .0008 
+  .0007 

17- 

18. 

—    .0192 
—     .O2O4 

—    .0003 
—    .0004 

7. 

—  .0072 

—    .0087 

+   .0006 

19. 

—    .O2l6 

—    .OOO5 

8. 

—  .0084 

—    .0101 

+  .0005 

20. 

—    .0228 

—    .0006 

9- 

—  .0096 

—  .0115 

+  .0004 

10. 

—  .0108 

—  .0129 

+  .0003 

SMITHSONIAN  TABLES. 


Johnston  and  Adams,  J.  Am.  Chem.  Soc.  34,  p.  563,  1912. 


TABLE  60.  g  o 

DENSITY  OR    MASS    IN   CRAMS   PER    CUBIC   CENTIMETER   OF  THE 
ELEMENTS,    LIQUID   OR    SOLID. 

N.  B.     The  density  of  a  specimen  may  depend  considerably  on  its  state  and  previous  treatment. 


Element. 

Physical  State. 

Grams  per 
cu.  cm.* 

Tempera- 
ture.t 

Authority. 

Aluminum 

cast 

2.56-2.58 

" 

wrought 

2.65-2.80 

« 

pure 

2.58 

4 

Mallet,  1882. 

Antimony 

vacuo-distilled 

6.618 

2O 

Kahlbaum,  1902. 

u 

ditto-compressed 

6.691 

20 

« 

« 

amorphous 

6.22 

Herard. 

Argon 

liquid 

1-3845 

-I83 

Baly-Donnan. 

" 

« 

M233 

—  I89 

u          « 

Arsenic 

crystallized 

5-73 

14 

" 

amorph.  br.-black 

3-70 

Geuther. 

" 

yellow 

3-88 

Linck. 

Barium 

3-78 

Guntz. 

Bismuth 

solid 

9.70-9.90 

" 

electrolytic 

9-747 

Classen,  1890. 

" 

vacuo-distilled 

9.781 

2O 

Kahlbaum,  1902. 

« 

liquid 

10.00 

271 

Vincentini-Omodei. 

« 

solid 

9.67 

271 

«                 u 

Boron 

crystal 

2.535 

Wigand. 

a 

amorph.  pure 

2.45 

Moissan. 

Bromine 

liquid 

3.12 

Richards-Stull. 

Cadmium 

cast 

8.54-8.57 

" 

wrought 

8.67 

« 

vacuo-distilled 

8.648 

20 

Kahlbaum,  1902. 

u 

solid 

8.37 

318 

Vincentini-Omodei. 

« 

liquid 

7-99 

318 

«             « 

Caesium 

I-873 

20 

Richards-Brink. 

Calcium 

i-54 

Brink. 

Carbon 

diamond 

3-52 

Wigand. 

« 

graphite 

2.25 

if 

Cerium 

electrolytic 

6.79 

Muthmann-  Weiss. 

« 

pure 

7.02 

4<                            « 

Chlorine 

liquid 

i-5°7 

-33-6 

Drugman-Ramsay. 

Chromium 

6.52-6.73 

u 

pure 

6.92 

20 

Moissan. 

Cobalt 

8.71 

21 

Tilden,  Ch.  C.  1898. 

Columbium 

8.4 

15 

Muthmann-  Weiss. 

Copper 

cast 

8.30-8.95 

M 

drawn 

8-93-8.95 

It 

wrought 

8.85-8.95 

« 

electrolytic 

8.88-8.95 

« 

vacuo-distilled 

8.9326 

2O 

Kahlbaum,  1902. 

« 
« 

Erbium 

ditto-compressed 
liquid 

8.9376 
8.217 
4-77 

2O 

Roberts-  Wrightson. 
St.  Meyer,  Z.  Ph.  Ch.  37. 

Fluorine 
Gallium 

liquid 

1.14 

5-93 

—  200 
23 

Moissan-Dewar. 
de  Boisbaudran. 

Germanium 

5.46 

2O 

Winkler. 

Glucinum 

1.85 

Humpidge. 

Gold 

cast 

19.3 

«« 
« 

wrought 
vacuo-distilled 

m 

20 

Kahlbaum,  1902. 

Helium 
Hydrogen 
Indium 

ditto-compressed 
liquid 
liquid 

19.27 
0.15 

0.070 
7.28 

20 
-269 

—  252 

Onnes,  1908. 
Dewar,  Ch.  News,  1904. 
Richards. 

*To  reduce  to  pounds  per  cu.  ft.  multiply  by  62.4. 
t  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 

Compiled  from  Clarke's  Constants  of  Nature,  Landolt-Bbrnstein-Meyerhoffer's  Tables,  and  other  sources.   Where 
no  authority  is  stated,  the  values  are  mostly  means  from  various  sources. 

SMITHSONIAN  TABLES. 


84 


TABLE    60  (continued). 

DENSITY  OR    MASS    IN    CRAMS    PER  CUBIC   CENTIMETER  OF  THE 
ELEMENTS,    LIQUID   OR   SOLID. 


r  

Element. 

Physical  State 

Grams  per 
cu.  cm.* 

Temper-- 
ature.f 

Authority. 

Iridium 

22.42 

17 

Deville-Debray 

Iodine 

4.940 

2O 

Richards-Stull 

Iron 

pure 

7.85-7.88 

M 

gray  cast 

7-03-7-I3 

« 

white  cast 

7.58-7.73 

« 

wrought 

7.80-7.90 

« 

liquid 

6.88 

Roberts-Austen 

M 

steel 

7.60-7.80 

Krypton 
Lanthanum 

liquid 

2.16 
6.15 

-I46 

Ramsay-Travers 
Muthmann-Weiss 

Lead 

cast 

n-37 

24 

Reich 

wrought 

11.36 

24 

M 

" 

solid 

11.005 

325 

Vincentini-Omodei 

« 

liquid 

10.645 

325 

U                              It 

« 

vacuo-distilled 

11.342 

20 

Kahlbaum,  1902 

« 

ditto-compressed 

n-347 

20 

"             " 

Lithium 

0-534 

2O 

Richards-Brink,  '07 

Magnesium 

1.741 

Voigt 

Manganese 
Mercury 

liquid 

7.42 
I3-596 

O 

Prelinger 
Regnault,  Volkmann 

" 

" 

I3-546 

2O 

u 

• 

13.690 

-38.8 

Vincentini-Omodei 

K 

solid 

I4-I93 

Mallet 

« 

" 

i4-383 

—  1  88 

Dewar,  1902 

Molybdenum 

9.01 

Moissan 

Neodymium 

6.96 

Muthmann-Weiss 

Nickel 

8.60-8.90 

Nitrogen 

liquid 

0.810 

—195 

Baly-Donnan,  1902 

M 

H 

0.854 

-—205 

"          "           " 

Osmium 

22.5 

Deville-Debray 

Oxygen 

liquid 

1.14 

—184 

Palladium 

12.  16 

Richards-Stull 

Phosphorus 

white 

1.83 

H 

red 

2.20 

M 

metallic 

2-34 

15 

Hittorf 

Platinum 

21.37 

20 

Richards-Stull 

Potassium 

0.870 

2O 

Richards-Brink,  '07 

M 

solid 

0.851 

62.1 

Vincentini-Omodei 

It 

liquid 

0.830 

62.1 

«                       u 

Praesodymium 

6-475 

Muthmann-Weiss 

Rhodium 

12.44 

Holborn  Henning 

Rubidium 

I-532 

2O 

Richards-Brink,  '07 

Ruthenium 

12.06 

0 

Toby 

Samarium 

7.7-7.8 

Muthmann-Weiss 

Selenium 

4.3-4.8 

Silicon 

cryst. 

2.42 

20 

Richards-Stull-Brink 

" 

amorph. 

2-35 

15 

Vigoroux 

Silver 

cast 

10.42-10.53 

" 

wrought 

10.6 

" 

vacuo-distilled 

10.492 

2O 

Kahlbaum,  1902 

" 

ditto-compressed 

10.503 

2O 

"              " 

" 

liquid 

9-51 

Wrightson 

Sodium 

0.9712 

20 

Richards-  Brink,  '07 

" 

solid 

0.9519 

97-6 

Vincentini-Omodei 

" 

liquid 

0.9287 

u             « 

" 

1.0066 

188 

Dewar 

Strontium 

2.50-2.58 

Matthiessen 

Sulphur 

2.O-2.I 

liquid 

I.SlI 

"3 

Vincentini-Omodei 

*To  reduce  to  pounds  per  cubic  ft.  multiply  by  62.4. 

t  Where  the  temperature  is  not  given,  ordinary  atmosphere  temperature  is  understood. 


SMITHSONIAN   TABLES. 


TABLES  60  (continued}  AND  61.    MASS  OF  VARIOUS  SUBSTANCES.         85 

TABLE  60  (continued).  — "Density  or  Mass  in  grams  per  cable  centimeter  and  pounds  per  cubic  foot  of  the 

elements,  liquid  or  solid. 


Element. 

Physical  State. 

Grams  per 
cu.  cm. 

Tempera- 
ture. 

Authority. 

Tantalum 

16.6 

Tellurium 

crystallized 

6.25 

« 

amorphous 

6.O2 

2O 

Beljankin. 

Thallium 

u.86 

Richards-Stull. 

Thorium 

12.16 

17 

Bolton. 

Tin 

white,  cast 

7.29 

Matthiessen. 

« 

"      wrought 

7-30 

« 

"      crystallized 

6.97-7.18 

« 

"      solid 

7.184 

226 

Vincentini-Omodei 

« 

"      liquid 

6.99 

226 

Vincentini-Omodei 

M 

gray 

5.8 

Titanium 
Tungsten 

4.5 

18.6-19.1 

18 

Mixter. 

Uranium 

18.7 

I3 

Zimmermann. 

Vanadium 

5.69 

Ruff-Martin. 

Xenon 
Yttrium 

liquid 

3*80 

109 

Ramsay-Travers. 
St.  Meyer. 

Zinc 

cast 

7.04-7.16 

« 

wrought 

7.19 

« 

vacuo-distilled 

6.92 

20 

Kahlbaum,  1902. 

M 
• 

ditto-compressed 
liquid 

p 

20 

«             <« 
Roberts-  Wrightson  . 

Zirconium 

6.44 

TABLE  61.  —  Mass  In  grams  per  cubic  centimeter  and  in  pounds  per  cubic  foot  of  different  kinds  of  wood. 

The  wood  is  supposed  to  be  seasoned  and  of  average  dryness. 


Wood. 

Grams 
per  cubic 
centimeter. 

Pounds 
3er  cubic 
foot. 

Wood. 

Grams 
per  cubic 
centimeter. 

Pounds 
per  cubic 
foot. 

Alder 

0.42-0.68 

26-42 

Hazel 

O.6b-O.8o 

37-49 

Apple 

0.66-0.84 

41-52 

Hickory 

0.60-0.93 

37-58 

Ash 

0.65-0.85 

40-53 

Holly 

0.76 

47 

Bamboo 

0.31-0.40 

Iron-bark 

1.03 

64 

Basswood.    See  Linden. 

Juniper 

0.56 

35 

Beech 
Blue  gum 

0.70-0.90 
I.OO 

43-56 
62 

Laburnum 
Lancewood 

0.92 

0.68-1.00 

42-62 

Birch 

0.51-0.77 

32-48 

Lignum  vitae 

1.17-1.33 

73-83 

Box 

0.95-1.16 

59-72 

Linden  or  Lime-tree 

0.32-0.59 

20-37 

Bullet-tree 

1.05 

65 

Locust 

0.67-0.71 

42-44 

Butternut 

0.38 

24 

Logwood 

.91 

57 

Cedar 
Cherry 
Cork 

0.49-0.57 
0.70-0.90 
0.22-0.26 

30-35 
43-56 
14-16 

Mahogany,  Honduras 
"           Spanish 
Maple 

0.66 
0.85 
0.62-0.75 

53 
39-47 

Dogwood 
Ebony 
Elm 

0.76 
I.II-I.33 
0.54-0.60 

47 
69-83 

34-37 

Oak 
Pear-tree 
Plum-tree 

0.60-0.90 
0.61-0.73 
0.66-0.78 

37-56 

38-45 
41-49 

Fir  or  Pine,  American 

Poplar 

0-35-0-5 

22-31 

White 

0.35-0.50 

22-31 

Satinwood 

0-95 

59 

Larch 

0.50-0.56 

3T~35 

Sycamore 

0.40-0.60 

24-37 

Pitch 

0.83-0.85 

52-53 

Teak,  Indian 

0.66-0.88 

41—55 

Red 
Scotch 

0.48-0.70 
0-43-0-53 

30-44 
27-33 

"      African 
Walnut 

0.98 
0.64-0.70 

61 

40-43 

Spruce 
Yellow 

0.48-0.70 
0.37-0.60 

30-44 
23-37 

Water  gum 
Willow 

I.OO 

0.40-0.60 

62 

24-37 

Greenheart 

0.93-1.04 

58-65 

*  Where  the  temperature  is  not  given,  ordinary  atmospheric  temperature  is  understood. 
SMITHSONIAN  TABLES. 


86 


TABLE  62. 


DENSITY  OR   MASS  IN   GRAMS   PER   CUBIC   CENTIMETER  AND   POUNDS 
PER   CUBIC   FOOT   OF   VARIOUS   SOLIDS. 

N.  B.     The  density  of  a  specimen  depends  considerably  on  its  state  and  previous  treatment ;  especially  is  this  the 
case  with  porous  materials. 


Material. 

Grams  per 
cu.  cm. 

Pounds  per 
cu.  foot. 

Material. 

Grams  per 
cu.  cm. 

Pounds  per 
cu.  foot. 

Agate 

2.5-2.7 

156-168 

Gum  arabic 

1.3-1.4 

80-  85 

Alabaster  : 
Carbonate 
Sulphate 

2.69-2.78 
2.26-2.32 

I68-I73 
141-145 

Gypsum 
Hematite 
Hornblende 

2.31-2.33 

4-9-5-3 
3-° 

144-145 
306-330 
187 

Albite 
Amber 

2.62-2.65 
I.06-I.II 

163-165 

66-  69 

Ice 
Ilmenite 

0.917 
4.5-5- 

57-2 
280-310 

Amphiboles 

2.9-3.2 

180-200 

Ivory 

1.83-1.92 

114-120 

Anorthite 

2.74-2.76 

171-172 

Labrador!  te 

2.7-2.72 

168-170 

Anthracite 
Asbestos 

I.4-I.8 

2.0-2.8 

87-112 
125-175 

Lava  :  basaltic 
trachytic 

2.8-3.0 

2.0-2.7 

175-183 
125-168 

Asphalt 

I.I-I.5 

69-  94 

Leather:  dry 

0.86 

54 

Basalt 

2.4-3.1 

150-190 

greased 

1.02 

64 

Beeswax 

0.96-0.97 

60-  61 

Lime  :  mortar 

1.65-1.78 

103-111 

Beryl 
Biotite 

2.69-2.7 
2.7-3.1 

168-168 
170-190 

slaked 
Limestone 

I.3-I.4 
2.68-2.76 

81-  87 
167-171 

Bone 

1.7-2.0 

106-125 

Litharge  : 

Brick 
Butter 

1.4-2.2 
0.86-0.87 

87-137 
53-  54 

Artificial 
Natural 

9-3-9-4 
7.8-8.0 

580-585 
490-500 

Calamine 

4-1-4-5 

255-280 

Magnetite 

4-9-5-2 

306-324 

Caoutchouc 

0.92-0.99 

57-  62 

Malachite 

3.7-4-  i 

231-256 

Celluloid 

1.4 

87 

Marble 

2.6-2.84 

160-177 

Cement,  set 

2.7-3.0 

170-190 

Meerschaum 

0.99-1.28 

62-  80 

Chalk 

1.9-2.8 

118-175 

Mica 

2.6-3.2 

165-200 

Charcoal  :   oak 
pine 

0-57 
0.28-0.44 

£.* 

Muscovite 
Ochre 

2.76-3.00 
3-5 

172-225 
218 

Chrome  yellow 

6.00 

374 

Oligoclase 

2.65-2.67 

165-167 

Chromite 

4-32-4-57 

270-285 

Olivine 

3.27—3.37 

204-210 

Cinnabar 

8.12 

5°7 

Opal 

2.2 

I37 

Clay 

1.8-2.6 

122-162 

Orthoclase 

2.58-2.61 

161-163 

Coal,  soft 

1.2-1.5 

75-  94 

Paper 

0.7-I.I5 

44-  72 

Cocoa  butter 

0.89-0.91 

56-  57 

Paraffin 

0.87-0.91 

54-  57 

Coke 

1.0-1.7 

62-105 

Peat 

0.84 

52 

Copal 

1.04-1.14 

65-  71 

Pitch 

1.07 

67 

Corundum 

3.9-4.0 

245-250 

Porcelain 

2.3-2.5 

143-156 

Diamond  : 

Porphyry 

2.6-2-9 

162-181 

Anthracitic 

1.66 

104 

Pyrite 

4-95-5.  l 

309-318 

Carbonado 

3.01-3.25 

188-203 

Quartz 

2.65 

165 

Diorite 

2.52 

J57 

Quartzite 

2-73 

170 

Dolomite 

2.84 

177 

Resin 

1.07 

67 

Ebonite 

72 

Rock  salt 

2.18 

136 

Emery 

4-o 

250 

Rutile 

6.00-6.5 

374-406 

Epidote 

3-25-3-5 

203-218 

Sandstone 

2.14-2.36 

I34-M7 

Feldspar 

2-55-2-75 

159-172 

Serpentine 

2.50-2.65 

156-165 

Flint 

2.63 

164 

Slag,  furnace 

2.0-3.9 

125-240 

Fluorite 

198 

Slate 

2.6-3.3 

162-205 

Gamboge 

1.2 

75 

Soapstone 

2.6-2.8 

162-175 

Garnet 

3-  i  5-4-3 

197-268 

Starch 

!-53 

95 

Gas  carbon 

1.88 

117 

Sugar 

1.61 

100 

Gelatine 

1.27 

180 

Talc 

2.7-2.8 

168-174 

Glass  :  common 

2.4-2.8 

150-175 

Tallow 

0.91-0.97 

57-  60 

flint 

2.9-5-9 

180-370 

Topaz 

3-5-3-6 

219-223 

Glue 

1.27 

80 

Tourmaline 

3-0-3-2 

190-200 

Granite 

2.64-2.76 

165-172 

Zircon 

4.68-4.70 

292-293 

Graphite 

2.30-2.72 

144-170 

SMITHSONIAN  TABLES. 


TABLE  63. 

DENSITY  OR   MASS  IN  CRAMS  PER  CUBIC  CENTIMETER 

AND  POUNDS  PER  CUBIC  FOOT  OF  VARIOUS 

ALLOYS  (BRASSES  AND  BRONZES). 


Alloy. 

Grams 
per  cubic 
centimeter. 

Pounds 
per  cubic 
foot. 

8.44 
8.56 
8.70 
8.60 

8.20 

8.78 
8.89 

8.74 
8-83 
8.30 
8.45 
8.34 
8.30 

8-77 
1  0.60 

10-33 
10.05 

9-43 

Fy 

10.56 
9.70 
7.70 
18.84 
18.36 

17-95 
17.52 
17.16 

1  6.8  1 
16.47 
7.69 

8-37 
8.69 
2.80 
21.62 
21.62 
21.87 
22.38 
8.88 

2.O 
8.5 
9-0 

527 

534 
54| 
536 
5" 
548 
555 
545 

& 

52? 
520 
518 

$ 

644 

627 
588 
545 
|i4 
659 
605 
480 
1176 
H45 

II2O 
1093 
1071 
1049 
1027 
480 
522 
542 
175 
1348 
1348 
I364 
1396 

554 
125 
530 
560 

«                «                 "              rolled      
"                "                 "              drawn      

German  Silver:  Chinese,  26.3Cu-f36.6Zn  +  36.8Ni 
"            '         Berlin  (i)  52Cu  +  26Zn  +  22Ni      .... 
"            '              "     (2)  59Cu  -j-  3oZn  -f  iiNi      .... 
"     (3)  63Cu  +  3oZn  +  6Ni        .... 
«            <          Nickelin             .         

"       "        «      77.8Pb+22.2Sn        
"       u       "      61  ?Pb4-  16  iSn 

"       "       "      A.6  ?Pb  4-  c.1  iSn 

"       "       "      30.5Pb-j-69.5Sn        
Bismuth,  Lead,  and  Tin:  53B1  +  40  Pb  +  7  Cd          .... 
Wood's  Metal:  5oBi+25Pb+  i2.5Cd+  1  2.5Sn     .... 

«      «         «          96Au  -j-  4^u         

"      "         "          94Au  -{•  6Cu        .                        .... 

«      "         «          9oAu  +  loCu      

«      «         «          88Au-|-i2Cu       

Aluminum  and  Copper:  loAl  +  9oCu       ....'.. 
"           "         "           cA14-Qt;Cu 

u          "         "          8<;Pt4-  it;Ir  .                                ... 

66.67  Pt  +  33-33^         

Platinoid  :  German  silver  -f  little  Tungsten       

SMITHSONIAN  TABLES. 


88  TABLES  64-65. 

TABLE  64.- DENSITIES  OF  VARIOUS  NATURAL  AND  ARTIFICIAL 

MINERALS. 

(See  also  Table  62.) 


1 

Density 

Sp.Vol. 

j 

Density 

Sp.  Vol. 

i 

Name  and  Formula. 

grams 

cc.  per 

£ 

Name  and  Formula. 

grams 

cc.  per 

per  cc. 

gram. 

& 

per  cc. 

gram. 

lu 

Pure    compounds,    all    at 

Feldspars  : 

25°C 

Albite  glass,  NaAlSi3O8, 

Magnesia,  MgO 

3-603 

•2775 

i 

art. 

2-375 

4210 

6 

Lime,  CaO 

3-306 

•3025 

2 

Albite  cryst.,  NaAlSi3O8, 

Forms  of  SiO2: 

art. 

2-597 

•3851 

" 

Quartz,  natural 

2.646 

•3779 

" 

Anorthite  glass, 

"       artificial 

2.642 

•3785 

" 

CaAl2Si2O8,  art. 

2.692 

•3715 

'< 

Cristobalite,  artificial 

2.319 

.4312 

M 

Anorthite  cryst., 

Silica  glass 

2.2O6 

•4533 

" 

CaAl2Si2O8,  art. 

2-757 

.3627 

u 

Forms  of  Al2SiO5  : 

Soda  anorthite, 

Sillimanite  glass 
Sillimanite  cryst. 

2.53 
3-022 

•395 
•33°9 

I 

NaAlSiO4,  art. 
Borax,  glass,  Na2B4O7 

2-563 
2-36 

.3902 
.423 

6 

Forms  of  MgSiO3  : 

"       cryst.        " 

2.27 

.440 

u 

ft  Monoclinic  pyroxene 

3-I83 

.3142 

5 

Fluorite,  natural,  CaF2 

a'  Orthorhombic  pyroxene 

3-166 

•3*59 

(20°) 

3.180 

•3T45 

8 

/3*  Monoclinic  amphibole 

" 

(NH4)2S04                 (30°) 

1-765 

.5666 

9 

7'  Orthorhombic  amphi- 

K3S04                       (30°) 

2.657 

•3764 

u 

bole 

2.849 

.3510 

" 

KC1,  fine  powder      (30°) 

1.984 

.5040 

u 

Glass 

2-735 

•3656 

" 

Forms  of  ZnS  : 

Forms  of  CaSiO8  : 

Sphalerite,  natural* 

4.090 

•2444 

10 

a  (Pseudo-wollastonite) 
ft  (Wollastonite) 

2|o6 

-3444 
•3441 

2 

Wurtzite,  artificial! 
Greenockite,  artificial 

4.087 
4.820 

•2447 
.2075 

ti 

Glass 

2.895 

•3454 

" 

Forms  of  HgS  : 

Forms  of  Ca2SiO4  : 

Cinnabar,  artificial 

8.176 

.1223 

•* 

a  —  calcium-orthosilicate 

3.26 

•3°7 

« 

Metacinnabar,  artifi- 

ft —      "                  " 

3-27 

.306 

U 

cial 

7.58 

.132 

" 

7-   ;;          ;; 

2.965 

•337 

" 

Minerals  : 

Lime-alumina  compounds  : 

Gehlenite,    from    Velar  - 

3CaO  '  A1203 
5CaO  •  3A]2OS 

3.029 
2.820 

•3301 
.3546 

3 

dena 
Spurrite,  from  Velardena, 

3-03 

•330 

II 

CaO  •  A1203 

2.972 

•3365 

it 

2Ca2SiO4  •  CaCO3 

3-005 

-3328 

<« 

3CaO  •  5A12OS 

Hillebrandite,  from  Vel- 

3CaO •  5A12O3,  unstable 

ardena, 

form 

3-°4 

-329 

U 

CaSi03'Ca(OH)2 

2.684 

.3726 

" 

Forms  of  MgSiO3  •  CaSiO3  : 
Diopside,  natural,  cryst. 

3-258 

.3069 

4 

Pyrite,  natural,  FeS^ 
Marcasite,  natural,  FeS2 

5.012 
4.873 

-T995 
.2052 

IO 

M 

artificial,  " 
glass 

3-265 
2.846 

•3063 
•35M 

u 

I 

*  Only  0.15%  Fe  total  impurity, 
t  Same  composition  as  Sphaler- 

ite. 

References:  I,  Larsen  1909;  2,  Day  and  Shepherd;  3,  Shepherd  and  Rankin,  1909;  4,  Allen  and 
White,  1909;  5,  Allen,  Wright  and  Clement,  1906;  6,  Day  and  Allen,  1905;  7,  Washington  and 
Wright,  1910;  8,  Merwin,  1911  ;  9,  Johnston  and  Adams,  1911;  10,  Allen  and  Crenshaw,  1912; 
II,  Wright,  1908. 

All  the  data  of  this  table  are  from  the  Geophysical  Laboratory,  Washington. 

TABLE  65. -DENSITIES  OF  MOLTEN  TIN  AND  TIN-LEAD  EUTECTIC. 


Temperature 
Molten  tin 
37  pts.  Pb,  63,  Sn  * 

25o°C. 
6.982 
8.01  1 

300° 
6-943 
7-965 

400° 
6.875 
7.879 

500° 
6.814 
7.800 

600° 

6-755 
7-731 

900° 
6.578 

1200° 

6-399 

1400° 
6.280 

1600° 
6.162 

*  Melts  at  181.    Day  and  Sosman,  Geophysical  Laboratory,  unpublished. 

For  further  densities  inorganic  substances  see  table  238. 
organic  "      "     244. 

SMITHSONIAN  TABLES. 


TABLES  66-67. 
WEIGHT  OF  SHEET    METAL. 

TABLE  66.— Weight  of  Sheet  Metal.    (Metric  Measure.) 

This  table  gives  the  weight  in  grams  of  a  plate  one  meter  square  and  of  the  thickness  stated  in  the 

first  column. 


89 


Thickness 

in  thou- 
sandths of 

Iron. 

Copper. 

Brass. 

Aluminum. 

Platinum. 

Gold. 

Silver. 

a  cm. 

1 

78.0 

89.0 

85.6 

26.7 

215.0 

193.0 

105.0 

2 

156.0 

178.0 

I7I.2 

53-4 

430.0 

386.0 

2IO.O 

3 

4 

234.0 
312.0 

267.0 
356.0 

256.8 
342.4 

80.  i 
106.8 

6450 
860.0 

579-0 
772.0 

3*5-0 
420.0 

5 

390.0 

445-0 

428.0 

133-5 

1075.0 

965.0 

525-0 

6 

468.0 

534-0 

513.6 

160.2 

1290.0 

1158.0 

630.0 

7 

546.0 

623.0 

599-2 

186.9 

I505-0 

"351-0 

735-o 

8 

624.0 

712.0 

684.8 

213.6 

1720.0 

1544.0 

840.0 

9 

7O2.O 

80  1.  o 

770.4 

240.3 

1  935-0 

i737.o 

945-0 

10 

780.0 

890.0 

856.0 

267.0 

2150.0 

1930.0 

1050.0 

TABLE  67.  -  Weight  of  Sheet  Metal.    (British  Measure.) 


Iron. 

Copper. 

Brass. 

Aluminum. 

Platinum. 

in  Mils. 

Pounds  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Ounces  per 
Sq.  Foot. 

Pounds  per 
Sq.  Foot. 

Ounces  per 
Sq.  Foot. 

1 

.04058 

.04630 

.04454 

.01389 

.2222 

.1119 

1.790 

2 

.08116 

.09260 

.08908 

.02778 

•4445 

.2237 

3-579 

3 

.12173 

.13890 

•J3363 

.04167 

.6667 

.3356 

4 

.16231 

.18520 

.17817 

•05556 

.8890 

•4474 

7-158 

5 

.20289 

.23150 

.22271 

.06945 

I.III2 

-5593 

8.948 

6 

.24347 

.27780 

.26725 

-08334 

J-3335 

.6711 

10.738 

9 

.28405 

.32463 
.36520 

.32411 

.37041 
.41671 

•31Z79 

.09723 
.11112 
.I25OI 

J-5557 
1.7780 

2.OOO2 

•7830 
.8948 
1.0067 

12.527 
16.106 

10 

.40578 

46301 

.44542 

.13890 

2.2224 

1.1185 

17.896 

Gold. 

Silver. 

Thickness 
in  Mils. 

Troy 
Ounces  per 
Sq.  Foot. 

Grains  per 
Sq.  Foot 

Troy 
Ounces  per 
Sq.  Foot. 

Grains  per 
Sq.  Foot. 

1 

1.4642 

702.8 

0.7967 

3824 

2 

2.9285 

I405-7 

1-5933 

764-8 

3 

4.3927 

2108.5 

2.3900 

II47.2 

4 

5-8570 

2811.3 

3-1867 

1529.6 

5 

7.3212 

35M-2 

39833 

I9I2.O 

6 

8.7854 

4217.0 

4.7800 

2294.4 

7 

10.2497 

4919.8 

5-5767 

2676.8 

8 

"•7I39 

5622.7 

6-3734 

3059-2 

9 

13.1782 

6325-5 

7.1700 

3441.6 

10 

14.6424 

7028.3 

7.9667 

3824.0 

SMITHSONIAN  TABLES. 


90  TABLE  68. 

DENSITY  OF  LIQUIDS. 

Density  or  mass  in  grams  per  cubic  centimeter  and  in  pounds  per  cubic  foot  of  various  liquids. 


Liquid. 

Grams  per 
cubic  centimeter. 

Pounds  per 
cubic  foot. 

Temp.  C. 

0.792         . 
0.807 
O.SlO 

i<<>35 

0.899 
3-187 
0.950-0.965 
1.293 
1.480 
0.736 
0.66-0.69 
1.260 
1.028-1.035 
0.848-0.810 
0.665 
0.800 
0.996 
0.910 
0.969 
0.925 
0.926 
1.040-1.100 
0.920 
0.877 
0.844 
0.942 
0.918 
0.905 
0.850-0.860 
0.924 
0.915 
0.913 

o-955 
0.918-0.925 

0.873 
0.965 
0.878 
0.795-0.805 
0.800 

1.  000 

494 

5°4 

56.1 
199.0 
59.2-60.2 
80.6 
92.3 
45-9 
41.0-43.0 
78.6 
64.2-64.6 
52.9-50.5 
4i-5 
49-9 
62.1 
56.8 
60.5 
57-7 
57-8 
64.9-68.6 
574 
54-7 
52-7 
58.8 

57-3 
56.5 
53.0-54.0 

57-7 
57-i 
57-0 
59-6 
57-3-57-7 
54-2 
60.2 
54-8 
49.6-50.2 

49-9 
62.4 

20° 
0 
0 

o 
o 

0 

15 

o 
18 

0 

o 
o 

15 

!l 

i5 

16 
15 

II 

16 
15 
15 
15 
15 

15 
15 
15 

16 
16 

0 

15 
o 

4 

Alcohol,  ethyl  . 

methyl       
Anilin        

Carbolic  acid  (crude)       

Ether        

Gasoline  

Milk          

Naphtha  (wood)       

Oils  :   Amber    
Anise-seed     

Castor    

Cocoanut       
Cotton  Seed  

Lard      ....                . 

Linseed  (boiled)    
Olive     .... 
Palm      ........ 

Pine       

Poppy    

"        (refined)         
Resin     . 

Train  or  Whale     

Valerian         
Petroleum        

(light)      

SMITHSONIAN  TABLES. 


TABLE  69.  gi 

DENSITY  OF  CASES. 

The  following  table  gives  the  density  of  the  gases  at  o°  C,  76  cm.  pressure,  at  sea-level  and  lati- 
tude 45°  relative  to  air  as  unity  and  under  the  same  conditions ;  also  the  weight  of  one  liter  in 
grams  and  one  cubic  foot  in  pounds. 


Gas. 

Specific 
Gravity. 

Grams 
per  liter. 

Pounds 
per  cubic 
foot. 

Reference. 

Air 

I.  COO 

1.2928 

.08071 

Rayleigh;  Leduc. 

Acetylene 

0.92 

1.1620 

.07254 

Berthelot,  1860. 

Ammonia 

°-597 

0.7706 

.048  1  1 

Leduc,  C.  R.  125,  1897. 

Argon 

1.379 

1.782 

.1112 

Ramsey-Travers,  Proc.  R.  Soc.  67,  1900. 

Bromine 

5-524 

7.1388 

•4457 

Jahn,  1882. 

Butane 

2.OI 

2.594 

.16194 

Frankland,  Ann.  Ch.  Pharm.  71. 

Carbon  dioxide 

1.5291 

1.9768 

.12341 

Guye,  Pintza,  1908. 

"       monoxide 
Chlorine 

0.9672 
2.491 

1.2506 
3-!674 

.07807 
•19774 

Rayleigh,  Proc.  R.  Soc.  62,  1897. 
Leduc,  C.  R.  125,  1897. 

Coal  gas  \  from 

0.320 

0.414 

.02583 

*     (  to 

0.740 

0-957- 

-°5973 

Cyanogen 

1.  806 

2.3229 

.14522 

Gay-Lussac. 

Ethane 

1.0494 

I-3567 

.08470 

Baume,  Perot,  J.  Ch.  et  Phys.  1908. 

Fluorine 

1.26 

1.697 

.1059 

Moissan,  C.  R.  109. 

Helium 

1.368 

0.1787 

.01116 

Ramsay-Travers,  Proc.  R.  Soc.  67,  1900. 

Hydrofluoric  acid 

0.7126 

0.894 

.05581 

Thorpe-Hambley,  J.  Chem.  Soc.  53. 

Hydrobromic  acid 

2.71 

3.6163 

.2258 

Lowig,  Gmelin-Kraut,  Org.  Chem. 

Hydrochloric  acid 

1.2684 

1.6398 

.10237 

Guye-Gazarian,  1908. 

Hydrogen 

0.0696 

0.09004 

.005621 

Rayleigh,  Proc.  R.  Soc.  53,  1893. 

Hydrogen  sulphide 

1.1895 

i.5230 

.09508 

Leduc,  C.  R.  125,  1897. 

Krypton 

2.868 

3.708 

•*3fS 

Watson,  J.  Ch.  Soc.  1910. 

Methane 
Neon 

0-5576 

0.6963 

0.7160 
0.9002 

.04470 
.0558 

Thomson. 
Watson,  J.  Ch.  Soc.  1910. 

Nitrogen 

0.9673 

1.2514 

.07812 

Rayleigh,  Proc.  R.  Soc.  62,  1897. 

Nitric  oxide,  NO 

1.0367 

1.3402 

•08367 

Guye,  Davila,  1908. 

Nitrous  oxide,  N2O 

1.5298 

1.9777 

•J2347 

Guye,  Pintza,  1908. 

Oxygen 

I-°53 

1.4292 

.08922 

Rayleigh,  Proc.  R.  Soc.  62,  1897. 

Sulphur  dioxide 

2.2639 

2.9266 

.18271 

Jaquerod,  Pintza,  1908. 

Steam  at  100° 

0.469 

0.581 

•0363 

Xenon 

4.526 

5-85I 

*/     +j 

•3653 

Watson,  J.  Ch.  Soc.  1910. 

Compiled  partly  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-Chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  70. 
DENSITY   OF   AQUEOUS   SOLUTIONS.' 


The  following  table  gives  the  density  of  solutions  of   various  salts  in   water.     The  numbers  give  the   weight  in 
grams  per  cubic  centimeter.     For  brevity  the  substance  is  indicated  by  formula  only. 


Substance. 

Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 
the  solution. 

u 

(i 
I 

Authority. 

5 

10 

15 

20 

25 

30 

40 

5° 

60 

K20  .     . 

1.047 

1.098 

i-i53 

I.2I4 

1.284 

1-354 

I-503 

1.659 

1.809 

15- 

Schiff. 

KOH      .     .     . 

.040 

1.082 

1.027 

I.O76 

1.229 

1.286 

I.4IO 

1-538 

1.666 

" 

Na2O      .     .     . 

-073 

1.144 

i.  218 

1.284 

1-354 

1.421 

i-557 

1.689 

1.829 

15- 

" 

NaOH    .     .     . 

.058 

I.II4 

1.169 

1.224 

1.279 

1.331 

1.436 

1-539 

1.642 

15- 

u 

NHS  .... 

0.9/8 

0-959 

0.940 

0.924 

0.909 

0.896 

— 

— 

16. 

Carius. 

NH4C1  .    .    . 

.015 

1.030 

1.044 

1.058 

1.072 

- 

- 

- 

- 

'5- 

Gerlach. 

KC1   .... 

O^I 

T  O(S  C 

I.OQQ 

T   I  7  C 

_ 

_ 

mm 

__ 

_ 

1C. 

<• 

NaCl      .    .     . 

O"j  c 

I.O72 

-v;/;/ 
I.  IIO 

I.I  CO 

I.TQI 

_ 

_ 

_ 

D 

I  C. 

« 

LiCl  .... 

1.029 

i  •*-'/  *• 

1-057 

1.085 

j;: 
I.ItO 

j.  •  j  y  j. 

1.147 

1.181 

.255 

- 

- 

3 

15- 

« 

CaCl2     .     .    . 

1.041 

1.086 

I.I32 

1.181 

1.232 

1.286 

.402 

— 

— 

15- 

" 

CaCl2  +  6H20 
A1C13      .     .     . 

1.019 
1.030 

1.040 
1.072 

1.  06  1 
I.  Ill 

1.083 

1.105 
1.196 

1.128 
1.241 

.176 
•340 

1.225 

1.276 

18. 
15- 

Schiff. 
Gerlach. 

MgCl2     .     .    . 

1.041 

1.085 

I.I30 

1.177 

1.226 

1.278 

— 

— 

15- 

M 

MgCl2+6H2O 
ZnCl2      .    .     . 

1.014 
1.043 

1.032 
1.089 

1.049 

1.067 
1.184 

1.085 
1.236 

1.103 
1.289 

.141 

.417 

1.183 
1-563 

1.222 
1-737 

24. 
19-5 

Schiff. 
Kremers. 

CdCl2     .    .    . 

1.043 

1.087 

I.I38 

1.193 

1.254 

1.319 

1.469 

1-653 

1.887 

19-5 

« 

SrCl2.    .     .     . 

T  O44 

1.092 

1.198 

1.257 

1.321 

_. 

_ 

I  C. 

Gerlach. 

SrCl2  +  6H2O 

1.027 

1.053 

i!o82 

;/ 

i.  in 

1.042 

1.174 

1.242 

1-317 

- 

0 

15. 

M 

BaCl2     .     .    . 

1.045 

1.094 

1.147 

1.205 

1.269 

— 

— 

— 

U 

BaCl2+2H2O 

1-035 

1-075 

1.119 

1.  1  66 

1.217 

1-273 

- 

- 

- 

21. 

Schiff. 

CuCl2     .    .     . 

1.044 

1.091 

1-155 

1.  221 

1.291 

1.360 

1.527 

_ 

- 

17-5 

Franz. 

NiCl2     .    .    . 

1.048 

1.098 

1-157 

1.223 

1.299 

— 

— 

— 

17-5 

" 

HgCl2     .    .     . 

1.041 

1.092 

- 

- 

- 

- 

20. 

Mendelejeff. 

Fe2Cl6    .     .    . 
PtCl4.     .    .    . 

1.041 
1.046 

i.  086 
1.097 

1.130 

1.153 

I.I79 
I.2I4 

1.232 
1.285 

1.290 
1.362 

•413 
.546 

1-545 
1.785 

1.668 

17.5 

Hager. 
Precht. 

SnCl2  -f-  2H2O 

1.032 

1.067 

1.104 

I.I43 

1.185 

1.229 

•329 

1.444 

1.580 

15. 

Gerlach. 

SnCl4+5H2O 

1.029 

1.058 

1.089 

1.  122 

1-157 

I-I93 

.274 

1-365 

1.467 

15- 

" 

LiBr  .... 

I-°33 

1.070 

I.  Ill 

LI54 

1.202 

1.252 

.366 

1.498 

— 

19.5 

Kremers. 

KBr  .... 

1-035 

1.073 

1.114 

I-I57 

1.205 

1.254 

.364 

- 

19-5 

H 

NaBr      .     .    . 

1.038 

1.078 

1.123 

I.I72 

1.224 

1.279 

.408 

1-563 

— 

19-5 

M 

MgBr2    .    .     . 

1.041 

1.085 

1.135 

I.I89 

1.245 

1.308 

•449 

1.623 

_ 

19-5 

H 

ZnBr2     .    .     . 

1.043 

1.091 

1.144 

I.2O2 

1.263 

1.328 

-473 

1.648 

1-873 

19-5 

M 

CdBr2     .     .    . 

1.041 

i.  088 

I.I97 

1.258 

1.324 

•479 

1.678 

— 

19.5 

it 

CaBr2     .     .     . 

1.042 

1.087 

1.137 

I.I92 

2.250 

-459 

1.639 

-  ' 

19-5 

U 

BaBr2     .     .     . 

1.043 

1.090 

1.142 

I.I99 

1.260 

1-327 

•483 

1.683 

— 

19-5 

" 

SrBr2      .    .    . 

1.043 

1.089 

1.140 

I.I98 

1.260 

1.328 

.489 

1.693 

1-953 

19-5 

« 

KI      .... 

1.036 

1.076 

1.118 

I.l64 

I.2I6 

1.269 

.394 

1-544 

I-732 

19-5 

H 

Lil      .... 

i.  077 

1.  122 

I.I7O 

1.222 

1.278 

1.573 

1.77  c, 

IQ.C 

1 

Nal    .    .    .     . 

1.038 

J..W/  / 
1.080 

I.I26 

/ 

I.I77 

1.232 

1.292 

•43° 

/  /  j 
1.808 

y  o 

19.5 

f| 

ZnI2  .    .    . 

1.043 

1.089 

1.138 

I.I94 

L253 

1.316 

.467 

1.648 

1.873 

19-5 

" 

CdI2  .    .    . 

1.042 

i.  086 

1.136 

I.I92 

I.25I 

I-3I7 

474 

1.678 

_ 

19-5 

« 

MgI2.     .    .    . 
CaI2  .... 

1.041 
1.042 

i.  086 
1.088 

I-I37 
1.138 

I.I92 
I.I96 

.1.252 
1.258 

1.318 
I-3J9 

.472 
1-475 

1.666 
1.663 

I-9I3 

19-5 

« 

SrI2    .... 

1.043 

1.089 

I.I4O 

I.I98 

1.260 

1.328 

1.489 

1.693 

1-953 

19-5 

H 

BaI2  .... 

1.043 

1.089 

I.I4I 

I.I99 

1.263 

i.33i 

1-493 

1.702 

1.968 

J9-5 

M 

NaClO3.    .    . 

L035 

1.068 

1.106 

I-I45 

I.I88 

J-233 

1.329 

_ 

_ 

19-5 

H 

NaBrO3  .     .     . 
KNO3     .    .    . 

1.039 
1.031 

1.081 
1.064 

1.127 
1.099 

I.I76 

I-J35 

1.229 

1.287 

: 

: 

i9-5 

M 

Gerlach. 

NaNO3  .     .     . 

1.031 

1.065 

I.IOI 

1.140 

I.ISO 

1.222 

1.313 

1.416 

_ 

20.2 

Schiff. 

AgN03  .    .    . 

1.044 

1.090 

1.140 

•'95 

1-255 

1.322 

1.479 

1.675 

1.918 

-5. 

Kohlrausch. 

*  Compiled  from  two  papers  on  the  subject  by  Gerlach  in  the  "  Zeit.  fur  Anal.  Chim.,"  vols.  8  and  27. 
SMITHSONIAN  TABLES. 


TABLE  70  (continued). 
DENSITY   OF   AQUEOUS   SOLUTIONS. 


93 


Substance. 

Weight  of  the  dissolved  substance  in  100  parts  by  weight  of 
the  solution. 

u 

Authority. 

S 

10 

IS 

20 

25 

30 

40 

5° 

60 

H 

NH4N03     .    .     . 
Zn(N08)2    .     .     . 
Zn(N03)2  +  6H2O 
Ca(N03)2    .     .     . 
Cu(NO3)2    .     .    . 

Sr(N03)2     .    .    . 
Pb(N03)2     .    .     . 
Cd(N03)2    .    .     . 
Co(N03)2    .    .    . 
Ni(N03)2     .    .    . 

Fe2(N03)6  .     .     . 
Mg(NO3)o+6H2O 
Mn(NO3)2+6H2O 
K2CO3 

1.020 
1.048 

1-037 
1.044 

1.039 
1.043 
1.052 
1.045 
1.045 

1.039 
I.OIO 

1.025 

I  Odd. 

1.041 

1.095 

1.054 

1.075 

1.093 
1.083 

1.091 
1.097 

1.090 
1.090 

1.076 

1.038 

1.052 
1.092 
1.072 

1.038 
1-055 

1.096 

1-053 

1.104 
1.050 

1.039 

1.064 
1.064 
L057 

1.045 

1-033 
i.  066 

1.058 
1.082 

1.071 
1.059 
1-053 

1.064 
1.042 

1.063 
i.i4( 

1.118 
I-I43 
1.129 

f-143 
1.150 

I-I37 
I-I37 
1.117 
i.  060 
1.079 
1.141 

I.  IIO 

!-057 
1.084 
1.150 
1.081 
1.161 

'-075 
1.059 
1.098 
1.099 
1.089 

i.  066 

1.051 

I.IOI 

1.090 
1.127 

1.108 
1.092 
1-070 

I.IOO 

1.066 

.085 
.201 
.ii' 
.162 
.203 

.179 
.199 

.212 
.192 
.192 

.I60 
.082 
.108 
.192 
.150 

.077 

•"3 

.207 
.in 

.221 
.101 

081 
r34 

"35 

122 
1.  088 
1-073 
I.I33 

1.  122 

I.I74 

I.I26 
I.II3 

I-I37 
1.089 

1.107 
1.263 

1.  211 
1.263 

1.262 
1.283 
1.252 
1.252 

I.2IO 
I.I05 
I.I38 
1.245 
I.I9I 

1.098 
I.I42 
I.27O 
I.I4I 
1.284 

I.I29 
1.  102 

I-I73 
1.174 
1.156 

1.  112 

1.099 

I.I54 
1.225 

I.I77 
I.II4 

I.I3I 

1.325 
I.I78 
1.260 
I.328 

1-332 

1-355 
1.318 
1.318 

1.261 
1.129 
1.169 
1.300 
1-233 
1.118 
1.170 
1-336 
i-i73 

I-I55 
1.124 
1.213 
1.214 
1.191 

1.141 
1.126 

1.191 
1.279 

1.220 
I.I40 

I.I78 

1.456 
1.250 

1.367 
I.47I 

1.536 
1.465 
1.465 

1-373 
1.179 

1-235 
1.417 
1.320 

1.226 
1.489 
1.238 

1.215 

I-3°3 
1.269 

1.188 
1-397 

1-315 
1.194 

1.229 
1-597 

!3B 

1-759 

1.496 
1.232 
1-307 
!-543 
1-415 

1.2*87 

1.278 

i-3~98 
I-351 

1.287 
1.426 

1.282 
1.604 

1.657 
1.386 
1.511 

J-443 
1-454 

!7-5 
r7-5 
14. 
J7-5 
*7-5 

'9-5 
J7-5 
!7-5 
r7-5 
J7-5 

'7-5 

21 

8 
15 
15- 

'5- 
19. 
18. 
17.2 
15 
15- 

11: 

'5- 

20.5 

'7-5 
'7-5 
15- 

19. 
!9-5 

19-5 
15- 
13 

T5- 
14. 

5- 
4- 
5- 
5- 
5- 

7-5 
5- 
4- 
3- 
5- 

7-5 
7-5 
5- 
5- 
5- 

Gerlach. 
Franz. 
Oudemans. 
Gerlach. 
P>anz. 

Kremers. 
Gerlach. 
Franz. 

n 
Schiff. 
Oudemans. 
Gerlach. 

« 

Schiff. 
Hager. 
Schiff. 
Gerlach. 
« 

Schiff. 
Gerlach. 
Schiff. 

Franz. 

« 

Schiff. 

« 
«« 

Kremers. 

Schiff. 

Gerlach. 
Schiff. 

Brineau. 
Schiff. 
Kolb. 
Gerlach. 

<« 
Kolb. 
Topsoe. 

Kolb. 

Stolba. 
Hager. 
Schiff. 
Kolb. 
Oudemans. 

K2CO3  +  2H2O  . 

Na2CO3ioH2O     . 
(NH4)2S04      .     . 
Fe2(S04)3    .     .     . 
FeS04  +  7H2O    . 
MgSO4    .... 

1-037 

1.019 

1.027 

1.045 
1.025 

I  O  i»I 

MgSO  +;H2O  . 
Na2So4-f  ioH2O 
CuS04+5H2O   . 
MnSO4  +  4H2O  . 
ZnSO4+7H2O    . 

Fe2(SO)3+K2S04 
+24H2O  .     .     . 
Cr2(SO)3+K2SO4 
-f-24H2O      .     . 
MgS04  +  KoSO4 
+  6HoO  .     .     . 
(NH4)2S04  + 
FeS04  +  6H2O 
K2CrO4  .... 

K2Cr2O7      .     .     . 
Fe(Cy)6K4  .     .     . 
Fe(Cy)6K3  .     .     . 
Pb(C2H302)2  + 
3H2O  .... 

1.025 
1.019 
1.031 
1.031 
1.027 

1.026 
1.016 
1.032 

1.028 
1.039 

1-035 

1.028 
1.025 

I.O1I 

2NaOH  -f  As2O5 
+  24H2O      .     . 

S03     
SQ2     

1.020 

5 

10 

IS 

20 

3° 

40 

60 

80 

ICO 

1.040 
[.Oil 

1.084 
1.028 
1.069 
1.047 
1.038 

1.039 
1.050 

1-073 
1.077 
1.069 

1.082 
1.077 
1.057 
1.056 
I.OI4 

1.132 

1.045 
1.104 
1.070 

1.058 
1.  060 

1-075 
1.114 
1.118 
1.106 

1.127 
1.119 

i.  086 
i.  088 
i.  02  1 

I.I79 
I.063 
I.I4I 
1.096 
1.079 

1.082 
I.IOI 
I.I58 
I.I65 

'•MS 
1.174 
1.167 
1.119 
1.119 
1.028 

[.277 

I.2I7 
I.I50 
I.I23 

I.I29 
I.I5I 

1-257 
I.27I 
1.223 

1-273 
I.27I 
I.I88 
I.l84 
I.04I 

1.389 

1.294 
1.207 
I.I70 

I.I78 
I.2OO 
1.376 
1.400 
I-3°7 

I-385 
1.264 
1.250 
1.052 

1.564 
1.422 

1-273 
1.289 

1.501 

1.676 
1.438 

IS 

1.840 
1.506 

I-732 

1-459 
1.075 

i.S~38 

.5*28 
•055 

NoOc 

[•Oil 

CdHftOA 

C6H807  .... 

Cane  sugar  .     .     . 
HC1    

I.OI8 

I.OI9 
I.O2i; 

HBr    
HI      

1-035 

H2SO4    .... 

H2SiFl6  .... 
P205  
P205  +  3H20.    . 
HNO.     .... 

1.032 
1.040 

I-°35 
1.027 
1.028 

CoH4Oo  . 

i.  007 

SMITHSONIAN  TABLES. 


94 


TABLE   71. 

DENSITY   OF    PURE    WATER    FREE    FROM    AIR. 

[Under  standard  pressure  (76  cm),  at  every  tenth  part  of  a  degree  of  the  international  hydrogen  scale  from  o°  to  41° 

C,  in  grams  per  milliliter  1] 


De- 
grees 
Centi- 
grade. 

Tenths  of  Degrees. 

Mean 
Differ- 
ences. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

0 

0.999  8681 

8747 

8812 

8873 

8936 

8996 

9053 

9109 

9163 

9216 

+  59 

i 

9267 

93^5 

9363 

9408 

9452 

9494 

9534 

9573 

9610 

9645 

~f~  41 

2 

9679 

9711 

9741 

9769 

9796 

982I 

&te 

9866 

9887 

9905 

+  24 

3 

9922 

9937 

995  1 

9962 

9973 

998i 

9988 

9994 

9998 

*0000 

+  8 

4 

I.OOO  OOOO 

*9999 

*9996 

*9992 

*9986 

*9979 

*997o 

*996o 

*9947 

*9934 

—  8 

5 

0.999  9919 

9902 

9884 

9864 

9842 

9819 

9795 

9769 

9742 

9713 

—  24 

6 

9682 

9650 

9617 

9582 

9545 

9507 

9468 

9427 

9385 

934i 

—  39 

i 

.  9296 
8764 

9249 
8703 

9201 
8641 

9I5I 

8577 

9IOO 

8512 

^48 
8445 

8994 
8377 

8938 
8308 

8237 

8823 
8165 

=.« 

9 

8091 

8017 

7940 

7863 

7784 

7704 

7622 

7539 

7455 

7369 

—  81 

10 

7282 

7194 

7105 

7014 

692I 

6826 

67  29 

6632 

6533 

6432 

—  95 

ii 

633! 

6228 

6124 

6020 

59  1  3 

5805 

5696 

5586 

5474 

5362 

—  1  08 

12 

5248 

5*32 

5016 

4898 

4780 

4660 

4538 

4291 

4166 

—  121 

13 

4040 

3912 

3784 

3654 

3523 

339  l 

3257 

3122 

2986 

2850 

—  133 

14 

2712 

2572 

243  1 

2289 

2147 

2003 

1858 

1711 

1564 

1416 

—  145 

15 

1266 

1114 

0962 

o8o9 

0653 

0499 

0343 

0185 

0026 

*9865 

—  156 

16 

0.998  9705 

9542 

9378 

9214 

9048 

8881 

8713 

8544 

8373 

8202 

—  168 

17 

8029 

7856 

7681 

7505 

7328 

715° 

697i 

679i 

6610 

6427 

-178 

18 

6244 

6058 

5873 

5686 

5498 

5309 

5IT9 

4927 

4735 

—190 

19 

4347 

4152 

3955 

3757 

3558 

3358 

3158 

2955 

2752 

2549 

—  200 

20 

2343 

2137 

1930 

1722 

1511 

1301 

IO9O 

0878 

0663 

0449 

—  211 

21 

0233 

0016 

*9799 

*958° 

*9359 

*9r39 

*89i7 

*8694 

*847o 

*8245 

—  221 

22 

0.997  8019 

7792 

7564 

7335 

7104 

6873 

6641 

6408 

593s 

—232 

23 

5702 

5466 

5227 

4988 

4747 

4506 

4264 

4021 

3777 

3531 

—242 

24 

3286 

3039 

2790 

2541 

229I 

2040 

1788 

1535 

1280 

1026 

—252 

25 

0770 

®5i3 

0255 

*9997 

*9736 

*9476 

*92I4 

*895i 

*8688 

*8423 

—26l 

2O 

0.9968158 

7892 

7624 

7356 

7087 

6817 

6545 

6273 

6000 

5726 

—271 

27 

545  l 

5176 

48(^8 

4620 

4342 

4062 

3782 

35oo 

3218 

2935 

-280 

!  28 

2652 

2366 

2080 

1793 

1505 

1217 

0928 

0637 

0346 

°°53 

-289 

29 

0.995  976i 

9466 

9171 

8876 

8579 

8282 

7983 

7684 

7383 

7083 

—  298 

30 

6780 

6478 

6174 

5869 

5564 

5258 

495° 

4642 

4334 

4024 

—  3°7 

31 

37H 

3401 

3089 

2776 

2462 

2147 

1832 

1198 

0880 

i  32 

0561 

0241 

*9920 

*9599 

*9276 

*89S4 

#8630 

#8304 

*7979 

*7^53 

—324 

i  33 

0-994  7325 

6997 

6668 

6338 

6007 

5676 

5345 

5011 

4678 

4343 

—332 

34 

4007 

3671 

3335 

2997 

2659 

2318 

1978 

1638 

I296 

0953 

—340 

i 

0610 
0.9937136 

0267 

6784 

*9922 

6432 

*9576 
6078 

*9230 

5725 

*8883 
5369 

*8534 
5OI4 

*8i86 
4658 

4301 

*7486 
3943 

—347 
—355 

37 

3585 

3226 

2866 

2505 

2144 

1782 

1419 

1055 

o69i 

0326 

38 

0.992  9960 

9593 

9227 

8859 

849o 

8120 

775* 

7380 

7008 

6636 

—370 

39 

6263 

5890 

55J6 

5140 

4765 

4389 

4011 

3634 

3255 

2876 

—377 

40 

2497 

2116 

1734 

1352 

0971 

0587 

0203 

*98i8 

*9433 

*9°47 

—384 

41 

0.991  8661 

*  According  to  P.  Chappuis,  Bureau  international  des  Poids  et  Mesures,  Travaux  et  Me"moires,  13;  1907. 
SMITHSONIAN  TABLES. 


TABLE  72. 


95 


VOLUME     IN    CUBIC    CENTIMETERS    AT    VARIOUS     TEMPERATURES    OF 

A   CUBIC   CENTIMETER   OF   WATER    FREE    FROM    AIR   AT    THE 

TEMPERATURE    OF    MAXIMUM    DENSITY. 

Hydrogen  Thermometer  Scale. 


Temp. 

.0 

.« 

.2 

•3 

•4 

•  5 

.6 

•7 

.8 

•9 

0 

1.000132 

125 

118 

112 

1  06 

100 

095 

089 

084 

079 

I 

073 

069 

064 

059 

055 

051 

047 

043 

°39 

035 

2 

032 

029 

026 

023 

020 

018 

016 

013 

on 

009 

3 

008 

006 

005 

004 

003 

002 

OOI 

OOI 

ooo 

OOO 

4 

000 

ooo 

ooo 

OOI 

OOI 

002 

003 

004 

005 

007 

5 

008 

010 

012 

014 

016 

018 

021 

023 

026 

029 

6 

032 

035 

039 

042 

046 

050 

054 

058 

062 

066 

7 

070 

075 

080 

085 

090 

095 

IOI 

1  06 

112 

118 

8 

124 

130 

137 

142 

149 

156 

162 

169 

I76 

184 

9 

191 

198 

206 

214 

222 

230 

238 

246 

254 

263 

10 
n 

272 

367 

281 

377 

$ 

299 

398 

308 
409 

317 

420 

327 
430 

337 
441 

347 
453 

464 

12 

476 
596 

I 

499 
623 

511 
636 

|22 
649 

664i 

547 
675 

6$J 

702 

584 

14 

729 

743 

757 

772 

786 

800 

830 

844 

859 

15 

873 

890 

905 

920 

935 

95  i 

967 

983 

998 

015* 

16 

1.001031 

047 

063 

080 

097 

"3 

130 

147 

164 

182 

17 

198 

216 

233 

252 

269 

287 

305 

323 

341 

358 

18 

378 

396 

415 

433 

452 

47i 

490 

529 

548 

19 

568 

588 

606 

626 

646 

667 

687 

707 

728 

748 

20 

769 

790 

811 

832 

853 

874 

895 

916 

938* 

960 

21 

981 

002* 

024* 

046* 

068* 

091* 

113* 

135* 

181* 

22 

23 
24 

1.002203 

436 

679 

226 

459 
704 

249 
483 
729 

271 
754 

295 
'  532 
'  779 

3*9 

804 

342 
581 
829 

1 

629 
879 

412 
654 
905 

25 

932 

958 

983, 

OIO* 

036* 

061* 

088* 

115* 

141* 

168* 

26 

1.003195 

221 

248 

275 

302 

330 

357 

384 

412 

439 

27 
28 

467 

749 

495 
776 

8^06 

550 
836 

579 
865 

607 

635 
922 

663 
951 

98? 

720 

Oil* 

29 

1.004041 

069 

100 

129 

160 

189 

220 

250 

280 

310 

30 

34i 

37i 

403 

432 

464 

494 

526 

557 

588 

619 

31 

651 

682 

713 

744 

777 

808 

840 

872 

904 

936 

32 

968 

OOI* 

033* 

066* 

098* 

132* 

163* 

197* 

229* 

263* 

33 
34 

1.005296 
631 

ti 

395 
732 

427 
768 

461 
802 

496 
836 

530 
871 

562 
904 

597 
940 

35 

975 

009* 

044* 

078* 

115* 

!50* 

185* 

219* 

255* 

290* 

Reciprocals  of  the  preceding  table. 


SMITHSONIAN  TABLES. 


96  TABLE  73. 

DENSITY  AND  VOLUME  OF  WATER. 

The  mass  of  one  cubic  centimeter  at  4°  C.  is  taken  as  unity. 


Temp.  C. 

Density. 

Volume. 

Temp.  C. 

Density. 

Volume. 

—10° 

0.99815 

1.00186 

+35° 

0.99406 

1.00598 

3 

843 
869 

157 
131 

36 

37 

371 
336 

1 

—7 

892 

1  08 

38 

300 

706 

—6 

912 

088 

39 

263 

743 

—5 

0.99930 

1.00070 

40 

0.99225 

1.00782 

—4 

945 

°55 

4i 

l87 

821 

—3 

958 

042 

42 

M7 

861 

—  2 

970 

031 

43 

I07 

901 

—  I 

979 

021 

44 

066 

943 

+0 

0.99987 

I.OOOI3 

45 

0.99025 

1.00985 

I 

993 

007 

46 

0.98982 

1.01028 

2 

997 

003 

47 

940 

072 

3 

999 

001 

48 

896 

116 

4 

I.OOOOO 

I.OOOOO 

49 

852 

162 

5 

0.99999 

1.  0000  1 

50 

0.98807 

1.01207 

6 

997 

003 

51 

762 

254 

7 

993 

007 

52 

V£ 

301 

8 

988 

012 

53 

669 

9 

981 

019 

54 

621 

398 

10 

0-99973 

1.00027 

55 

0.98573 

1.01448 

ii 

963 

037 

60 

324 

705 

12 

952 

048 

65 

059 

979 

13 

940 

060 

70 

0.97781 

1.02270 

14 

927 

073 

75 

489 

576 

15 

0.99913 

1.00087 

80 

0.97183 

1.02899 

16 

103 

85 

0.96865 

1.03237 

lt 

880 

I2O 

9° 

534 

590 

18 

862 

138 

95 

192 

959 

19 

843 

157 

IOO 

0.95838 

1-04343 

20 

0.99823 

I.OOI77 

110 

0.9510 

'•OPS 

21 

802 

I98 

1  20 

•9434 

i.  060  1 

22 

780 

220 

130 

•9352 

1.0693 

23 

757 

244 

140 

.9264 

.0794 

24 

733 

268 

150 

•9J73 

.0902 

25 

0.99708 

1.00293 

160 

0.9075 

.1019 

26 

682 

320 

170 

•8973 

•"45 

27 

655 

347 

1  80 

.8866 

.1279 

28 

62l 

375 

190 

.8750 

.1429 

29 

598 

404 

200 

.8628 

.1590 

30 

31 

0.99568 
537 

1.00434 
465 

210 

220 

0.850 
.837 

.177 
•195 

32 

506 

497 

230 

.823 

.215 

33 

473 

530 

24O 

.809 

-236 

34 

440 

563 

250 

•794 

•259 

*  From  —  10°  to  o°  the  values  are  due  to  means  from  Pierre,  Weidner,  and 
Rosetti;  from  o°  to  41°,  to  Chappuis,  42°  to  100°,  to  Thiesen;  110°  to  250°,  to 
means  from  the  works  of  Ramsey,  Young,  Waterston,  and  Hirn. 

SMITHSONIAN  TABLES. 


TABLE   74. 
DENSITY   OF   MERCURY. 

Density  or  mass  in  grams  per  cubic  centimeter,  and  the  volume  in  cubic 
centimeters  of  one  gram  of  mercury. 


97 


1 

Temp.C. 

Mass  in 
grams  per 
cu.  cm. 

Volume  of 
i  gram  in 
cu.  cms. 

Temp.  C. 

Mass  in 
grams  per 
cu.  cm. 

Volume  of 
i  gram  in 
cu.  cms. 

—10° 

13.6202 

0.0734205 

30° 

I3-52I7 

0.07395£2 

—9 

6177 

4338 

31 

5193 

9685 

—8 

6152 

4472 

32 

5168 

9819 

—7 

6128 

4606 

33 

5M4 

9953 

—6 

6103 

4739 

34 

5ll9 

40087 

—5 

13.6078 

0.0734873 

35 

I3-5095 

0.0740221 

—4 

6053 

5006 

36 

5070 

0354 

—3 

6029 

5MO 

37 

5046 

0488 

—  2 

6004 

5273 

38 

5021 

0622 

—  I 

5979 

5407 

39 

4997 

0756 

0 

13-5955 

0.0735540 

40 

13-4973 

0.0740890 

I 

593° 

5674 

5° 

4729 

2230 

2 

59°  5 

5808 

60 

4486 

3572 

3 

5880 

594i 

70 

4243 

4916 

4 

5856 

6075 

80 

4001 

6262 

5 

13-5831 

0.0736208 

90 

I3-3776 

0.0747611 

6 

5807 

6342 

IOO 

3518 

8961 

7 

5782 

6476 

no 

3283 

50285 

8 

5757 

6609 

120 

3044 

1633 

9 

5733 

6743 

130 

2805 

2982 

10 

13-5708 

0.0736877 

140 

13.2567 

0-0754334 

ii 

5683 

7010 

150 

2330 

5688 

12 

5659 

7U4 

160 

2093 

7044 

13 

5634 

7278 

170 

1856 

8402 

14 

5610 

7411 

180 

1620 

9764 

15 

I3-5585 

0.0737545 

190 

13-1384 

0.0761128 

16 

556° 

7679 

200 

1148 

2495 

17 

5536 

7812 

210 

0917 

3865 

18 

7946 

220 

0678 

19 

5487 

8080 

230 

0443 

6616 

20 

13.5462 

0.0738213 

240 

13.0209 

0.0767996 

21 

5438 

8347 

250 

12.9975 

9381 

22 

8481 

260 

974i 

70769 

23 

5389 

8615 

270 

95°7 

2161 

24 

5364 

8748 

280 

9273 

3558 

25 

13.5340 

0.0738882 

290 

12.9039 

0.0774958 

26 

9016 

300 

8806 

6364 

28 

5266 

9*5° 
9284 

310 
320 

8572 
8339 

7774 
9189 

29 

5242 

9417 

330 

8105 

80609 

30 

I3-52I7 

0.0739551 

340 

12.7872 

0.0782033 

350 

7638 

3464 

360 

7405 

4900 

Thiesen  und  Scheel,  Tatigkeitber.  Phys.-Techn.  Reichsanstalt,  1897-1898;  Chappuis, 
Trav.  Bur.  Int.  13,  1903. 
Thiesen,  Scheel,  Sell;  Wiss.  Abh.  Phys.-Techn.  Reichsanstalt  2,  p.  184,  1895. 


SMITHSONIAN  TABLES. 


98 


TABLE  75. 


DENSITIES  OF  MIXTURES  OF  ETHYL  ALCOHOL  AND  WATER    IN  CRAMS 

PER  MILL1LITER. 

The  densities  in  this  table  are  numerically  the  same  as  specific  gravities  at  the  various  temperatures  in  terms  of  water 
at  4°  C.  as  unity.  Based  upon  work  done  at  U.  S.  Bureau  of  Standards.  See  Bulletin  Bur.  Stds.  vol.  9,  no.  3  ;  con- 
tains extensive  bibliography ;  also  Circular  19,  1913. 


Per  cent 
C2H5OH 

by  weight 

•       Temperatures. 

10°  C. 

15°  C. 

ao°C. 

25°  C. 

30°  C. 

35°  C. 

40°  C. 

O 

0-99973 

0.99913 

0.99823 

0.99708 

0.99568 

0.99406 

0.99225 

I 

785 

725 

636 

520 

379 

217 

034 

2 

602 

542 

453 

336 

194 

031 

.98846 

3 

426 

365 

275 

157 

014 

.98849 

663 

4 

258 

195 

103 

.98984 

.98839 

672 

485 

5 

098 

032 

.98938 

8l7 

670 

501 

311 

6 

.98946 

.98877 

780 

656 

507 

335 

142 

7 

§01 

729 

627 

500 

172 

8 

660 

584 

478 

346 

189 

009 

808 

9 

524 

442 

193 

031 

.97846 

641 

10 

393 

3°4 

187 

043 

•97875 

685 

475 

ii 

267 

171 

047 

.97897 

723 

527 

312 

12 

145 

041 

.97910 

753 

573 

37i 

150 

13 

026 

.97914 

775 

611 

424 

216 

.96989 

14 

.97911 

790 

643 

472 

278 

063 

829 

'5 

800 

669 

cI4 

334 

133 

.96911 

670 

16 

692 

552 

387 

199 

.96990 

760 

512 

17 

583 

433 

259 

062 

844 

607 

352 

18 

473 

313 

129 

.96923 

697 

452 

i$g 

*9 

363 

191 

•96997 

782 

547 

294 

023 

20 

252 

068 

864 

639 

395 

134 

•95856 

21 

139 

.96944 

729 

495 

242 

•95973 

687 

22 

024 

818 

592 

348 

087 

809 

516 

23 

24 

.96907 
787 

558 

453 
312 

199 

048 

•95929 
769 

643 
476 

m 

25 
2O 

665 

539 

424 

287 

168 
020 

•95895 
738 

607 
442 

306 

.94991 

810 

27 
28 

406 
268 

144 
•95996 

•95867 
710 

576 
410 

272 
098 

•94955 
774 

43» 

29 

125 

844 

548 

241 

.94922 

590 

248 

30 
31 

•95977 
823 

686 

524 

382 

212 

067 
.94890 

74i 

557 

403 
214 

055 
.93860 

32 

665 

357 

038 

709 

370 

021 

662 

33 
34 

502 
334 

186 

Oil 

.94860 
679 

525 
337 

180 
.93986 

•93825 
626 

461 

257 

35 

162 

.94832 

494 

146 

790 

425 

051 

36 

.94986 

650 

306 

.93952 

221 

•92843 

37 

805 

464 

114 

756 

39° 

016 

634 

38 

620 

273 

•93919 

556 

1  86 

.92808 

422 

39 

43i 

079 

720 

353 

•92979 

597 

208 

40 

238 

.93882 

518 

148 

770 

385 

.91992 

41 

042 

682 

.92940 

558 

170 

774 

42 

.93842 

478 

107 

729 

344 

.91952 

554 

43 

639 

271 

.92897 

516 

128 

733 

332 

44 

433 

062 

685 

301 

.91910 

5*3 

108 

45 

226 

.92852 

472 

085 

692 

291 

.90884 

47 

017 
.92806 

640 
426 

257 
041 

.91868 
649 

472 
250 

069 
.90845 

660 
434 

48 

593 

211 

.91823 

429 

028 

621 

207 

49 

379 

•91995 

604 

208 

.90805 

396 

.89979 

50 

162 

776 

384 

.90985 

580 

168 

750 

SMITHSONIAN    TAHLF«S. 


TABLE  75  (continued). 


99 


DENSITY  OF  MIXTURES  OF  ETHYL  ALCOHOL  AND  WATER  IN  CRAMS 

PER    MILLILITER. 


1  Per  cent 
C,H5OH 
by  weight 

Temperature. 

10°  C. 

15°  C. 

20°  C. 

25°  C. 

30°  C. 

35°  C. 

40°  C. 

5° 

0.92162 

0.91776 

0.91384 

0.90985 

0.90580 

0.90168 

0.89750 

51 

•9  '943 

555 

160 

760 

353 

.89940 

5T9 

52 

723 

333 

.90936 

534 

I25 

710 

288 

53 

502 

no 

711 

3°7 

.89896 

479 

056 

54 

279 

.90885 

485 

079 

667 

248 

.88823 

55 

°55 

659 

258 

.89850 

437 

016 

589 

56 

.90831 

433 

031 

621 

206 

.88784 

356 

57 

607 

207 

.89803 

392 

.88975 

552 

122 

58 

381 

.89980 

574 

162 

744 

.87888 

59 

"54 

752 

344 

•88931 

512 

085 

653 

60 

.89927 

523 

TI3 

699 

278 

.87851 

417 

61 

698 

293 

.88882 

466 

044 

615 

180 

62 

468 

062 

650 

233 

.87809 

379 

•86943 

63 

237 

.88830 

417 

.87998 

574 

142 

7°5 

64 

006 

597 

183 

763 

337 

.86905 

466 

65 

.88774 

364 

.87948 

527 

IOO 

667 

227 

66 

54^ 

130 

713 

291 

.86863 

429 

.85987 

67 

308 

•87895 

477 

054 

625 

190 

747 

68 

074 

660 

241 

.86817 

.85950 

507 

69 

.87839 

424 

004 

579 

148 

710 

266 

70 

602 

187 

.86766 

340 

.85908 

470 

025 

365 

.86949 

527 

IOO 

667 

228 

.84783 

72 

127 

710 

287 

.85859 

426 

.84986 

540 

73 

.86888 

470 

047 

618 

184 

743 

297 

74 

648 

229 

.85806 

376 

.84941 

500 

053 

75 

408 

.85988 

564 

'34 

698 

257 

.83809 

;6 

77 

1  68 

•85927 

747 
5°5 

322 
079 

.84891 
647 

455 

211 

013 
.83768 

564 

78 
79 

685 
442 

262 
018 

•84835 
590 

403 
158 

.83966 
720 

523 

277 

074 
.82827 

80 

197 

.84772 

344 

.8391  1 

473 

029 

578 

81 

.84950 

525 

096 

664 

224 

.82780 

329 

82 

702 

277 

.83848 

4I5 

.82974 

530 

079 

83 

453 

028 

599 

164 

724 

279 

.81828 

84 

203 

.83777 

348 

.82913 

473 

027 

576 

11 

.83951 
697 

525 
271 

095 
.82840 

660 
405 

220 
.81965 

.81774 

322 
067 

87 

441 

014 

583 

148 

708 

262 

.80811 

88 

181 

•82754 

323 

.81888 

448 

003 

SS2 

89 

.82919 

492 

062 

626 

186 

.80742 

291 

90 
92 

654 
386 
114 

227 

.81959 
688 

.81797 
529 

237 

362 
094 
.80823 

.80922 
384 

478 

211 

028 
.79761 
491 

93 

.81839 

413 

.80983 

549 

in 

669 

220 

94 

561 

134 

705 

272 

•79835 

393 

.78947 

1 

278 
.80991 

.80852 
566 

424 
138 

.79991 
706 

555 
271 

114 

.78831 

388 

698 

274 

.79846 

415 

.78981 

542 

IOO 

98 

399 

•79975 

547 

117 

684 

247 

.77806 

99 

094 

670 

243 

.78814 

382 

.77946 

507 

IOO 

.79784 

360 

.78934 

506 

075 

641 

203 

SMITHSONIAN  TABLES. 


IOO  TABLE  76. 

DENSITIES  OF  AQUEOUS  MIXTURES  OF  METHYL  ALCOHOL, 
CANE  SUGAR,  OR  SULPHURIC  ACID. 


Per  cent 

by  weight 
of 
substance. 

Methyl 
Alcohol. 

Cane 
Sugar. 

20° 

Sulphuric 
Acid. 

4 

Per  cent 
by  weight 
of 
substance. 

Methyl 
Alcohol. 

Cane 
Sugar. 

20° 

Sulphuric 
Acid. 

O 

0.99913 

0.998234 

0.99823 

50 

0.91852 

1.229567 

L39505 

I 

.99727 

1.  002  1  20 

1.00506 

51 

•91653 

L235085 

1.40487 

2 

•99543 

1.006015 

1.01178 

52 

•9M51 

I.24O64I 

1.41481 

3 

.99370 

1.009934 

1.01839 

53 

.91248 

1.246234 

1.42487 

4 

.99198 

I.OI388I 

1.02500 

54 

.91044 

I.25I866 

1  -43  5°3 

5 

.99029 

1.017854 

1.03168 

55 

.90839 

J-257535 

1-44530 

5 

.98864 

I.02I855 

1.03843 

56 

.90631 

1.263243 

7 

.98701 

1.025885 

1.04527 

57 

.90421 

1.268989 

1.46615 

8 

.98547 

1.029942 

1.05216 

58 

.90210 

1.274774 

1.47673 

9 

.98394 

1.034029 

1.05909 

59 

.89996 

1.280595 

1.48740 

10 

.98241 

1.038143 

1.06609 

60 

.89781 

1.286456 

1.49818 

ii 

.98093 

1.042288 

1.07314 

61 

.89563 

1.292354 

1.50904 

12 

•97945 

1.046462 

1.08026 

62 

.89341 

1.298291 

1.51999 

13 

.97802 

1.050665 

1.08744 

63 

.89117 

1.304267 

1.53102 

14 

.97660 

1.054900 

1.09468 

64 

.88890 

1.310282 

1-54213 

11 

•97518 
•97377 

1.059165 
1  .063460 

1.10199 
1.10936 

If 

.88662 
•88433 

1-316334 

1.322425 

1.56460 

17 

•97237 

1.067789 

1.11679 

67 

.88203 

1-328554 

J.57595 

18 

.97096 

I.072I47 

1.12428 

68 

.87971 

1-334722 

L58739 

*9 

•96955 

I-076537 

1.13183 

69 

•87739 

1.340928 

1.59890 

20 

.96814 

1  .080959 

I-I3943 

70 

•87507 

1.347174 

1.61048 

21 

•96673 

1.085414 

1.14709 

.87271 

I-353456 

1.62213 

22 
23 

•96533 
•96392 

1.089900 
1.094420 

1.15480 
1.16258 

72 
73 

•87033 
.86792 

L359778 
1.366139 

1.63384 
1.64560 

24 

.96251 

1.098971 

1.17041 

74 

.86546 

1.372536 

1.65738 

25 

.96108 

I-I°3557 

1.17830 

75 

.86300 

1.378971 

1.66917 

27 

.95963 

1.108175 
1.112828 

1.18624 
1.19423 

76 

77 

.86051 
.85801 

1.385446 
I.39I956 

1.68095 

1.69268 

28 

.95668 

1.117512 

1.20227 

78 

•85551 

1  -398  505 

1  -70433 

29 

•955!8 

1.122231 

1.21036 

79 

.85300 

1.405091 

1-71585 

3° 

.95366 

1.126984 

1.21850 

80 

.85048 

1.411715 

1.72717 

•95213 

i-i3i773 

1.22669 

81 

.84794 

1.418374 

1.73827 

32 

.95056 

1.136596 

1.23492 

82 

•84536 

1.425072 

1.74904 

33 

.94896 

I-MI453 

1.24320 

83 

.84274 

1.431807 

1-75943 

34 

•94734 

1-146345 

1.25154 

84 

.84009 

I.438579 

1.76932 

35 

•94570 

1.151275 

1.25992 

85 

.83742 

1.445388 

1.77860 

36 

.94404 

1.156238 

1.26836 

86 

.83475 

1.452232 

1.78721 

37 

•94237 

1.161236 

1.27685 

87 

.83207 

1.459114 

1.79509 

38 
39 

.94067 
.93894 

1.166269 
1.171340 

1.28543 
1.29407 

88 
89 

•82937 
.82667 

1.466032 
1.472986 

1.80223 
1.80864 

40 

•9.3720 

1.176447 

1.30278 

90 

.82396 

1.479976 

1.81438 

41 

•93543 

1.181592 

I-3II57 

91 

.82124 

1.487002 

1.81950 

42 

.93365 

1-186773 

1.32043 

92 

.81849 

1.494063 

1.82401 

43 
44 

•93185 
•93001 

1.191993 
1.197247 

1.32938 
L33843 

93 
94 

.81568 
.81285 

1.501158 
1.508289 

1.82790 
1-83115 

45 
46 

.92815 
.92627 

1.202540 
1.207870 

1-34759 
1.35686 

95 
96 

.80999 
.80713 

i-5T5455 
1.522656 

1.83368 
1.83548 

47 

.92436 

1.213238 

1.36625 

.80428 

1.529891 

1.83637 

48 
49 

.92242 
.92048 

1.218643 
1.224086 

1-37574 
I.38533 

99 

.80143 
•79859 

1.537161 
1.544462 

1.83605 

50 

.91852 

1.229567 

L39505 

IOO 

•79577 

1.551800 

(I) 


Calculated  from  the  specific  gravity  determinations  of  Doroschevski  and  Rozhdestvenski  at 
I5°/I5°  C. ;  J.  Russ.,  Phys.  Chem.  Soc.,  41,  p.  977,  1909. 

According  to  Dr.  F.  Plato;  Wiss.  Abh.  der  K.  Normal-Eichungs-Kommission,  2,  p.  153, 1900. 
Calculated  from  Dr.  Domke's  table ;  Wiss.  Abh.  der  K.  Normal-Eichungs-Kommission, 
5,  p.  131,  1900. 

All  reprinted  from  Circular  19,  U.S.  Bureau  of  Standards,  1913. 
SMITHSONIAN  TABLES. 


(2) 

(3) 


TABLE  77. 
VELOCITY   OF  SOUND   IN   SOLIDS. 


IOI 


The  numbers  given  in  this  table  refer  to  the  velocity  of  sound  along  a  bar  of  the  substance,  and  hence  depend  on  the 
Young's  Modulus  of  elasticity  of  the  material.  The  elastic  constants  of  most  of  the  materials  given  in  this  table 
vary  through  a  somewhat  wide  range,  and  hence  the  numbers  can  only  be  taken  as  rough  approximations  to  the 
velocity  which  may  be  obtained  in  any  particular  case.  When  temperatures  are  not  marked,  between  10°  and  20° 
is  to  be  understood. 


Substance. 

Temp.  C. 

Velocity  in 
meters  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Metals:  Aluminum 

o 

5104 

16740 

Masson. 

Brass          .... 

- 

35°° 

11480 

Various. 

Cadmium   .... 

- 

2307 

7570 

Masson. 

Cobalt         .... 

— 

4724 

15500 

" 

Copper       .        . 

2O 

3560 

11670 

Wertheim. 

"            .... 

IOO 

3290 

10800 

« 

. 

200 

2950 

9690 

" 

Gold  (soft) 

20 

1743 

5717 

" 

"     (hard) 

_ 

2IOO 

6890 

Various. 

Iron  and  soft  steel     . 

_ 

5OOO 

16410 

H 

Iron    

20 

5^30 

16820 

Wertheim. 

"..... 

IOO 

5300 

17390 

M 

"   cast  steel     . 

200 

2O 

4720 
4990 

15480 
16360 

« 

«           U            (« 

2OO 

4790 

I57IO 

" 

Lead  ...'!! 

20 

1227 

4026 

u 

Magnesium 

_ 

4602 

15100 

Melde. 

Nickel         .... 

- 

4973 

16320 

Masson. 

Palladium  .... 

— 

3*5° 

10340 

Various. 

Platinum     .... 

20 

2690 

8815 

Wertheim. 

"             .... 

IOO 

2570 

8437 

M 

"            .... 

2OO 

2460 

8079 

« 

Silver          .... 

2O 

2610 

8553 

" 

"              .... 

IOO 

2640 

8658 

« 

Tin     .        .        .        .        . 

- 

2500 

8200 

Various. 

Zinc    

— 

3700 

I2I40 

u 

Various  :  Brick         .... 

— 

3652 

11980 

Chladni. 

Clay  rock 

— 

3480 

II42O 

Gray  &  Milne. 

Cork          .... 

— 

500 

1640 

Stefan. 

Granite     .... 

- 

395° 

12960 

Gray  &  Milne. 

Marble      .... 

— 

3810 

12500 

«' 

Paraffin     .... 

15 

i  -704 

4280 

Warburg. 

Slate         .... 

4510 

14800 

Gray  &  Milne. 

Tallow      .... 

16 

390 

1280 

Warburg. 

Tuff  

- 

2850 

9350 

Gray  &  Milne. 

Glass         .        .       jfr°m 

— 

5000 
6000 

16410 

Various. 

Ivory         .... 
Vulcanized  rubber            ) 

o 

3013 
54 

177 

Ciccone  &  Campanile. 
Exner. 

(black)  J 

5° 

102 

« 

"     (red)     . 

o 

69 

226 

u 

«        «        ^ 

70 

34 

III 

«' 

Wax         .        .        . 

17 

880 

2890 

Stefan. 

"            .... 

28 

441 

145° 

« 

Woods  :  Ash,  along  the  fibre  . 

- 

4670 

I53IO 

Wertheim. 

"    across  the  rings 

— 

1390 

4570 

•« 

"    along  the  rings 

- 

1260 

4140 

" 

Beech,  along  the  fibre 

— 

3340 

10960 

« 

"      across  the  rings     . 

— 

1840 

6030 

M 

"      along  the  rings      . 

- 

1415 

4640 

" 

Elm,  along  the  fibre 

- 

4120 

I35I6 

" 

"      across  the  rings 

— 

1420 

4665 

" 

"      along  the  rings 

— 

1013 

3324 

" 

Fir,  along  the  fibre  . 

- 

4640 

I522O 

" 

Maple 

— 

4110 

13470 

M 

Oak              " 

- 

3850 

12620 

« 

Pine             " 

— 

10900 

" 

Poplar 

— 

4280 

14050 

«« 

Sycamore    " 

~ 

4460 

14640 

SMITHSONIAN  TABLES. 


IO2 


TABLE  78. 
VELOCITY   OF   SOUND   IN    LIQUIDS   AND  CASES, 


For  gases,  the  velocity  of  sound  =  "VyP/p,  where  P  is  the  pressure,  p  the  density,  and  y  the  ratio  of  specific  heat  at 
constant  pressure  to  that  at  constant  volume  (see  Table  265). 


Substance. 

Temp.  C. 

Velocity  in 
meters  per 
second. 

Velocity  in 
feet  per 
second. 

Authority. 

Liquids  :  Alcohol,  95% 

o 
12.5 

1241. 

4072. 

Dorsing,  1908. 

" 

20.5 

1213. 

398o. 

M 

Ammonia,  cone.    . 

1  6. 

1663. 

5456. 

" 

Benzol 

17- 

1  1  66. 

3826. 

" 

Carbon  bisulphide 

IS 

1161. 

3809. 

II 

Chloroform  . 

IS 

983- 

3225. 

" 

Ether    .... 

15. 

1032. 

3386. 

II 

NaCl,  10%  sol. 

15- 

1470. 

4823. 

II 

"       15%  " 

I53°- 

5020. 

II 

«         20%     "            .            . 

15. 

1650. 

5414. 

II 

Turpentine  oil 

is 

1326. 

4351- 

" 

Water,  air-free 

13- 

1441. 

4728. 

(1 

ii        u      i< 

19. 

1461. 

4794- 

II 

it       ii     u 

1505. 

493s- 

U 

"      Lake  Geneva    . 

9- 

J435- 

4708. 

Colladon-Sturm. 

"      Seine  river 

IS 

1437- 

4714. 

Wertheim. 

II                   It                14     ^ 

30. 

1528. 

5OI3- 

" 

<{                   II                II     ^ 

60. 

1724. 

5657- 

M 

Gases  :  Air,  dry,  COa-free  . 

0. 

33I-78 

Io88.5 

Rowland. 

U           44 

o. 

33I-36 

1087.1 

Violle,  1900. 

"      "     CCVfree  .' 

o. 

33I-92 

1089.0 

Thiesen,  1908. 

"       i  atmosphere 

o. 

331-7 

1088. 

Mean. 

"     25          " 

0. 

332.0 

1089. 

(Witkowski). 

•'     50          "         •        - 

0. 

334-7 

1098. 

ii                 K 

"    IOO             " 

o. 

20. 

350.6 

9AA. 

1150. 

II2Q. 

ii                 ii 

ii 

IOO. 

jjy 

A  A  ^.v/. 
1266. 

Stevens. 

u 

500. 

553- 

1814. 

"     .            .            .            .            . 

1000. 

700. 

2297. 

" 

Ammonia 

0. 

Masson. 

Carbon  monoxide   . 

o. 

337-1 

I  I  O6. 

Wullner. 

"              " 

o. 

337-4 

1107. 

Dulong. 

"       dioxide 

0. 

258.0 

846. 

Brock  endahl,  1906. 

"       disulphide  . 

o. 

189-    . 

620. 

Masson. 

Chlorine  .... 

o. 

206.4 

677. 

Martini. 

" 

0. 

205.3 

674. 

Strecker. 

Ethylene  .... 
Hydrogen 

o. 
o. 

3i4. 
1269.5 

IO3O. 
4165. 

Dulong. 

" 

o. 

1286.4 

4221. 

Zoch. 

Illuminating  gas 

o. 

4904 

« 

Methane  .... 

o. 

432. 

1417. 

Masson. 

Nitric  oxide 

o. 

325- 

1066. 

" 

Nitrous  oxide  . 

o. 

26i.8 

859. 

Dulong. 

Oxygen    .... 

o. 

317.2 

1041. 

" 

Vapors:  Alcohol 

o. 

230.6 

7  s6- 

Masson. 

Ether    . 

o. 

179.2 

588. 

u 

Water  .... 

o. 

401. 

I3I5- 

M 

it 

IOO. 

404.8 

1328. 

Treitz,  1903. 

II 

130. 

424.4 

1392. 

NOTE  :  The  values  from  Ammonia  to  Methane  inclusive  are  for  closed  tubes. 
SMITHSONIAN  TABLES. 


TABLES  79-8O. 
MUSICAL  SCALES. 


103 


The  pitch  relations  between  two  notes  may  be  expressed  precisely  (i)  by  the  ratio  of  their  vibration  frequencies; 
(2)  by  the  number  of  equally-tempered  semitones  between  them  (E.  S.);  also,  less  conveniently,  (3)  by  the  common 
logarithm  of  the  ratio  in  (i);  (4)  by  the  lengths  of  the  two  portions  of  the  tense  string  which  will  furnish  the  notes; 
and  (5)  in  terms  of  the  octave  as  unity.  The  ratio  in  (4)  is  the  reciprocal  of  that  in  (i);  the  number  for  (5)  is  1/12  of 
that  for  (2);  the  number  for  (2)  is  nearly  40  times  that  for  (3). 

Table  79  gives  data  for  the  middle  octave,  including  vibration  frequencies  for  three  standards  of  pitch;  a  =  435  double 
vibrations  per  second,  is  the  international  standard  and  was  adopted  by  the  American  Piano  Manufacturers'  Associa- 
tion. The  "just-diatonic  scale  "of  C-major  is  usually  deduced,  following  Chladni,  from  the  ratios  of  the  three  perfect 
major  triads  reduced  to  one  octave,  thus:  4:5:6 

4:5:6  4:5:6 

F  A  C  E  G  B  D 

16  20  24  30  36  45  54 

24     27     30    32     36    40    45     48 

Other  equivalent  ratios  and  their  values  in  E.  S.  are  given  in  Table  80.  By  transferring  D  to  the  left  and  using  the 
ratio  10:12:15  the  scale  of  A-minor  is  obtained,  which  agrees  with  that  of  C-major  except  that  D  —  26  2/3.  Nearly  the 
same  ratios  are  obtained  from  a  series  of  harmonics  beginning  with  the  eighth;  also  by  taking  12  successive  perfect 
or  Pythagorean  fifths  or  fourths  and  reducing  to  one  octave.  Such  calculations  are  most  easily  made  by  adding  and 
suotracting  intervals  expressed  in  E.  S.  The  notes  needed  to  furnish  a  just  major  scale  in  other  keys  may  be  found 
by  successive  transpositions  by  fifths  or  fourths  as  shown  in  Table  80.  Disregarding  the  usually  negligible  difference 
of  0.02  E.  S.,  the  table  gives  the  24  notes  to  the  octave  required  in  the  simplest  enharmonic  organ;  the  notes  fall  into 
-pairs  that  differ  by  a  comma,  0.22  E.  S.  The  line  "mean  tone"  is  based  on  Dom  Bedos'  rule  for  tuning  the  organ 
(1746).  The  tables  have  been  checked  by  the  data  in  Ellis'  Helmholtz's  "Sensations  of  Tone." 

TABLE  79. 


Interval. 

Ratios. 

Logarithms. 

Number  of  Vibrations  per  second. 

Beats 

Tem- 
pered. 

Just. 

Just. 

Tem- 
pered. 

Just. 

Tem- 
pered. 

Just. 

Just. 

Just. 

Tem- 
pered. 

E.  S. 

E.  S. 

E.  S. 

c' 

o 

0. 

I.OO 

I.OOOOO 

0.0000 

0.00000 

256 

264 

258.7 

258.7 

1.50 

I 

1.05926 

.02509 

274.0 

d' 

2 

2.04 

I.I25 

1.12246 

•OS"5 

.05017 

288 

297 

291.0 

290.3 

1.68 

3 

1.18921 

.07526 

307.6 

e' 

4 

3.86 

1.25 

1.25992 

.09691 

.10034 

320 

330 

323-4 

325-9 

1.89 

f 

5 

4-98 

i-33 

1.33484 

.12494 

.12543 

341-3 

352 

344-9 

345-3 

2.00 

6 

1.41421 

•^S1 

365-8 

g' 

7 

7.02 

1.50 

1.49831 

.17609 

.17560 

384 

396 

388 

387.5 

2.25 

8 

1.58740 

.20069 

410.6 

a' 

9 

8.84 

1.67 

1.68179 

.22185 

.22577 

426.7 

440 

43I-I 

435-0 

2.52 

10 

1.78180 

.25086 

460.9 

b' 

ii 

10.88 

1-875 

1.88775 

.27300 

•27594 

480 

49  S 

485.0 

488.3 

2-83 

c" 

12 

I2.OO 

2.OO 

2.OOOOO 

.30103 

.30103 

512 

528 

5T7-3 

Sl7-3 

3-oo 

TABLE  80. 


Key  of 

C 

D 

E 

F 

G 

A 

B 

C 

1   tt<5 

r# 

1.14 

3-i8 

5.00 

6.12 

8.16 

9.98 

12.  02 

7  *s 

V^TT 

0.92 

2.96 

4.78 

5-90 

7-94 

9.76 

II.SO 

6« 

Ftf 

1.14 

2.96 

5.00 

6.12 

8.16 

9.98 

II.  10 

f  Tf 

0.92 

2-74 

4.78 

5.90 

7-94 

9.76 

10.88 

c  « 

B 

1.14 

2.96 

4.08 

6.12 

7-94 

9.98 

11.  10 

o 

0.92 

2.74 

3-86 

5-90 

7.72 

9.76 

10.88 

A    " 

0.92 

2.96 

4.08 

6.12 

7-94 

9.06 

II.  10 

4 

0.70 

2.74 

3-86 

5-9° 

7.72 

8.84 

10.88 

3M 

0.92 

2.04 

4.08 

5-90 

7-94 

9.06 

II.  10 

. 

0.70 

1.82 

3-86 

5.68 

7.72 

8.84 

10.88 

2    " 

D 

0.92 

2.04 

4.08 

5.90 

7.02 

9.06 

10.88 

I  tf 

G 

o.oo 

2.04 

3.86 

5.90 

7.02 

9.06 

10.88 

I2.OO 

C 

0.00 

2.04 

3.86 

4.98 

7.02 

8.84 

10.88 

I2.OO 

ib 

F 

o.oo 

1.82 

3-86 

4.98 

7.02 

8.84 

9.96 

12.00 

2  i?S 

Bb 

o.oo 

1.82 

2.94 

4.98 

6.80 

8.84 

9.96 

12.00 

3" 

El? 

-.22 

1.82 

2.94 

4.98 

6.80 

7.92 

9.96 

11.78 

4" 

A!? 

-.22 

0.90 

2.94 

4.76 

6.80 

7.92 

9.96 

11.78 

5" 

Db 

-.22 

0.90 

2.94 

4.76 

5.88 

7.92 

9-74 

11.78 

6'< 

Gb 

0.90 

2.72 

476 

5.88 

7.92 

9-74 

10.86 

7" 

C> 

0.90 

2.72 

3-84 

5.88 

7.70 

9-74 

10.86 

Harmonic  Series 

8 

0.0 

(t.7A 
\i.os/ 

9 
2.04 

(.$) 

IO 

3-86 

/2I\ 

\4-7°) 

ii 

5-51 

12 

7.02 

(**) 

\7-73/ 

8^1 

14 

9.69 

15 

10.88 

16 

I2.OO 

Cycle  of  fifths 
Cycle  of  fourths 
Mean  tone 

0.0 
0.0 
O.O 

I.I4 
0.90 
0.76 

2.04 
1.  80 
1-93 

3.l8 
2.94 
3"" 

4.08 

3-84 
3-86 

5.22 
4.98 
5-03 

6.12 

5.88 

5-79 

7.02 
6.78 
6.97 

8.16 
7.92 
7-72 

9.06 
8.82 
8.90 

10.20 
9.96 
10.07 

II.  IO 

10.86 
10.83 

12.24 
11.76 
12.00 

Equal  7  step 

O.O 

I.7I 

343 

5-M 

6.86 

8.57 

10.29 

12.00 

SMITHSONIAN  TABLES. 


104 


TABLE  81. 
ACCELERATION  OF  GRAVITY. 

For  Sea  Level  and  Different  Latitudes. 

Calculated  from  Helmert's  formula  : 
rrr  gin. 78030  (i  +0.005302  sin.2  $  — 0.000007  sin.22$) 


Latitude 
* 

9 

cm.  per  sec. 
per  sec. 

Log.  g 

ff 

feet  per  sec. 
per  sec. 

Latitude 

• 

ff 

cm.  per  sec. 
per  sec. 

Log.  g 

g 

feet  per  sec. 
per  sec. 

0° 

978.030 

2.9903522 

32.0875 

50° 

981.066 

2.9916982 

32.1871 

5 

.069 

.9903695 

.0888 

51 

•!55 

.9917376 

.1901 

10 

.186 

.9904214 

.0927 

52 

•244 

.9917770 

.1930 

12 

•253 

.9904512 

.0949 

53 

•331 

.9918156 

•  1959 

14 

•332 

.9904863 

.0974 

54 

.418 

.9918540 

.1987 

15 

16 

978.376 
.422 

2.9905058 
.9905262 

32.0989 
.1004 

55 
56 

981.503 

.588 

2.9918916 
.9919292 

32.2015 
•2043 

17 

•47  * 

.9905480 

.1020 

57 

.672 

.9919664 

.2070 

18 
'9 

.523 

•577 

.9905710 
.9905950 

•1037 
•1055 

58 
59 

•754 
•835 

.9920027 
.99203*5 

•2097 
.2124 

20 
21 
22 

978.634 
.693 
•754 

2.9906203 
.9906465 
.9906736 

32.1074 
.1093 
.IH3 

60 
61 
62 

981.914 
.992 
982.068 

2.9920735 
.9921080 
.9921415 

32.2150 
.2175 

.2200 

23 
24 

.818 
.884 

.9907019 
•9907313 

•1134 
."56 

63 
64 

.142 
.215 

•9921743 
.9922066 

.2224 
.2248 

25 
26 

978.952 
979.022 

2.9907614 
.9907925 

32.H78 
.1201 

65 
66 

982.285 
•354 

2.9922375 
.9922680 

32.227T 
•2294 

27 

.094 

.9908244 

.1224 

67 

.420 

.9922972 

•  2316 

28 

.168 

.990^572 

.1249 

68 

•485 

.9923259 

•2337 

29 

.244 

.9908909 

.1274 

69 

.546 

.9923529 

•2357 

30 
31 

979-321 
.400 

2.9909250 
.9909601 

32.1299 
•1325 

70 
7' 

982.606 
•663 

2.9923794 
.9924046 

32.2377 
•2395 

32 

.481 

.9909960 

•1351 

72 

.718 

.9924289 

.2413 

33 

•562 

.9910319 

•1378 

73 

•77° 

.9924519 

.2430 

34 

.646 

.9910691 

.1406 

74 

.820 

.9924740 

.2447 

35 

979-730 

2.991  1064 

32.1433 

75 

982.866 

2.9924943 

32.2462 

36 

-.815 

.9911441 

.I46l 

76 

.911 

.9925142 

•2477 

37 

.902 

.9911827 

.1490 

77 

•952 

.9925323 

.2490 

38 

.989 

.9912212 

.1518 

78 

.990 

.9925491 

•2503 

39 

980077 

.9912602 

•1547 

79 

983.026 

.9925650 

.2514 

40 

980.166 

2.9912996 

32.1576 

80 

983.058 

2.9925791 

32.2525 

4* 

•255 

•991339* 

.1605 

81 

.088 

.9925924 

•2535 

42 

•345 

.9913789 

•1635 

82 

•"5 

.0926043 

•2544 

43 

•435 

.9914188 

.1664 

83 

•  138 

.9926145 

•2551 

44 

•525 

.9914587 

.1694 

84 

.159 

.9926238 

.2558 

45 

980.616 

3.9914989 

32.1724 

85 

983.176 

2.9926312 

32.2564 

46 

.706 

.9915388 

•'753 

86 

.190 

.9926375 

.2568 

47 

•797 

.9915791 

.1783 

87 

.201 

.9926423 

.2572 

48 

.887 

.9916190 

.1813 

88 

.209 

.9926459 

•2574 

49 

•977 

.9916588 

.1842 

90 

.2l6 

.9926489 

•2577 

To  reduce  log.  fir  (cm.  per  sec.  per  sec.)  to  log.  g  (ft.  per  sec.  per  sec.)  add  log.  0.03280833  =  8.5159842  —  10. 


CORRECTION  FOR  ALTITUDE. 

—  0.0003086  cm.  per  meter  when  altitude  is  in  meters. 

—  0.000003086  ft.  per  foot  when  altitude  is  in  feet. 


Altitude. 

Correction. 

Altitude. 

Correction. 

200  m. 

0.0617  cm  ./sec.2 

200  ft. 

0.000617  ft./sec.2 

300 

.0926 

300 

.000926 

400 

.1234 

400 

.001234 

500 

000 

•1543 
.1852 

500 
600 

.001543 
.001852 

700 

.2160 

700 

.002160 

800 

.2469 

800 

.002469 

900 

.2777 

900 

.602777 

SMITHSONIAN  TABLES. 


TABLE  82. 
GRAVITY. 


In  this  table  the  results  of  a  number  of  the  more  recent  gravity  determinations  are  biOught  t< 
show  the  degree  of  accuracy  which  may  be  assumed  for  the  numbers  in  Table  Si.  In  gt 
lower  than  the  calculated  value  for  stations  far  inland  and  slightly  higher  on  the  coast  line. 


105 

together.     They  serve  to 
general,  gravity  is  a  little 


Place. 

Latitude. 

N.  +,  S.  —  . 

Elevation 
in  meters. 

Gr™*>  ^ 

Refer- 
ence. 

Observed. 

Reduced  to 
sea  level. 

Singapore 

1°    If 
-7     56 
—  7     57 
—  8    49 

—  10      00 

13    04 
—  i5    55 
—  15     57 
20    43 
20    52 
20     56 

21       18 

32  23 

-33    5J 
—  33    56 
35    4i 
—  36"    52 
37    20 
37     20 
37    47 
37    47 
38     53 
39    54 
39    58 
40    27 
40    28 
40    44 
40    46 
41     49 
42    49 
45    3i 

46      12 
46      12 

46    57 
47     23 
48     50 
5i     28 
52     3° 
54    34 
55     59 
56    28 
57    03 
57    07 
58     18 
59    10 
59    32 

14 

686 
46 

2 

18 

IO 

533 
3001 

3 
117 

3 

2 

43 
ii 
6 

43 
1282 
1282 
114 
114 

IO 

1645 

122 
65I 

348 
II 
1288 
I65 

450 
100 

405 
405 

4^6 

67 

7 
49 
6 
o 

12 

5 
5 
4 

978.08 
978.25 
978.10 
978.15 
978.37 
978.18 
978.67 

978.53 
978.28 
978.86 
978.91 
978.97 

979-77 
979.68 
979.62 

979-95 
979.68 
979.66 
979.68 
979.96 
980.02 
980.  1  1 
979-68 
980.12 
980.08 
980.09 
980.27 
979.82 
980.34 
980.34 
980.73, 
980.58 
980.60 
980.61 
980.67 
980.96 
981.20 
981.26 
981.46 
981.51 
981.60 
981.69 
981.67 
981.74 
981.82 
981.83 

978.08 
97f.25 
978.23 
978.16 

978.37 
978.18 
978.67 
978.59 
978.85 
978.86 

978.93 
978.97 

979-77 
979.69 
979.62 

979-95 
979.69 
979.91 
979.92 
979.98 
980.04 
980.11 
979.98 
980.14 
980.20 
980.15 
980.27 
980.05 
980.37 
980.42 
980.75 
980.64 
980.66 
980.69 
980.74 
980.97 
981.20 
981.27 
981.46 

981.51 
981.60 
981.69 
981.67 
981.74 
981.82 
981.83 

I 
2 
2 
2 

3 
2 
2 
2 
3 
3 

3 
3 

i 

2 
I 

4 
5 
4 
5 
4 

1 

6 
6 

4 

5 
5 
7 

1 

9 
9 

8 
8 
4 
4 
4 
4 
4 
4 
4 
4 

Georgetown,  Ascension    .... 
Green  Mountain,  Ascension  .     .     . 
Loanda  Angola  

Caroline  Islands                           . 

Bridgetown,  Barbadoes     .... 
Jamestown,  St.  Helena     .... 
Longwood,                          .... 
Pakaoao,  Sandwich  Islands.     .     . 
Lahaina,           "               "... 
Haiki,               "               "... 
Honolulu,         "              "... 
St.  Georges,  Bermuda      .... 
Sidney  Australia 

Cape  Town      

Tokio,  Japan  .     .          

Auckland,  New  Zealand    .... 
Mount  Hamilton,  Cal.  (Lick  Obs.) 

<(                              «                          U                         « 

San  Francisco  Cal                     . 

Washington,  D.  C.*     

Denver  Colo.  .     .          

York  Pa               ... 

Allegheny,  Pa  

Hoboken   N  J         

Salt  Lake  City,  Utah  

Chicago,  111  

Pampaluna  Spain    

Montreal   Canada 

«                « 

Berne               "               

Zurich              " 

Port  Simpson,  B.  C  

Burroughs  Bay,  Alaska     .... 
Wrangell,                 "           .... 
Sitka,                       "          .... 
St.  Paul's  Island,    «          .... 
Juneau,                                 .... 
Pyramid  Harbor,    "           .... 
Yakutat  Bay,                      .    .t  .    . 

i  Smith  :  "  United  States  Coast  and  Geodetic  Survey  Report  for  1884,"  App.  14. 
2  Preston  :  "  United  States  Coast  and  Geodetic  Survey  Report  for  1890,  '  App.  12. 
3  Preston  :  Ibid.  1888,  App.  14. 
4  Mendenhall  :   Ibid.  1891,  App.  15. 
5  Defforges  :  "  Comptes  Rendus,"  vol.  118,  p.  231. 
6  Pierce  :  «  U.  S.  C.  and  G.  S.  Rep.  1883,"  App.  19- 
7  Cebrian  and  Los  Arcos  :  "Comptes  Rendus  des  Seances  de  la  Commission  rerma- 
nente  de  1'  Association  Geodesique  International,"  1893. 
8  Pierce:  «  U.  S.  C.  and  G.  S.  Report  1876,  App.  15,  and  1881,  App.  17.'* 
9  Messerschmidt  :  Same  reference  as  7. 

*  For  references  1-4,  values  are  derived  by  comparative  experiments  with  invariable  pendulums,  the  value  for 
Washington  taken  as  980.111.     For  the  latter  see  Appendix  5  of  the  Coast  and  Geodetic  Survey  Report  tor  1901. 

SMITHSONIAN  TABLES. 


io6 


TABLE  83. 


SUMMARY  OF   RESULTS  OF  THE  VALUE  OF   GRAVITY  (g)  AT  STATIONS 
IN    THE    UNITED   STATES   ANDrALASKA.* 


Station. 


Latitude. 


Longitude. 


Elevation. 


observed. 


Calais,  Me..        .        '.        .        .        .        .  45  11  11 

Boston,  Mass. 42  21  33' 

Cambridge,  Mass 42  22  48 

Worcester,  Mass 42  1 6  29 

New  York,  N.  Y 40  48  27 

Princeton,  N.  J 40  20  57 

Philadelphia,  Pa. 39  57  06 

Ithaca,  N.  Y 42  27  04 

Baltimore,  Md 39  17  50 

Washington,  C.  &  G.  S 38  53  13 

Washington,  Smithsonian  .         .         .         .  38  53  20 

Charlottesville,  Va 38  02  01 

Deer  Park,  Md 39  25  02 

Charleston,  S.  C 32  47  14 

Cleveland,  Ohio 41  30  22 

Key  West,  Fla 24  33  33 

Atlanta,  Ga. 33  44  58 

Cincinnati,  Ohio 39  08  20 

Terre  Haute,  Ind 39  28  42 

Chicago,  111 41  47  25 

Madison,  Wis.  (Univ.  of  Wis.)  .        .        .  43  °4  35 

New  Orleans,  La 29  56  58 

St.  Louis,  Mo 38  38  03 

Little  Rock,  Ark 34  44  57 

Kansas  City,  Mo 39  °5  5° 

Galveston,  Tex. 29  1812 

Austin,  Texas  (University)          .     __.        .  30  17  n 

Austin,  Texas  (Capitol)       .        .        .        .  30  16  30 

Ellsworth,  Kan 38  43  43 

Laredo,  Tex 27  30  29 

Wallace,  Kan 38  54  44 

Colorado  Springs,  Col 38  50  44 

Denver,  Col 39  40  36 

Pike's  Peak,  Col 38  50  20 

Gunnison,  Col .  38  32  33 

Grand  Junction,  Col 39  04  09 

Green  River,  Utah       .         .         .         .         .  38  59  23 

Grand  Canyon,  Wyo 44  43  16 

Norris  Geyser  Basin,  Wyo.         .        .         .  44  44  09 

Lower  Geyser  Basin,  Wyo.         .         .         .  44  33  21 

Pleasant  Valley  Jet,  Utah .         .        .  39  50  47 

Salt  Lake  City,  Utah 40  46  04 

Ft.  Egbert,  Eagle,  Alaska  .        .        .        .  64  47  22 


O         t          ff 

67  16  54 
7i  03  50 

71  o?  45 
71  48  28 

73  57  43 

74  39  28 

75  ll  40 

76  29  oo 

76  37  30 

77  o°  32 

77  01  32 

78  30  16 

79  19  50 

79  56  °3 
81  36  38 
81  48  25 
84  23  18 

84  25  20 

87  23  49 
87  36  03 

89  24  oo 

90  04  14 

9O  12  13 

92  16  24 
94  35  21 
94  47  29 
97  44  14 

97  44  16 

98  13  32 

99  31  12 
101  35  26 
104  49  02 

104  56  55 

105  02  02 

1 06  56  02 

108  33  56 
no  09  56 
no  29  44 
no  42  02 
no  48  08 

III  00  46 

i"  53  46 
141  12  24 


cm.  /sec.2 
980.630 

980-395 
980.397 
980.323 
980.266 
980.177 
980.195 
980.299 
980.096 
980.111 
980.113 

979-937 
979-934 
979-545 
980.240 
978.969 

979-523 
980.003 
980.07  1 
980.277 
980.364 

979-323 
980.000 
979.720 
979.989 
979.271 
979.282 
979.287 


979.081 

979-7^ 

979- 

97< 

9/-953 

979-341 

979.632 

979-635 
979.898 

979-949 
979-931 
979-5  r  i 
979.802 
982.182 


*  All  the  values  in  this  table  depend  on  relative  determination  of  gravity  and  an  adopted  value  for  gravity  at  Wash- 
ington (Coast  and  Geodetic  Survey  Office)  of  980.111.  This  adopted  value  was  the  result  of  the  determination  in 
1900  of  the  relative  value  of  gravity  at  Potsdam  and  at  Washington.  See  footuote  on  previous  page. 

SMITHSONIAN  TABLES 


TABLES  84-85. 
LENGTH  OF  THE  SECONDS  PENDULUM. 

TABLE  84.  —  Length  of  Seconds  Pendulum  at  Sea  Level  for  Different  Latitudes.* 


107 


Lati- 
tude. 

Length 
in  centi- 
meters. 

Log. 

Length  in 
inches. 

Log. 

Lati- 
tude. 

Length 
in  centi- 
meters. 

Log. 

Length  in 
inches. 

Log. 

0 

5 

10 

15 
20 

99.0950 
.0989 
.1108 
.1302 
.1562 

1.996052 
6069 

6121 

6206 
6320 

39.0131 
.0152 
.0200 
.0274 
.0378 

1.591218 

1234 
1287 
1372 
1485 

50 

£ 

65 
70 

994027 
.4471 
.4888 
.5263 
.5587 

1.997398 

7592 
7774 
7938 
8079 

39-  i  348 

.1524 
.1687 

•1835 
.1962 

I-592563 
2758 
2939 
3103 
3244 

25 

3° 
35 
40 

45 

99.1884 
.2259 
.2672 
.3116 
•3571 

1.996461 
6625 
6806 
7000 
7I99 

39.0506 
.0652 
.O8l6 
.0990 
.1109 

1.591627 
1790 
1972 
2166 
2364 

75 

80 

85 
90 

99-5850 
•6045 
.6165 
.6206 

1.998194 
8279 
8331 
8349 

39.2067 
.2143 
.2190 
.2206 

1  -593360 
3444 
3496 
35M 

*  Calculated  from  force  of  gravity  table  by  the  formula  /  =  g  /ir*.     For  each  100  feet  of  elevation  subtract  0.000596 
centimeters,  or  0.000235  inches,  or  .0000196  feet. 

TABLE  85.  -Length  of  the  Seconds  Pendulum.4 


Date  of 
determi- 

Number 
of  obser- 
vation 

Range  of  latitude  included  by 
the  stations. 

Length  of  pendulum  in  meters, 
for  latitude  </>. 

Correspond- 
ing length 
of  pendulum 

Refer- 
ence. 

stations. 

for  lat.  45° 

1799 

15 

From  -f  67°05/  to  —  33°  56' 

o-99o63i+.oo5637  sin2</> 

0.993450 

I 

1816 
1821 
1825 

25 

-     +738°40'  «  =6o°45; 
"     +79°  50'  "—12°  59' 

0.990880-}-  .005340  sin  2  <£ 
o.99O977-j-.oo5i42  sin2<£ 

0.993976 
0.993550 
0.993548 

2 

3 

4 

1827 

41 

"     +79°5o'"-5i°35' 

o.99io26+.oo5O72sin2<f> 

0.993562 

5 

1829 

5 

0°  o'  "  +67°  04' 

o-99°555~r".oo5679  sin  2  <j> 

0-993395 

6 

1830 

49 

11     +79°5i'  "  —  5'°35' 

0.99101  7-j-  .005087  sin2  ^ 

o.99356o 

7 

1833 
1869 
1876 
1884 

73 
123 

"     +79°  5°'  "—  5T°35' 
"     +79°  50'  "  —62°  56' 
"     +79°  50'  "-62°  56' 

0.99094  1  -f-  .00  5  1  4  2  s  i  n  2  </> 
0.990970+.  005  1  85  sin2  (f> 
0.99101  i-j-,005105  sin2  <j> 
0.9909  1  8-f-.oo5262  sin2  <p 

0.993512 
o-993554t 
0.993563 
0-993549 

8 

9 
10 
ii 

Combining  the 

:  above  results  

0.990910+.  005290  sin2^ 

0-993555 

12 

1  Laplace  ?  "  Traite  de  Mecanique  Celeste,"  T.  2,  livre  3,  chap.  5,  sect.  42. 

2  Mathieu :  "  Sur  les  experiences  du  pendule ; "   in  "  Connaissance  des  Temps  1816." 
Additions,  pp.  314-341,  P-  332. 

3  Biot  et  Arago:  "  Recueil  d' Observations  geodesiques,  etc."     Paris,  1821,  p.  575. 

4  Sabine :  "  An  Account  of  Experiments  to  determine  the  Figure  of  the  Earth,  etc.,  by 
Sir  Edward  Sabine."     London,  1825,  p.  352. 

5  Saigey:  "Comparaison  des  Observations  du  pendule  a  diverses  latitudes;  faites  par 
MM.  Biot,  Kater,  Sabine,  de  Freycinet,  et  Duperry;"  in  "Bulletin  des  Sciences  Mathe- 
matiques,  etc.,"  T.  i,  pp.  31-43,  and  171-184.     Paris,  1827. 

6  Pontecoulant :  "Theorie  analytique  du  Systeme  du  monde,"  Paris,  1829,  T.  2,  p.  466. 

7  Airy :  "  Figure  of  the  Earth ; "  in  "  Encyc.  Met."  2d  Div.  vol.  3,  p.  230. 

8  Poisson:  "Traite  de  Mecanique,"  T.  i,  p.  377;   "Connaissance  des  Temps,"  1834, 
pp.  32-33 ;  and  Puissant :  "  Traite  de  geodesic,"  T.  2,  p.  464. 

9  Unferdinger :  "  Das  Pendel  als  geodatisches  Instrument ; "  in  Grunert's  "Archiv,"  1869, 
p.  316. 

10  Fischer :  "  Die  Gestalt  der  Erde  und  die  Pendelmessungen ; "  in  "  Ast.  Nach."  1876, 
col.  87. 

11  Helmert:   "Die  mathematischen  und  physikalischen  Theorieen  der  hoheren  Geo- 
dasie,  von  Dr.  F.  R.  Helmert,"  II.  Theil.    Leipzig,  1884,  p.  241. 

12  Harkness. 


*  The  data  here  given  with  regard  to  the  different  determinations  which  have  been   made  of  the  length  of  the 
seconds  pendulum  are  quoted  from  Harkness  (Solar  Parallax  and  its  Related  Constants,  Washington,  1891). 
t  Calculated  from  a  logarithmic  expression  given  by  Unferdinger. 

SMITHSONIAN  TABLES. 


loS 


TABLES  86-87. 
MISCELLANEOUS  GEODETIC  DATA.* 

TABLE  86. 


Length  of  the  seconds  pendulum  at  sea  level  =7=39.01 2540+0.208268  sin2  0  inches. 

=3.251045+0.017356  sin2  0  feet. 
=0.9909910+0.005290  sin2  0  meters. 

Acceleration  produced  by  gravity  per  second 

per  second  mean  solar  time      .         .         .  =^=32.086528+0. 1 7 1 293  sin2  0  feet. 

=977.9886  +  5.2210  sin2  0  centimeters. 


Equatorial  radius  =0=6378206  meters ; 

3963.225  miles. 
Polar  semi-diameter       =£.=6356584  meters ; 

3949.790  miles. 

Reciprocal  of  flattening=— -^=295.0 

Square  of  eccentricity    =^=^-^—=0.006768658 


6378388+18  meters; 

§  3963-339 miles- 

ss,  635^909  meters ; 

^  3949-992  miles- 

^  297.0+0.5 

i 

^  0.0067237  ±0.0000120. 


Difference  between  geographical  and  geocentric  latitude=0— 0'= 

688.2242"  sin  2  0—i. 1482"  sin  40+0.0026" sin60. 

Mean  density  of  the  Earth =5. 5 247  ±0.00 13  (Burgess  Phys.  Rev.  1902). 

Continental  surface  density  of  the  Earth  =  2.67          ")  jjarkness 
Mean  density  outer  ten  miles  of  earth's  crust=2.4O  / 

Moments  of  inertia  of  the  Earth;  the  principal  moments  being  taken  as  A,  £,  and  C,  and 
Cthe  greater: 

C-A  i 

— — -  =0.0032652 1  =  — -, ; 

C  306.259 

C— ^=0.001064767  Ea*; 
A  =^=0.32  5029  Eaz ; 
C  =0.326094  £a* ; 
where  E  is  the  mass  of  the  Earth  and  a  its  equatorial  semidiameter. 


TABLE  87.  -  Length  of  Degrees  on  the  Earth's  Surface. 


Miles  per  degree 

Km.  per  degree 

Miles  per  degree 

Km.  per  degree 

At 

At 

Lat. 

Lat. 

of  Long. 

of  Lat. 

of  Long. 

of  Lat. 

of  Long. 

of  Lat. 

of  Long. 

of  Lat. 

0° 
10 

69.17 
68.13 

68.70 
68.72 

111.32 

110.57 
II0.60 

55° 

39-77 

69.17 
69.23 

64.00 

55.80 

111.42 

2O 

30 
40 

45 

65-03 

53.06 
49.00 

68.79 
68.88 
68.99 
69.05 

104.65 

96.49 
85.40 
78.85 

110.70 
110.85 
111.03 
III.I3 

65 
70 

y 

29.32 

23-73 
17.96 
12.05 

69.28 
69.32 
69-36 
69-39 

47-18 
38.19 
28.90 

19-39 

111.50 

1  I  1-57 
111.62 
111.67 

50 

44-55 

69.11 

71.70 

111.23 

90 

0.00 

69.41 

o.oo 

III.7O 

For  more  complete  table  see  "  Smithsonian  Geographical  Tables." 


SMITHSONIAN  TABLES. 


TABLE  88.  109 

MISCELLANEOUS  ASTRONOMICAL  DATA. 


Length  of  sidereal  5^1=365.2563578  mean  solar  days ; 

=365  days  6  hours  9  minutes  9.314  seconds. 

Length  of  tropical  year=365.242i9987o — 0.0000062124—  ^-^mean  solar  days; 

=365  days  5  hours  48  minutes  [46-069 — 0.53675— ^—  j  seconds. 

Length  of  sidereal  month 

=27.321661162 — 0.00000026240—      —days; 

=27  days  7  hours  43  minutes  [  n-524 — 0.022671 j  seconds. 

Length  of  synodical  month 

,.  ,  t — 1800  . 
= 29. 530588435 — 0.00000030696 days  ; 

=29  days  12  hours  44  minutes  [2.841  —  0.026522 —      -A  seconds. 

V  '    } 

Length  of  sidereal  day  =86164.09965  mean  solar  seconds. 

N.  B.  —  The  factor  containing  /in  the  above  equations  (the  year  at  which  the  values  of  the 
quantities  are  required)  may  in  all  ordinary  cases  be  neglected. 

Mean  distance  from  earth  to  sun  =  92900000  miles  =  149500000  kilometers. 
Eccentricity  of  the  earth's  orbit  =  e  = 

//— 1900X2 

V     I0°    )' 
Solar  parallax  =  8.7997"^-  0.003  (Weinberg,  A.  N.  165,  1904) ; 

8.807  -J-  0.0027  (Hinks,  Eros,  7); 

8.799  (Samson,  Jupiter  satellites ;  Harvard  observations). 
Lunar  parallax  =  3422.68". 

Mean  distance  from  earth  to  moon  =  60.2669  terrestrial  radii ; 

=  238854  miles ; 
=  384393  kilometers. 

Lunar  inequality  of  the  earth  =  L  =  6.454". 

Parallactic  inequality  of  the  moon  =  Q  =  1 24.80".  /_i8oo  X 

Mean  motion  of  moon's  node  in  365.25  days  =  /*  =  —  19°  21'  19.6191"  +  0.14136"  f — IOO/ 
Eccentricity  and  inclination  of  the  moon's  orbit  =  e2  =  0.05490807. 
Delaunay's  y  =  sin  ^  7=  0.044886793. 

7=  50  08'  43-3546". 
Constant  of  nutation  =  9.2'. 

Constant  of  aberration  =  20.4962  ^-  0.006  (Weinberg,  1.  c.).* 
Time  taken  by  light  to  traverse  the  mean  radius  of  the  earth's  orbit 

=  498.82  -|-  o.i  seconds  (Weinberg) ; 
=  498.64  (Samson). 

Velocity  of  light  =  186330  miles  per  second  (Weinberg) ; 
=  299870  ^  0.03  kilometers  per  second. 
General  precession  =  50.2564"  +  0.000222  (t — 1900). 
Obliquity  of  the  ecliptic  =  23°  27'  8.26"  —  0.4684  (/—  1900). 

Gravitation  constant  =  666.07  X  IQ-10  cm8/gr.  sec2  ^  0.16  X  lO"10. 


0.01675104  —  0.0000004180  (/ — 1900)  — 0.000000126 


*  Recent  work  of  Doolittle's  and  others  indicates  a  value  not  less  than  20.51. 
SMITHSONIAN  TABLES. 


no 


TABLES  89-91  .-ASTRONOMICAL   DATA. 

Table  89. -Planetary  Data. 


i 

Body. 

Reciprocals 
of  masses. 

Mean  distance 
from  the  sun. 
Km. 

Sidereal 
period. 
Mean  days 

Equatorial 
diameter. 
Km. 

Inclination 
of  orbit. 

Mean 

densitv. 
H20=i 

Gravity 
at  surface,  j 

1 

Sun 

I. 

_ 

_ 

1391067 

__ 

i-39 

27.6 

Mercury 

6000000. 

58  x  io6 

87.97 

4842 

7°.oo3 

4.86 

•3 

Venus 

408000. 

108  " 

224.70 

12394 

3-393 

S-2 

7-9 

Earth* 

329390. 

149  " 

365.26 

12756 

5-52 

1.  00 

Mars 

3093500. 

228 

686.98 

7320 

1.850 

3-90 

-4 

Jupiter 

1047-35 

778 

4332-59 

145250 

1.308 

1.36 

2.6 

Saturn 

3501.6 

1426 

10759.20 

I  23040 

2.492 

•63 

I.OI 

Uranus 

Neptune 

22869. 
19700. 

2869 
4495 

30586.29 
60188.71 

48590 
56040 

0-773 
1.778 

3 

•95 
•97 

Moon 

t  81.45 

38  x  io* 

27.32 

3473 

5-M7 

3-37 

•17 

*  Earth  and  moon,    t  Relative  to  earth.     Inclination  of  axes  :  Sun  7°. 25 ;  Earth  230.45 ;  Mars  24°.6 ;  Jupiter  3°.!; 
Saturn  26°. 8;   Neptune  27°.2.    Others  doubtful. 


Table  90.  —  Equation  of  Time. 

The  equation  of  time  when  -|-  is  to  be  added  to  the  apparent  solar  time  to  give  mean  time. 
When  the  place  is  not  on  a  standard  meridian  (75'th,  etc.)  its  difference  in  longitude  in  time 
from  that  meridian  must  be  subtracted  when  east,  added  when  west  to  get  standard  time  (75'th 
meridian  time,  etc.).  The  equation  varies  from  year  to  year  cyclically,  and  the  figure  following 
the  ;;{-  sign  gives  a  rough  idea  of  this  variation. 


!  

M.          S. 

M.         S. 

. 

M.        S. 

M.         S. 

Jan.   i 

+  326J 

!-T4 

Apr.   i 

+4     2j 

-  7 

July    i 

+3  3i=| 

=5 

Oct.    i 

—  IO    12- 

L  8 

15 

+  9  25d 

-  9 

15 

+o    8- 

-  S 

15 

+5  42, 

-3 

15 

—H    5- 

-  6 

Feb.  i 

+  13  423 

-  4 

May    i 

—2  54= 

-10 

Aug.   i 

+6     9- 

-3 

Nov.  i 

—  16  19- 

-    2 

15 

+  14    20^ 

-    2 

15 

—3  49- 

15 

+4   24- 

-S 

15 

—  15    22- 

-  4 

Mar.  i 

+12  34- 

-  4 

June  i 

—2    28- 

-  3 

Sept.  i 

+0       2-_ 

-7 

Dec.  i 

—  10   58-j 

-  8 

15 

+  9.  9d 

L  o 

15 

+o    8J 

=  4 

15 

—4  4i=j 

-9 

15 

~  4  53d 

-10 

Table  91.  —  Miscellaneous  Astronomical  Data. 
jApex  of  Solar  Motion  : 

From  proper  motions,  R.  A.isio  =  17  51™,  Dec.i8io=  +  31.4  (Weersma,  Gron.  Publ.  21.) 

From  radial  velocities,  R.  A.igoo  =  i7A54m,  Dec.i9oo=+  25.1  (Campbell,  Lick.  Bull.  196.) 
Velocity  =  19.5  Km.  per  sec.     (Campbell.) 

Nearest  star  so  far  as  known:  a  Centauri,  parallax  =  0.7 59"  (Gron.  Publ.  24)  distance  =  4. 3 
light  years. 

Stars  of  both  greatest  proper  motion  and  greatest  radial  velocity  so  far  as  known  :*  Cordova, 
V243;  proper  motion  =  8.70"  in  position  angle  130°  radial  velocity-)-  242  Km.  per  sec.  (Camp- 
bell, Stellar  Motions,  1913).  Parallax  =  0.319""  (Gron.  Publ.  24,  also  proper  motion).  Distance  = 
10.2  light  years. 

Average  velocities  with  regard  to  center  of  gravity  of  the  stellar  system,  according  to  Camp- 
bell (Stellar  Motion,  1913)  : 

Type  B  Stars  :    6.6  Km.  per  sec.     Type  G  Stars  :  15.0  Km.  per  sec. 
"      A    "         10.9    "      "      "          "    K     "        16.8    "      "     " 
F    "         14.4    "     «      "          «    M     "        17.1     "      "     " 

Sun's  magnitude  = —  26.5,  sending  the  earth  90,000,000,000  times  as  much  light  as  the  star 
Aldebaran. 

Ratio  of  total  radiation  of  sun  to  that  of  moon  about  100,000  to  i  )  T  n     , 
••     "      "     light         ««    ««    «•     «    «      «         «      400,000  to  i  J  LanSley- 

*  Lalande,  1966,  R.A.1910  ift3m.9,  Dec.1910  6i°.4'  in  1913  was  found  to  have  a  radial  velocity  (of  approach)  of  326 
Km.  per  sec.    (Mount  Wilson  Solar  Observatory.) 

SMITHSONIAN  TABLES. 


TABLE  92.  Ill 

TERRESTRIAL    MAGNETISM. 

Secular  Change  of  Declination. 

Changes  in  the  magnetic  declination  between  1810,  the  date  of  the  earliest  available  observa- 
tions, and  1910,  for  one  or  more  places  in  each  state  and  territory. 


State. 

Station. 

1810 

1820 

1830 

1840 

1850 

i860 

1870 

1880 

1890 

1900 

1910 

o 

o 

o 

o 

o 

o 

o 

o 

0 

o 

0 

Ala. 

Montgomery 

5.6E 

5-8E 

S.8E 

S.6E 

S4E 

S.oE 

4-SE 

3-9E 

3.2E 

2.8E 

2.9E 

Alas. 

Sitka 

- 

- 

- 

- 

- 

28.?E 

29-oE 

29-3E 

29.SE 

29-7E 

30.2E 

Kodiak 

- 

- 

- 

- 

- 

26.iE 

2S.6E 

25.  IE 

24.7E    24-4E  J24.iE 

Unalaska 

- 

- 

- 

- 

- 

20.4E 

20.IE 

I9.6E 

19-oE    I8.3E 

I7-SE 

St.  Michael 

— 

— 

— 

— 

— 

— 

— 

24.7E 

23.iE 

22.  lE 

21.  4E 

Ariz. 

Holbrook 

_ 

_ 

_ 

_ 

13.  6E 

I3-7E 

I3-8E 

I3-7E 

13  4E 

I3-5E 

I3-9E 

Prescott 

- 

- 

- 

- 

I3-3E 

I3-SE 

I3-7E 

I3-6E 

I3-5E 

I3-7E 

14.3  E 

Ark. 

Little  Rock 

8.6E 

8.8E 

9.oE 

Q.oE 

8.8E 

8.6E 

8.2E 

7.6E 

?.oE 

6.6E. 

6.9E 

Cal. 

Los  Angeles 

12.  IE 

I2.6E 

I3-2E 

I3-6E 

14-oE 

I4.2E 

I4-4E 

I4.6E 

I4.6E 

I4-9E 

IS-SE 

San  Jose 

15-oE 

IS-SE 

i6.oE 

I6-4E 

I6.8E 

17.  lE 

I7-3E 

I7-SE 

I7-SE 

I7-8E 

rS.sE 

Cal. 

Redding 

I5-6E 

i6.iE 

I6.6E 

I7.0E 

I7-4E 

I7.8E 

iS.iE 

I8.2E 

I8.3E 

I8.6E 

I9-3E 

Colo. 

Pueblo 

- 

- 

- 

- 

I3-8E 

I3.8E    I3.8E 

I3-SE 

i3.oE 

I2.9E 

I3-3E 

Glen  wood  Sp. 

— 

— 

— 

— 

i6.iE 

I6.2E  ii6.3E 

i6.iE 

IS-7E 

I5-6E    i6.iE 

Conn. 

Hartford 

S.iW 

S-6W 

6.iW 

6.8W 

7-SW 

8.2W 

8.?W 

9.4W 

9.8W 

I0.4W 

n.oW 

Del. 

Dover 

I.6W 

i.pW 

2.3W 

2.8W 

3-4W 

4-oW 

4-7W 

S-3W 

S-9W 

6.4W 

7-oW 

D.  C. 

Washington 

o.sE 

0-3E 

0.0 

o.sW 

LOW 

I.7W 

2.4W 

3-oW 

3.6W 

4.2W 

4-7W 

Fla. 

Jacksonville 

S-iE 

S.iE 

4-9E 

4.6E 

4.2E 

3-7E 

3.iE 

2.4E 

I.8E 

I.3E 

i.aE 

Pensacola 

7-7E 

7.8E 

7-7E 

7-SE 

7.2E 

6.8E 

6.2E 

5-6E 

S.OE 

4-5E 

4-4E 

Tampa 

6.4E 

6.2E 

S-9E 

5-5E 

5-oE 

4-SE 

3.9E 

3-3E 

2.8E 

2.3E 

2.0E 

Ga. 

Macon 

5-9E 

S-9E 

5-7E 

S-4E 

S.oE 

4-SE 

3.9E 

3.2E 

2.6E 

2.IE 

2.0E 

Haw. 

Honolulu 

_ 

_ 

_ 

_ 

9-4E 

9-4E 

9.SE 

9.8E 

lo.iE 

io.4E 

io.6E 

Idaho 

Pocatello 

- 

- 

- 

- 

I7-4E 

I7.7E 

I7-8E 

17-  9E 

I7-7E 

I7-8E 

I8.4E 

Boise 

— 

— 

— 

— 

iS.oE 

I8.4E 

I8.6E 

i8.?E 

I8.6E 

I8.8E 

I9-4E 

111. 

Bloomington 

6.3E 

6.SE 

6.6E 

6.SE 

6.3E 

5-9E 

S.4E 

4-7E 

4.iE 

3-6E 

3-4E 

Ind. 

Indianapolis 

5-oE 

S-iE 

S.oE 

4-7E 

4-4E 

3.8E 

3-2E 

2.6E 

2.0E 

i.4E 

i.iE 

la. 

Des  Moines 

_ 

I0.2E 

I0.4E 

O.sE 

O-4E 

I0.2E 

9-7E 

9-iE 

8.4E 

7-9E 

S.iE 

Kans. 

Emporia 

— 

— 

— 

— 

H.6E 

n.sE 

II.2E 

io.?E 

lo.iE 

9.8E 

10.  lE 

Ness  City 

- 

- 

- 

- 

I2.4E 

I2.4E 

12.  2E 

H.9E 

H.4E 

li.iE 

n.4E 

Ky. 

Lexington 

4-5E 

4-SE 

4-4E 

4.iE 

3.6E 

3-iE 

2.SE 

i.9E 

I.2E 

o.?E 

o.sE 

Princeton 

6.8E 

7-oE 

7-oE 

6.8E 

6.5E 

6.iE 

S.6E 

S.oE 

4-3E 

3.8E 

3-7E 

La. 

Alexandria 

8.4E 

8.7E 

8.8E 

8.8E 

8.?E 

8.4E 

S.oE 

7-4E 

6.9E 

6.6E 

6.8E 

Me. 

Eastport 

13.  6W 

I4-4W 

IS.2W 

r6.oW 

7-oW 

17.  7  W 

I8.2W 

I8.6W 

8.7W 

19-oW 

I9-4W 

Portland 

9-oW 

9.6W 

I0.3W 

n.oW 

n.6W 

I2.3W 

12.  8W 

I3-4W 

13-  9W 

I4-4W 

I4-8W 

Md. 

Baltimore 

0.9W 

i.iW 

i.4\V 

i.gW 

2.4W 

3.iW 

3-8W 

44W 

S.oW 

S.6W 

6.iW 

Mass. 

Boston 

7-3W 

7-8W 

8.4W 

9-iW 

9.8W 

io.sW 

n.oW 

n.SW 

I2.0W 

I2.6W 

13.  iW 

Mass. 

Pittsfield 

5-7W 

6.iW 

6.?W 

7-4W 

8.iW 

8.7W 

9-3W 

lO.oW 

io.4W 

n.oW 

n.SW 

Mich. 

Marquette 

- 

6.?E 

6.?E 

6-sE 

6.oE 

5-4E 

4.6E 

3-8E 

3-oE 

2.3E 

2.0E 

Lansing 

- 

4.2E 

4.iE 

3-8E 

3-3E 

2.8E 

2.IE 

I.3E 

O.sE 

o.oE 

0.4E 

Minn. 

Northome 

— 

I0.4E 

io.?E 

I0.8E 

I0.7E 

I0.4E 

lo.oE 

9-3E 

8.6E 

S.oE 

S.iE 

Mankato 

" 

H.3E 

II.6E 

H.7E 

n.6E 

II.3E 

io.9E 

io.4E 

9-SE 

9.oE 

9.iE 

*  Tables  have  been  compiled  from  United  States  Magnetic  Tables  and  Magnetic  Charts  for  1905,  published  by 
the  Coast  and  Geodetic  Survey  in  1908. 
SMITHSONIAN  TABLES. 


112 


TABLE  92  (continued). 

TERRESTRIAL    MAGNETISM  (continued). 
Secular  Change  of  Declination  (continued). 


State. 

Station. 

1810 

1820 

1830 

1840 

1850 

i860 

1870 

1880 

1890 

1900 

1910 

Miss. 

Jackson 

8.2E 

8.4E 

8.5E 

8.4E 

8.2E 

7-9E 

7-SE 

6.9E 

6.4E 

6.0E 

6.2E 

Mo. 

Sedalia 

_ 

o.oE 

0.2E 

0.2E 

lO.iE 

9.8E 

9-4E 

8.7E 

8.0E 

7.6E 

7-9E 

Mont. 

Forsyth 

_ 

- 

- 

8.2E 

I8.SE 

8.6E 

8.6E 

8.4E 

17.  9E 

7.8E 

8.3E 

Helena 

_ 

- 

- 

8.QE 

I9-3E 

9.6E 

9.8E 

9.6E 

I9-4E 

9-SE 

o.oE 

Nebr. 

Hastings 

- 

I.6E 

2.0E 

2.IE 

I2.IE 

2.0E 

i.7E 

I.2E 

lO.sE 

0.2E 

o.sE 

Nebr. 

Alliance 

_ 

_ 

- 

- 

IS-4E 

5-4E 

5-3E 

4.8E 

M-3E 

4-2E 

4-5E 

Nev. 

Elko 

— 

— 

— 

— 

I7-3E 

7.6E 

7-7E 

7-7E 

I7.6E 

7-8E 

8.3E 

Hawthorne 

- 

- 

- 

- 

I6.3E 

6.6E 

6.9E 

7-oE 

17.  oE 

17.  3E 

7.8E 

N.  H. 

Hanover 

?.iW 

7-SW 

8.2W 

8.9W 

9.8W 

o.sW 

i.iW 

I.6W 

2.0W 

I2.SW 

3-oW 

N.J. 

Trenton 

2.8W 

3-iW 

3-SW 

4.iW 

4-7W 

S-4W 

6.oW 

6.?W 

7.2W 

7-8W 

8.4W 

N.'M. 

Santa  Rosa 

_ 

- 

- 

- 

I2.7E 

2.8E 

2.7E 

2.5E 

2.IE 

I2.0E 

2.4E 

Laguna 

- 

- 

- 

- 

I3-4E 

3-6E 

3.6E 

3-4E 

3-oE 

13-oE 

3-SE 

N.  Y. 

Albany 

S-6W 

S-8W 

6.3W 

6.QW 

7.6W 

8.4W 

9.iW 

9.8W 

0.2W 

io.8W 

I.4W 

Elmira 

2.2W 

2.4W 

2.8W 

3-3W 

4.oW 

4-8W 

5-4W 

6.3W 

7-OW 

7-6W 

8.iW 

N.  C. 

Newbern 

i.7E 

I.6E 

I.3E 

0.8E 

o.3E 

0.3W 

i.oW 

I.6W 

2.2W 

2.8W 

3-3W 

N.  C. 

Salisbury 

3-9E 

3-8E 

3-6E 

3-2E 

2.7E 

2.IE 

i.SE 

O.SE 

0.2E 

0.4W 

0.7W 

N.  Dak. 

Jamestown 

- 

- 

- 

- 

I4-SE 

4-3E 

4-oE 

3-SE 

I2.7E 

I2.4E 

2.8E 

Dickinson 

— 

— 

— 

— 

17.  6E 

7-6E 

7-4E 

?.oE 

I6.4E 

i6.2E 

6.6E 

Ohio 

Columbus 

3-4E 

3-4E 

3-2E 

2.9E 

2.4E 

I.8E 

I.2E 

o.6E 

0.0 

o.?W 

I.iW 

Okla. 

Okmulgee 

- 

— 

— 

— 

I0.2E 

lO.iE 

9.8E 

94E 

8.8E 

8.5E 

8.9E 

Okla. 

Enid 

_ 

_ 

•  

_ 

II.2E 

u.iE 

I0.9E 

lO.sE 

9-9E 

9-7E 

lo.iE 

Oreg. 

Sumpter 

- 

- 

- 

- 

I9-3E 

I9.?E 

20  .oE 

20.2E 

20.2E 

20.  4E 

2I.OE 

Detroit 

6.7  E 

7.4E 

8.oE 

8.6E 

I9.2E 

I9-7E 

20.  lE 

20.  4E 

20.sE 

20.8E 

2i.5E 

Pa. 

Philadelphia 

2.2W 

2.4W 

2.8W 

3-4W 

4.iW 

4.8W 

5-SW 

6.3W 

6.8W 

7-4W 

8.oW 

Altoona 

o.sW 

0.6W 

o.gW 

I.3W 

I.8W 

2.4W 

3-iW 

3.8W 

4-SW 

S-iW 

5-6W 

P.  R. 

San  Juan 

- 

- 

- 

- 

- 

_ 

_ 

_ 

_ 

I.oW 

2.0W 

R.I. 

Newport 

6.6W 

7-iW 

7-7W 

8.4W 

9-iW 

9.8W 

I0.3W 

I0.8W 

H.3W 

n.9W 

I2.4W 

S.  C. 

Columbia 

4-4E 

4-3E 

4-iE 

3-7E 

3.2E 

2.7E 

2.IE 

i.4E 

0.8E 

0.2E 

o.iW 

S.  D. 

Huron 

- 

~i 

- 

3-iE 

13.  lE 

I2.9E 

I2.6E 

I2.IE 

H.4E 

II.  lE 

H.4E 

Rapid  City 

— 

~ 

-- 

— 

I6.4E 

I6.4E 

I6.3E 

IS-8E 

IS-3E 

IS-  iE 

IS.4E 

Tenn. 

Chattanooga 

5-3E 

5-3E 

S.iE 

4.8E 

4-4E 

3-9E 

3-3E 

2.6E 

2.0E 

i.SE 

I.3E 

Huntington 

- 

7-4E 

7-4E 

7-3E 

?.oE 

6.6E 

6.iE 

5-SE 

4-9E 

44E 

4-3E 

Tex. 

Houston 

- 

8.QE 

9.2E 

9-3E 

9-3E 

9.2E 

8.9E 

8-sE 

7-9E 

7.?E 

S.iE 

San  Antonio 

- 

- 

9.6E 

9.8E 

9-9E 

9.8E 

9.6E 

9-3E 

8.9E 

8.7E 

9.iE 

Pecos 

— 

— 

I0.8E 

n.oE 

n.iE 

U.iE 

n.oE 

I0.8E 

IO-4E 

io.3E 

io.?E 

Tex. 

Floydada 

_ 

_ 

_ 

_ 

II.3E 

n.3E 

II.2E 

IO.9E 

I0.4E 

io.3E 

io.?E 

Utah 

Salt  Lake 

- 

- 

- 

- 

I6.4E 

i6.6E 

i6.?E 

i6-sE 

I6.3E 

i6.sE 

i7.oE 

Vt. 

Rutland 

6.8W 

7-2W 

7.8W 

8.5W 

9-2W 

lO.oW 

I0.6W 

II.2W 

n.6W 

I2.IW 

I2.?W 

Va. 

Richmond 

0.8E 

o.6E 

o.sW 

o.iW 

0.6W 

I.2W 

I.8W 

2.5W 

3-iW 

3-7W 

4-2W 

Lynchburg 

I.9E 

I.8E 

I.6E 

I.2E 

o.8E 

0.2E 

O.sW 

I.2W 

I.8W 

2.4W 

2.8W 

Wash. 

Wilson  Creek 

2I.3E 

2I.6E 

2i.gE 

2I.9E 

22.  lE 

22.4E 

22.9E 

Seattle 

IQ.lE 

I9-7E 

20.3E 

20.8E 

2I.3E 

2I.8E 

22.  lE 

22.3E 

22.  6E 

23-oE 

23-SE 

W.  Va. 

Charleston 

2.3E 

2.2E 

2.0E 

I.6E 

l.iE 

o.sE 

0.2W 

0.9W 

i.SW 

2.IW 

2.6W 

Wis. 

Madison 

- 

8.6E 

8.?E 

8.6E 

8.3E 

7-8E 

7.2E 

6.4E 

5-6E 

S.oE 

4-9E 

Wyo. 

Douglas 

- 

- 

- 

- 

IS.8E 

i6.oE 

i6.oE 

IS.8E 

IS-4E 

I5-3E 

IS-7E 

Green  River 

I6.8E 

i7.oE 

17-oE 

i6.9E 

I6.6E 

I6.6E 

I7.0E 

SMITHSONIAN  TABLES. 


TABLES  93-94.  113 

TERRESTRIAL  MAGNETISM  (continued). 

TABLE  93.  —  Dip  or  Inclination. 

This  table  gives  for  the  epoch  January  i,  1905,  the  values  of  the  magnetic  dip,  I,  corresponding 
to  the  longitudes  west  of  Greenwich  in  the  heading  and  the  north  latitudes  in  the  first  column. 


65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

115° 

120° 

125° 

o 

o 

0 

0 

0 

o 

o 

0 

0 

0 

0 

0 

0 

o 

19 

_ 

- 

48.8 

49-  i 

47-5 

46.3 

44-8 

44.2 

43-9 

- 

- 

- 

- 

21 

— 

— 

51.0 

5W 

50.0 

49-3 

48.2 

47.0 

4b.,5 

— 

— 

— 

— 

23 
25 

*? 

_ 

53-7 
56.3 

53-0 
56.0 

524 

55-° 

51.8 
54-5 

5°-7 

53-2 

49.6 
52.4 

48.8 
fi-5 

48.2 
50.6 

49.8 

48.3 

~* 

27 

- 

- 

5&9 

58.1 

57.6 

56.8 

55-6 

54-7 

53-9 

S3-1 

52.6 

51.0 

— 

29 

_ 

60.7 

61.0 

60.2 

S9-8 

S8.9 

S8.2 

57-2 

S6.2 

55-5 

S4-8 

53-7 

_ 

31 

33 

— 

63.0 
65.0 

63.1 
65.0 

62.6 
64.6 

62.0 
64.0 

61.3 
63-5 

60.6 
62.7 

59.6 
62.0 

58.7 
61.0 

57-7 
S9-8 

56.7 
S8.9 

56.0 

— 

35 
37 

- 

67.0 

68.6 

66.9 
68.9 

66.5 
68.6 

66.0 
68.2 

65.6 
67.7 

64.9 
66.9 

& 

62.7 
65.1 

62.3 
64.6 

61.0 
62.9 

62^2 

- 

39 

_ 

70.3 

70.6 

70.4 

70.2 

697 

68.8 

68.1 

67.2 

66.1 

65.0 

64.0 

62.8 

41 

— 

71.8 

72.2 

72.2 

71.9 

71.4 

70.8 

69.8 

68.9 

67.8 

66.8 

6s-6 

64.7 

43 

- 

73-5 

73-9 

74.1 

73-8 

73-3 

72.6 

71.6 

70.7 

69.6 

68.6 

67.5 

66.3 

45 
47 

74-4 
75-7 

74-8 
76.2 

7M 

75-4 
76.9 

75-° 
76.8 

74.3 
76.0 

73-6 

75-2 

72.4 
74.2 

71-5 
73-0 

70.3 
71.8 

69.2 
70.8 

68.1 
69.9 

49 

76.8 

78.1 

78.2 

78.3 

78.7 

78.1 

77-5 

76.8 

75-8 

74-5 

73-5 

72.3 

71.4 

TABLE  94.  -Secular  Change  o!  Dip. 

Values  of  magnetic  dip  for  places  designated  by  the  north  latitudes  and  longitudes  west  of 
Greenwich  in  the  first  two  columns  for  January  ist  of  the  years  in  the  heading.  The  degrees 
are  given  in  the  third  column  and  minutes  in  the  succeeding  columns. 


Lati- 
tude. 

Longi- 
tude. 

1855 

1860 

1865 

1870 

I87S 

1880 

I88S 

1890 

I89S 

I90O 

I9OS 

1910 

0 

0 

o 

, 

, 

, 

, 

, 

, 

r 

f 

, 

t 

t 

, 

25 

80 

55+ 

49 

49 

48 

46 

43 

40 

35 

35 

39 

48 

60 

77 

25 

no 

49+ 

08 

20 

3° 

39 

46 

61 

68 

76 

86 

96 

106 

30 

3° 

83 

IOO 

60+ 
57+ 

66 
44 

70 
49 

74 
67 

73 
70 

65 

g 

51 
61 

63 

77 

78 
90 

96 
I05 

30 

115 

54+ 

53 

62 

69 

70 

72 

75 

79 

85 

91 

96 

101 

35 

80 

66+ 

57 

58 

57 

54 

45 

35 

26 

21 

20 

22 

30 

38 

35 

90 

65+ 

65 

59 

51 

44 

37 

32 

26 

25 

25 

27 

36 

48 

35 
35 

105 

120 

62+ 
60+ 

°3 

06 

08 

11 

30 
07 

3 

3 

24 
II 

28 

34 
14 

42 
12 

50 
08 

40 

75 

82 

82 

78 

73 

65 

55 

43 

33 

27 

24 

24 

24 

40 
40 

90 

I05 

70+ 
67+ 

30 

3_' 

34 

37 
56 

36 
53 

32 

51 

29 
51 

26 

25 

52 

26 
56 

63o° 

if 

40 

120 

64+ 

— 

48 

4~6 

44 

44 

44 

44 

44 

45 

45 

48 

48 

45 
45 

65 

75 

74+ 
75+ 

116 
103 

no 

99 

101 

95 

92 
90 

80 
85 

68 
73 

§ 

46 
53 

35 
43 

28 
38 

24 
36 

20 
34 

45 

90 

74+ 

81 

81 

81 

79 

77 

75 

68 

63 

61 

59 

60 

60 

45 

I05 

72+ 

— 

— 

— 

— 

— 

22 

20 

20 

21 

22 

24 

27 

45 

122.5 

68+ 

35 

34 

37 

40 

40 

39 

37 

34 

3° 

26 

24 

20 

49 

92 

78+ 

26 

25 

24 

22 

20 

20 

15 

12 

II 

09 

06 

04 

49 

120 

72+ 

" 

26 

24 

22 

22 

19 

20 

19 

19 

19 

18 

16 

SMITHSONIAN  TABLES. 


114 


TABLES  95-96. 

TERRESTRIAL   MAGNETISM  (continued). 
TABLE  95. -Horizontal  Intensity. 


This  table  gives  for  the  epoch  January  i,  1905,  the  horizontal  intensity,  H,  expressed  in  C.  G.  S. 
units,  corresponding  to  the  longitudes  in  the  heading  and  the  latitudes  in  the  first  column. 


65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

115° 

120° 

125° 

0 

19 

_ 

„ 

.307 

.3H 

•3i9 

.322 

.328 

•332 

•331 

21 

- 

- 

.301 

•309 

.3M 

.316 

.320 

•324 

•324 

23 

— 

— 

•293 

•303 

•305 

•309 

.312 

•315 

.317 

.320 

25 

— 

— 

.284 

.292 

•295 

.299 

•3°4 

•307 

.308 

•309 

.312 

•304 

27 

- 

- 

.274 

.280 

.286 

.289 

.296 

.298 

•300 

•303 

•306 

.298 

29 

_ 

.257 

.262 

.269 

.276 

.281 

.286 

.289 

.292 

.294 

.297 

.291 

31 

- 

.246 

.251 

.256 

.263 

.269 

.274 

.277 

.282 

.284 

.285 

.282 

33 

_ 

•233 

•239 

'•245 

.251 

•257 

.262 

.266 

.270 

•273 

.274 

.274 

35 

— 

.220 

.225 

.232 

.240 

.242 

.248 

.253 

.256 

•259 

.262 

.265 

37 

- 

.208 

.209 

.218 

.222 

.226 

.232 

.238 

•245 

.246 

.252 

.251 

39 

— 

.197 

.198 

.203 

.206 

.212 

.217 

.224 

.229 

•237 

.240 

.242 

.245 

_ 

.184 

.185 

.186 

.192 

.196 

.202 

.207 

.216 

.223 

.228 

.240 

.236 

43 

_ 

.170 

.170 

.169 

•'75 

.178 

.187 

.194 

.201 

.210 

.215 

.222 

.226 

45 

.161 

•157 

•'55 

.156 

.162 

.169 

.177 

.190 

.192 

.208 

.215 

47 

•145 

.144 

.140 

.142 

.142 

.150 

.152 

.161 

.170 

.180 

.188 

.196 

.2OI 

49 

.129 

.125 

.126 

.124 

.129 

•  138 

.146 

•'53 

.165 

•J75 

.182 

.187 

TABLE  98.  —Secular  Change  of  Horizontal  Intensity. 

Values  of  horizontal  intensity  in  C.  G.  S.  units  for  places  designated  by  the  latitude  and  longi- 
tude in  the  first  two  columns  for  January  I  of  the  years  in  the  heading. 


Latitude.  1 

tf 

I8S5 

i860 

1865 

1870 

1875 

1880 

1885 

1890 

I89S 

1900 

1905 

1910 

0 

0 

25 

80 

•3099 

.3086 

•3°73 

•3057 

.3042 

•3°25 

.3008 

.2990 

.2970 

.2949 

.2920 

.2890 

25 

no 

.3229 

.3218 

.3204 

.3189 

.3170 

.3155 

•3T43 

.3130 

.3117 

.3104 

.3090 

•3075 

3° 

83 

.2803 

•2795 

.2788 

.2780 

.2772 

.2763 

.2752 

.2740 

.2725 

.2706 

.2680 

.2644 

30 

TOO 

— 

— 

.2961 

.2942 

.2924 

.2907 

.2891 

.2877 

.2865 

.2850 

.2830 

.2804 

3° 

"5 

.3040 

.3026 

.3011 

.2996 

.2979 

.2964 

.2952 

.2940 

.2929 

.2920 

.2910 

.2898 

35 

80 

.2384 

•2379 

•2374 

.2369 

.2367 

•2363 

•2359 

•2352 

•2347 

•2337 

.2320 

.2296 

35 

90 

— 

.2462 

.2462 

.2461 

.2458 

•2455 

.2447 

•2437 

.2430 

•2399 

35 
35 

105 
120 

_ 

~ 

— 

.2720 

.2620 
.2707 

.2608 
.2695 

•2599 
.2683 

.2590 
.2672 

.2583 
.2663 

•2573 
.2656 

.2650 

•2544 
.2644 

40 

75 

.1880 

.1883 

.1891 

.1902 

.1911 

.1919 

.1925 

.1930 

.1928 

.1920 

.1909 

40 

90 

_ 

.2086 

.2082 

.2079 

.2076 

.2075 

.2074 

.2072 

.2068 

.2060 

.2050 

.2036 

40 

105 

- 

- 

- 

.2272 

.2266 

.2261 

.2257 

•2253 

.2248 

.2240 

.2230 

.2217 

40 

120 

- 

— 

— 

.2429 

.2420 

.2412 

.2406 

.2399 

.2392 

.2386 

.2380 

•2379 

45 

65 

.1504 

.1514 

•1525 

•'537 

•J553 

.i567 

.1578 

.1589 

.lOOO 

.1608 

.1610 

.1610 

45 

75 

.1483 

.1485 

.1488 

•M95 

.1506 

.1516 

•1527 

•!538 

.1546 

•1550 

•1550 

•T554 

45 

90 

- 

•1635 

•1633 

.1631 

.1628 

.1626 

.1624 

.1623 

.1624 

.1623 

.1620 

.1616 

45 

105 

— 

.1920 

.1919 

.1918 

.1916 

.1913 

.I9IO 

.1906 

.1900 

.1892 

45 

122.5 

•2175 

.2170 

.2162 

•2153 

.2145 

•2135 

2127 

.2121 

.2117 

.2115 

.2115 

.2115 

49 

92 

•1332 

•1330 

.1328 

.1324 

.1321 

.1318 

.1318 

.1321 

.1324 

49 

120 

.1841 

.1841 

.1840 

.1839 

.1836 

'^83? 

.1826 

.1821 

.1819 

.1820 

.1820 

^4 

SMITHSONIAN  TABLES. 


TABLES  97-98.    '  115 

TERRESTRIAL   MAGNETISM   (continued). 

TABLE  97.  —  Total  Intensity. 

This  table  gives  for  the  epoch  January  i,  1905,  the  values  of  total  intensity,  F,  expressed  in  C.  G.  S. 
units  corresponding  to  the  longitudes  in  the  heading  and  the  latitudes  in  the  first  column. 


65° 

70° 

75° 

80° 

85° 

90° 

95° 

100° 

105° 

110° 

HS° 

120° 

125° 

0 

19 

_ 

.466 

.480 

.472 

.466 

.462 

•463 

•459 

_ 

_ 

_ 

_ 

21 

- 

- 

•478 

.492 

•489 

485 

.480 

•475 

.471 

- 

- 

- 

- 

23 

- 

- 

•495 

•504 

.500 

.yOQ 

•493 

.486 

.481 

.480 

- 

- 

- 

25 

— 

— 

.512 

•522 

•5'4 

•515 

•5°7 

•5°3 

•495 

.487 

.483 

•457 

— 

27 

— 

— 

•530 

•530 

•534 

.528 

•  524 

.516 

•509 

•505 

•5°4 

•474 

"• 

29 

_ 

•525 

•540 

•541 

•549 

•544 

•543 

•534 

•525 

.519 

•515 

•492 

- 

31 

-• 

•542 

.556 

.560 

.560 

•558 

•547 

•543 

•531 

•519 

•5°4 

- 

33 

- 

.566 

•571 

•572 

.576 

.571 

.567 

•557 

•543 

•53° 

.518 

— 

35 

- 

•563 

•574 

.582 

•590 

.586 

.584 

•571 

•558 

•557 

•540 

•533 

— 

37 

- 

•570 

.581 

•598 

•598 

.596 

•591 

•590 

.582 

•573 

•553 

.538 

— 

39 

_ 

.584 

.596 

.605 

.608 

.611 

.600 

.600 

•591 

•585 

.568 

•552 

•536 

41 
43 

: 

.589 
•599 

.605 
.613 

.608 
.617 

.618 
.627 

.614 
.619 

.614 
.625 

.600 
.614 

.600 
.608 

•590 
.602 

•579 
•589 

:|o 

•552 
.562 

45 
47 

•599 
•587 

•599 
.604 

.623 
.618 

.623 
.622 

.623 
.626 

.626 
•657 

.624 
.628 

.627 
.630 

.628 
.624 

.605 
.616 

•590 
.602 

'.586 
.596 

•576 
.583 

49 

•574 

.626 

.611 

.621 

•633 

.626 

.638 

•639 

.624 

.617 

.616 

•599 

.58§ 

TABLE  98.  -  Secular  Change  of  Total  Intensity. 

Values  of  total  intensity  in  C.  G.  S.  units  for  places  designated  by  the  latitudes  and  longitudes  in  the 
first  two  columns  for  January  I  of  the  years  in  the  heading.    (Computed  from  Tables  92  and  94.) 


Lati- 
tude 

Longi- 
tude. 

1855 

1860 

1865 

1870 

1875 

1880 

1885 

1890 

1895 

1900 

1905 

1910 

0 

0 

25 

80 

•55J6 

•5493 

.5467 

•5434 

•5400 

•5364 

•5322 

.5290 

.5264 

•5247 

•5o^ 

.5206 

25 

110 

•4935 

•4938 

•4933 

•4925 

.49o8 

.4902 

.4891 

•4883 

.4876 

4873 

.4868 

.4860 

30 

83 

.5800 

•5796 

•5790 

•5777 

•5757 

.5720 

.5668 

.5625 

.5600 

•5590 

•5581 

•5559 

3° 
30 

IOO 

115 

.5285 

.5280 

•5583 
•5269 

•5570 
•5247 

•5544 
•5215 

•5499 
•S194 

•5456 
•5'79 

•5432 
•5l67 

.5427 
.5160 

•5421 
.5158 

.5416 
•Sl$l 

•5405 
.5140 

35 

80 

.6089 

.6080 

.6063 

.6038 

•5996 

•5946 

.5900 

.5863 

.5874 

•5830 

.5818 

•5789 

35 

90 

- 

— 

•5991 

•5964 

•5942 

.5912 

.5901 

.5882 

.5865 

•5858 

•5852 

35 

105 

- 

- 

- 

•5674 

.5629 

.5610 

•5590 

.5588 

•5585 

•5582 

•5572 

35 
40 

1  20 

75 

.6206 

.6216 

•6220 

.5462 
.6227 

•5433 
.6212 

.5406 
.6182 

•5388 
.6136 

•5374 

•536i 
.6070 

•535° 
.6045 

•5332 
.6019 

•5309 
•5985 

40 

90 

- 

.6254 

.6258 

.6264 

.6250 

.6226 

.6208 

.6187 

.6170 

.6151 

.6141 

•6i35 

40 

105 

— 

— 

- 

.6048 

.6019 

•5997 

,5986 

•5976 

•5967 

•5963 

•5953 

•5940 

40 

1  20 

— 

- 

— 

.5691 

.5670 

•565! 

•5637 

.5620 

.5608 

•5593 

•5590 

•5591 

45 

65 

.6188 

.6186 

.6167 

.6152 

.6134 

.6107 

.6077 

.6048 

.6019 

.6005 

•5987 

.5962 

45 

75 

•6454 

.6431 

.6413 

.6404 

.6412 

•6363 

.6327 

.6306 

.6266 

.6247 

•6233 

•6235 

45 

90 

- 

.6465 

•6457 

•6434 

.6408 

.6386 

•633° 

.6291 

.6382 

.6264 

.6259 

.6244 

45 

I05 

— 

— 

— 

— 

— 

•6332 

.63^14 

•6303 

.6299 

.6392 

.6284 

.6275 

45 

122.5 

•5956 

'I?38 

•5930 

i9^ 

.5896 

.5§64 

•5834 

•5804 

•5776 

•5754 

•5745 

•H 

49 

92 

.6643 

.6624 

.6604 

.6566 

•6533 

•6523 

.6472 

.6445 

.6451 

.6447 

.6450 

.6456 

49 

120 

.6100 

.6085 

.6071 

.6061 

.6028 

.6017 

•5995 

.5988 

•5992 

.5986 

.5988 

SMITHSONIAN  TABLES. 


n6 


TABLE  99. 
AGONIC  LINE. 

The  line  of  no  declination  appears  to  be  still  mov- 
ing westward  in  the  United  States,  but  the  line  of  no 
annual  change  is  only  a  short  distance  to  the  west  of 
it,  so  that  it  is  probable  that  the  extreme  westerly 
position  will  soon  be  reached. 


Lat. 

N. 

Longitudes  of  the  agonic  line  for  the  years  — 

1800 

1850 

1875 

1890 

1905 

0 

0 

o 

0 

0 

0 

25 

- 

- 

- 

75-5 

76.1 

30 

- 

— 

— 

78.6 

79-7 

35 

6 

75-2 

76.7 

77-3 

79.0 
79-7 

L9:?, 

81.7 
82.8 

7 

76.3 

77-7 

80.6 

82.2 

83-5 

8 

76.7 

78.3 

81.3 

82.6 

83.6 

9 

76.9 

78.7 

81.6 

82.2 

83-6 

40 

77.0 

79-3 

81.6 

82.7 

84.0 

i 

77-9 

80.4 

81.8 

82.8 

84.6 

2 

79.1 

81.0 

82.6 

83-7 

84.8 

3 
4 

79-4 
79.8 

81.2 

83-1 
83-3 

84-3 
84.9 

85.0 
85.5 

45 

_ 

_ 

83.6 

85.2 

86.0 

6 

- 

- 

84.2 

84.8 

86.4 

I 

9 

- 

- 

85-1 
86.0 
86.5 

85-4 
85-9 
86.3 

86.4 
86.5 
87.2 

SMITHSONIAN  TABLES. 


TABLE  1 00.  11 

RECENT  VALUES  OF  THE  MAGNETIC  ELEMENTS  AT  MAGNETIC 

OBSERVATORIES. 

(Compiled  by  the  Department  of  Terrestrial  Magnetism,  Carnegie  Institution  of  Washington.) 


Place. 

Latitude. 

Longitude. 

Middle 
of 
year. 

Magnetic  Elements. 

Declination 

Inclination 

Intensity  (C.G.S.  units). 

Hor'l. 

Ver'l. 

Total,  i 

[  Pawlowsk 
Sitka 
Katharinenburg 
Rude  Skov 
Eskdalemuir 
Stonyhurst 
Wilhelmshaven 
Potsdam 
Seddin 
Irkutsk 
De  Bilt 
Valencia 
Clausthal 
Bochum 
Kew 
Greenwich 
Uccle 
Hermsdorf 
Beuthen 
Falmouth 
Prague 
Cracow 
St.  Helier  (Jersey) 
Val  Joyeux 
Munich 
Kremsmlinster 
O'Gyalla  (Pesth) 
Odessa 
Pola 
Agincourt  (Toronto) 
Perpignan 
Tiflis 
Capodimonte 
Ebro  (Tortosa) 
Coimbra 
Mount  Weather 
Baldwin 
Cheltenham 
Athens 
San  Fernando 
Tokio 
Tucson 
Zi-ka-wei 
Dehra  Dun 
Helwan 
Barrackpore 
Hongkong 
Honolulu 
Toungoo 
Alibag 
Vieques 
Antipolo 
Kodaikanal 
Batavia-Butenzorg 
St.  Paul  de  Loanda 
Samoa  (Apia) 
Tananarive 
Mauritius 

Rio  de  Janeiro 

0         / 

59  4iN 
5703N 
57  03N 
555'N 
55i9N 

535'N 
5332N 

5223N 

52  i;N 
52  i6N 
52o6N 
5I56N 
51  48N 
51  29N 
51  28N 
51  28N 
5048N 
5046N 
50  2iN 
5009N 
5005N 
5004N 
49  i2N 
4849N 
48  o§N 
48o3N 

47  53N 
4626N 
4452N 
4347N 
4242N 
41  43N 
40  52N 
4049N 

40  I2N 

3904N 
3847N 
3844N 
3759N 
3628N 
354iN 
32  isN 

31    I2N 

30  igN 

2952N 

22  46N 

22  I8N 

21  igN 

1  8  56N 
I838N 
i8o9N 
i436N 
10  I4N 
6  iiS 
8488 
13488 
18558 
20068 

22558 

0          / 

30  29E 

135  20  W 

6o38E 

12  27E 

3  I2W 

2  28W 

8o9E 
I304E 
13  oiE 
104  i6E 
5  nE 
10  I5W 

IO  2OE 

7  ME 
o  igW 
o  oo 
4  2iE 
16  I4E 

i855E 
So5W 
I425E 
I958E 

205W 

20lE 

ii  37E 
I408E 
18  i2E 
3o46E 

J3  5lE 
79i6W 

253E 
4448E 
14  i5E 
o  3iE 
825W 
77  53  W 
95  loW 
765oW 
2342E 
6  i2W 

139  45E 
no  5oW 

121  26E 

78o3E 
31  2oE 
8822E 
114  loE 
1  58  04  W 
9627E 

72  52E 
6526W 

121   IOE 

7728E 
106  49E 

i3i3E 
171  46W 

47  32E 
5733E 

43  "W 

1907 
1910 
1907 
1910 
1911 
1912 
1910 
1912 
1912 

1905 
1910 
1911 

r9Q5 
1911 
1911 
1911 
1911 
1912 
1908 
1912 
1910 
1911 
1907 
1911 
1910 
1904 
1911 
1910 
1911 
1910 
1910 

1905 
1911 
1911 
1911 
1908 
1908 
1910 
1908 
1911 
1910 
1910 
1907 
1910 
1912 
1910 
1910 
1910 
1910 
1912 
1910 
1911 
1910 
1909 
1910 
1908 
1907 
1911 
(1906 
I  i9J<> 

O            1 

i  O9-9E 
30  i6.4E 

10  35-5E 
9  28.7  W 
18  I2.4W 
17  03.6  W 
ii  37.0  W 
8  45-9W 
8  47.2W 
i  58.iE 
12  58.2W 

20  38.  1  W 

10  40.3W 
ii  48.3  W 
15  55-3W 
15  33-o  W 
13  13  9W 
7  o6.9W 
6  I2.3W 

17  24.2W 

8  09.6W 
5  iS.iW 
16  274W 
14  I7.6W 
93i.5W 
9  02.4\V 
6  25.6W 
3  35-9  W 
8  I7.5W 
6  03.9  W 
1  2  44.8  W 
2  41  .6E 

13  I&6W 
1  6  27.  4  W 
3  39-2W 
8  33.oE 
5  4L4W 
4  53-oW 
15  05.2W 
4  5».2W 
13  25.8E 
2  33-6W 
2  3r-9E 

2  25.4W 

o  55-5E 
o  oo.4E 
9  297E 
o  24.9E 
o  51.  2E 

2  20.6W 

o  4O-9E 
o  55.oW 
o  49.  5E 
16  i2.3W 
9  4I.9E 
9  29.7W 
9  i8.5W 
8  55-3W 
9  40.oW 

o        / 

70  37-7N 
74  32-2N 
70  52.  2N 
68  45.oN 
69  37.  i  N 
684i.4N 
67  30-5N 
66  2o.4N 
66  i;.4N 
70  25.oN 
66  46.5N 
68  i2.iN 

.1650 

•1559 
.1762 

.1738 
.1685 
.1740 
.1812 
.1880 
.1884 
.2OOI 
.1854 
.1789 

.4694 
.5637 
.5081 
.4468 

•4534 
.4460 

4377 
.4291 
.4290 
•5625 
•4321 
•4473 

•4975 
.5849  ! 
•5378  j 
•4794 

•4837  ; 

.4787  ! 

.4737 
.4685 
.4685! 
.5970 
.4702 
.4817 

66  57.2N 
66  52.  i  N 
66  oo.iN 

.1850 
.1852 
.1902 

•4349 
•4337 
•4273 

.4726 
.4716 
.4677 

66  26.6N 

.1880 

•4312 

.4704 

64  I5-5N 

65  34-  5N 
644I.6N 
63  o8.4N 

.1974 
.2064 

.4176 
•4075 

.4619 

.4568 

62  26.9N 

60  03-6N 
74  38-5N 

.2107 
.2171 
.2219 
.1627 

.4161 
.3853 
•5923 

.4693 

.4446 
.6142 

56  02.8N 
56  ii.7N 
57  54-8N 
58  46-4N 

•2545 

.2326 
.2301 

•378o 

•3709 
•3795 

•4557 

•4378 
4438 

68  47.8N 
70  35-4N 
52  n.  7N 

54  3I-5N 
49  07-3N 
59  I9-6N 
45  36.6N 
43  54.8N 
40  43.7  N 

30  42.2N 

30  58.8N 
39  47.2N 
23  02.  i  N 
23  56.  i  N 
49  52.oN 
16  i8.2N 
3  45-2N 
31  09.28 
35  32-28 
29  21.78 
54  05.78 
53  30.68 
13  57.28 

.2171 
.1983 
.2620 
.2489 
.3001 
.2741 
.3306 
.3326 
.3006 

•3733 
•3711 
.2916 
.3880 
.3687 
.2886 
.3820 
.3748 
.3668 
.2012 
•356i 
•2533 
•2331 
.2477 

:!& 

•3361 

.6003 
.5966 
.4262 

.3467 
.4621 

•3377 
.3202 
.2588 
.2217 
.2228 
.2428 
.1650 
•1637 
.3424 
.1117 
.0246 
.2218 

•1437 
.2004 

•3499 
.3151 
.0617 

•4585 
•5372 
.4726 
.4617 
.3967 
.4341 
.4328 

•3795 
.4216 

•4034 
.4478 
•398i| 

:432l| 

.2473 
.4086 

•43  !9 
.3920 

•2553 

SMITHSONIAN  TABLES. 


n8 


TABLE  101. 


PRESSURE    OF   COLUMNS    OF    MERCURY   AND   WATER, 

British  and  metric  measures.     Correct  at  o°  C.  for  mercury  and  at  4°  C.  for  water. 


I  — 

METRIC  MEASURE. 

BRITISH  MEASURE. 

Cms.  of 
Hg. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
Hg. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I3-5956 

0.193376 

1 

34-533 

0.491174 

2 

27.1912 

0.386752 

2 

69.066 

0.982348 

3 

40.7868 

0.580128 

3 

103.598 

I-473522 

4 

54-3824 

0.773504 

4 

I38.I3I 

1.964696 

5 

67.9780 

0.966880 

5 

172.664 

2.455870 

6 

8L5736 

1.160256 

6 

207.197 

2.947044 

7 

95.1692 

I-353632 

7 

241.730 

3.438218 

8 

108.7648 

1.547008 

8 

276.262 

3.929392 

9 

122.3604 

1.740384 

9 

310.795 

4.420566 

10 

I35-9560 

1.933760 

10 

345-328 

4.911740 

Cms.  of 
H,0. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

Inches  of 
H20. 

Pressure 
in  grams  per 
sq.  cm. 

Pressure 
in  pounds  per 
sq.  inch. 

1 

I 

0.0142234 

1 

2-54 

0.036127 

2 

2 

0.0284468 

2 

5.08 

0.072255 

3 

3 

0.0426702 

3 

7.62 

0.108382 

4 

4 

0.0568936 

4 

10.16 

0.144510 

5 

5 

0.07III70 

5 

12.70 

0.180637 

6 

6 

0.0853404 

6 

15-24 

0.216764 

7 

7 

0.0995638 

7 

17.78 

0.252892 

8 

8 

0.1137872 

8 

20.32 

0.289019 

9 

9 

O.I280I06 

9 

22.86 

0.325M7 

10 

10 

0.1422340 

10 

25.40 

0.361274 

SMITHSONIAN  TABLES. 


TABLE  102.  Il'g 

REDUCTION  OF  BAROMETRIC  HEIGHT  TO  STANDARD   TEMPERATURE, 


Corrections  for  brass  scale  and 
English  measure. 

Corrections  for  brass  scale  and 
metric  measure. 

Corrections  for  glass  scale  and 
metric  measure. 

Height  of 
barometer  in 
inches. 

a 

in  inches  for 
temp.  F. 

Height  of 
barometer  in 
mm. 

a 

in  mm.  for 
temp.  C. 

Height  of 
barometer  in 
mm. 

a 

in  mm.  for 
temp.  C. 

15.0 

0.00135 

400 

0.0651 

50 

0.0086 

1  6.0 

.00145 

410 

.0668 

IOO 

.0172 

17.0 

.00154 

420 

.0684 

150 

.0258 

*7-S 

.00158 

43° 

.0700 

200 

•°345 

18.0 

.00163 

440 

.0716 

250 

.0431 

18.5 

.00167 

45° 

.0732 

300 

•0517 

19.0 

.00172 

460 

.0749 

350 

.0603 

J9-5 

.00176 

470 

.0765 

480 

.0781 

400 

0.0689 

200 

O.OOlSl 

490 

.0797 

45° 

•0775 

20.5 

.00185 

500 

.0861 

21.0 

.00190 

500 

0.0813 

520 

.0895 

21-5 

.00194 

5io 

.0830 

540 

.0930 

22.O 

.00199 

520 

.0846 

560 

.0965 

22.5 

.OO2O3" 

530 

.0862 

580 

.0999 

23.0 

.00205 

540 

.0878 

23-5 

.00212 

550 

.0894 

600 

0.1034 

560 

.0911 

610 

.1051 

24.0 

0.00217 

570 

.0927 

620 

.1068 

24-5 

.00221 

580 

•0943 

630 

.1085 

25.0 

.OO226 

590 

•0959 

640 

.1103 

25-5 

.00231 

650 

.11  2O 

26.0 

.00236 

600 

0.0975 

660 

•1137 

26.5 

.00240 

610 

.0992 

27.0 

.  .00245 

620 

.1008 

670 

0.1154 

27-5 

.00249 

630 

.1024 

680 

.1172 

640 

.1040 

690 

.1189 

28.0 

O.OO254 

650 

.1056 

700 

.1206 

28.5 

.00258 

660 

.1073 

710 

.1223 

29.0 

.00263 

670 

.1089 

720 

.1240 

29.2 

.00265 

680 

.1105 

73° 

.1258 

29.4 

.00267 

690 

.1121 

29.6 

.00268 

740 

0.1275 

29.8 

.00270 

700 

O.II37 

750 

.1292 

30.0 

.00272 

710 

•1154 

760 

.1309 

720 

.1170 

770 

.1327 

30.2 

0.00274 

73° 

.1186 

780 

•1344 

3°-4 

.00276 

740 

.I2O2 

790 

.1361 

30.6 

.00277 

75° 

.1218 

800 

.1378 

30.8 

.OO279 

760 

•I235 

31.0 

.OO28l 

770 

.1251 

850 

0.1464 

31.2 

.00283 

780 

.1267 

900 

•*SSl 

3M 

.00285 

790 

.1283 

95° 

.1639 

31.6 

.00287 

800 

.1299 

1000 

.1723 

on  the  brass  case.  This  relative  expansion  is  practically  proportional  to  the  first  power  of  the  tem- 
perature. The  above  tables  of  values  of  the  coefficient  of  relative  expansion  will  be  found  to  give 
corrections  almost  identical  with  those  given  in  the  International  Meteorological  Tables.  The 
numbers  tabulated  under  a  are  the  values  of  a  in  the  equation  ///  =  ///  —  a(t'  — t)  where  Ht  is  the 
height  at  the  standard  temperature,  Ht'  the  observed  height  at  the  temperature/',  and  a  (t'—t)  the 
correction  for  temperature.  The  standard  temperature  is  o°  C.  for  the  metric  system  and  28°.5  F. 
for  the  English  system.  The  English  barometer  is  correct  for  the  temperature  of  melting  ice  at  a 
temperature  of  approximately  28°.  5  F.,  because  of  the  fact  that  the  brass  scale  is  graduated  so  as 
to  be  standard  at  62°  F.,  while  mercury  has  the  standard  density  at  32°  F. 

EXAMPLE.— A  barometer  having  a  brass  scale  gave  H=  765  mm.  at  25°  C. ;  required,  the  cor- 
responding reading  at  o°  C.  Here  the  value  of  a  is  the  mean  of  .1235  and  .1251,  or  .1243; .  •.  a  (t'  —  t) 
=  .1243  X  25  =  3.11.  Hence  ffQ  =  765  —  3.11  =  761.89, 

N.  B. — Although  a  is  here  given  to  three  and  sometimes  to  four  significant  figures,  it  is  seldom 
worth  while  to  use  more  than  the  nearest  two-figure  number.  In  fact,  all  barometers  have  not  the 
same  values  for  a,  and  when  great  accuracy  is  wanted  the  proper  coefficients  have  to  be  deter* 
mined  by  experiment. 

SMITHSONIAN  TABLES. 


I2O 


TABLE  103. 


CORRECTION  OF  BAROMETER  TO  STANDARD  GRAVITY, 

Altitude  term.    Correction  is  to  be  subtracted. 


Height 
above  sea 
level  in 
meters. 

Observed  height  of  barometer  in  millimeters. 

15000 
14500 
I4OOO 
13500 
13000 
12500 
12000 
II500 
IIOCO 
10500 
1  0000 

9500 

9000 

8500 
8000 
7500 

7000 

6500 
6000 

5500 

5000 

4500 

4000 

3500 
3000 
2500 

2000 
I5OO 
1000 
500 

400 

450 

500 

55° 

600 

650 

700 

75o 

800 

100 
2OO 
300 
400 
|00 
600 
700 
800 
900 
1000 
IIOO 
I2OO 
1300 
1400 
I5OO 
1600 
1700 
I800 
I9DO 
2OOO 
2IOO 
2200 
2300 
24OO 
2500 
2600 
27OO 
2800 
2900 
3OOO 
3IOO 
3200 
3300 
3400 

3500 
3600 
3700 
3800 
3900 
4000 

c 

ters 
sea 
and 
in  t( 

.195 
.203 
•211 
.219 
.227 
•235 
•243 
.2SI 

3 
$ 

.291 
•299 
•307 
•3H 

orrectioi 
for  ele 
level  in 
height 
>p  line. 

.176 
.185 
.194 
•203 
.212 
.220 
.229 
.238 

•247 
.256 
.265 
.274 
.283 
.292 
.201 
•309 

j   in  mi 
vation 
first  C( 
of  baro 

.147 

-1!7 

.167 
.177 
.187 
.I96 
.206 
.216 
.226 
.236 
•245 
•255 
.265 

•275 
.285 
.294 

llime- 
above 
>lumn 
meter 

.108 
.118 
.129 
.140 

:X 

.172 
•183 
.194 
.204 
•215 
.226 

•237 
.248 

•259 

.270 

.118 
.130 
.142 

•'53 
.165 
.176 
.188 
.200 

.212 
.224 

•235 
.247 

•259 

[283 
•295 

.064 
.077 
.090 
.103 

•**l 

.128 

.141 

:!S 

.179 
.191 
.204 
.217 
.230 
.242 
•255 

.014 
.028 
.041 

•°55 
.068 
.082 
.096 
.109 
.123 
•137 

£ 

.178 
.191 

.205 

.015 
.030 
.044 
•059 
•073 
.088 
.102 
.117 

*I3I 
.146 

.016 
.032 
.047 
.063 

.078 

•255 
•213 
.172 
.130 

.088 
.046 
1.004 
.962 

.920 
.879 
.837 
•795 

•753 

edths 
ibove 
and 
rttom 

1.340 
1.292 
1.244 
I.I96 
I.I49 

i.ior 

!-°53 
1.005 

•957 
.909 
.861 
.813 
•765 

in   hundr 
levation  < 
5t  column 
icter  in  b< 

I-34S 
1.291 

1-237 
1.184 
1.130 
1.076 
i.  022 
.969 

fif 

.807 

•753 
.700 

rections 
nch  for  e 
vel  in  la 
of  baron 

i-3i5 

1.255 
1.196 
1.136 
1.076 
1.016 
•957 
•897 
•837 
•777 
.718 
.658 
.598 

Cor 
of  an 
sea  le 
heigh 
line. 

1.077 
1.005 

.790 
.718 
.646 
•574 
•503 
•43  i 
•359 
.287 
.215 

1.050 

p 
$ 

.721 
.6.5 

•789 
.724 
•658 
.592 
.526 
.461 

•395 

•779 
.701 
.623 

•545 
.467 

•389 
•311 

•233 

•T53 
.078 

•503 
.419 

•335 
•251 
.167 
.084 

.192 
.096 

•359 
.269 
.179 
.090 

32 

30 

28 

26 

24 

22 

20 

18 

16 

*4 

Height 
above  sea 
level  in 
feet. 

Observed  height  of  barometer  in  inches. 

SMITHSONIAN  TABLES. 

TABLE  104. 


121 


REDUCTION   OF   BAROMETER   TO   STANDARD   GRAVITY.* 

Reduction  to  Latitude  46°.  —  English  Scale. 

N.  B.     From  latitude  o°  to  44°  the  correction  is  to  be  subtracted. 
From  latitude  90°  to  46°  the  correction  is  to  be  added. 


Latitude. 

Height  of  the  barometer  in  inches. 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

Inch. 

0° 

90° 

0.051 

0-053 

0.056 

0.059 

O.O6  1 

0.064 

0.067 

0.069 

0.072 

0.074 

0.077 

O.oSo 

5 

85 

0.050 

0.052 

0.055 

0.058 

O.o6o 

0.063 

0.066 

0.068 

O.O7I 

0.073 

0.076 

0.079 

6 

84 

.049 

.052 

•055 

•057 

.060 

.062 

.065 

.068 

.070 

•073 

.076 

.078 

7 

83 

.049 

.052 

•054 

•057 

•059 

.062 

.065 

.067 

.070 

.072 

•075 

.077 

8 

82 

.049 

.051 

•054 

.056 

.059 

.061 

.064 

.067 

.069 

.072 

.074 

.077 

9 

81 

.048 

.051 

•053 

.056 

.058 

.061 

.063 

.066 

.068 

.071 

•073 

.076 

10 

80 

0.048 

0.050 

0.053 

0.055 

0.058 

O.o6o 

0.063 

0.065 

0.068 

0.070 

0.073 

0.075 

ii 

79 

.047 

.049 

.052 

•054 

•057 

.059 

.062 

.064 

.067 

.069 

.072 

.074 

12 

78 

.046 

.049 

.051 

•054 

.056 

.058 

.061 

.063 

.066 

.068 

.071 

•073 

J3 

77 

•045 

.048 

.050 

•053 

•°55 

•057 

.060 

.062 

.065 

.067 

.069 

.072 

14 

76 

•045 

.047 

.049 

.052 

•054 

.056 

•059 

.061 

.063 

.066 

.068 

.071 

15 

75 

0.044 

0.046 

0.048 

0.051 

0-053 

0-055 

0.058 

0.060 

0.062 

0.065 

0.067 

0.069 

16 

74 

•043 

•045 

.047 

.050 

.052 

•054 

.056 

•059 

.061 

.063 

.065 

.068 

17 

73 

.042 

.044 

.046 

.049 

.051 

•053 

•055 

•057 

.060 

.062 

.064 

.066 

18 

72 

.041 

•043 

•045 

.047 

.050 

.052 

•054 

.056 

.058 

.060 

.062 

.065 

19 

7i 

.040 

.042 

.044 

.046 

.048 

.050 

.052 

•055 

•057 

•°59 

.061 

.063 

20 

70 

0.039 

0.041 

0-043 

0.045 

0.047 

0.049 

0.051 

0.053 

0.055 

0.057 

0.059 

0.061 

21 

69 

.038 

.040 

.042 

.044 

•045 

.047 

.049 

.051 

•053 

•055 

•057 

•059 

22 

68 

.036 

.038 

.040 

.042 

.044 

.046 

.048 

.050 

.052 

•054 

.056 

•057 

23 

67 

•°35 

•037 

•039 

.041 

•043 

.044 

.046 

.048 

.050 

.052 

•054 

.055 

24 

66 

•034 

.036 

•037 

•039 

.041 

•043 

.045 

.046 

.048 

.050 

.052 

•053 

25 

65 

0.033 

0.034 

0.036 

0.038 

0.039 

0.041 

0.043 

0.044 

0.046 

0.048 

0.050 

0.051 

26 

64 

.031 

•033 

•034 

.036 

.038 

.039 

.041 

•043 

.044 

.046 

.048 

.049 

27 

63 

.030 

.031 

•033 

•034 

.036 

.038 

•039 

.041 

.042 

.044 

•045 

.047 

28 

62 

.028 

.030 

.031 

•033 

•034 

.036 

•037 

•039 

.040 

.042 

•043 

•045 

29 

61 

.027 

.028 

.030 

.031 

.032 

•034 

•035 

•037 

.038 

•039 

.041 

.042 

30 

60 

0.025 

0.027 

0.028 

0.029 

0.031 

0.032 

0-033 

0.035 

0.036 

0.037 

0.039 

0.040 

31 

59 

.024 

.025 

.026 

.027 

.029 

.030 

.031 

.032 

•034 

•035 

.036 

•037 

32 

58 

.022 

.023 

.025 

.026 

.027 

.028 

.029 

.030 

.032 

•033 

.034 

•035 

33 

57 

.021 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

.031 

.032 

34 

56 

.019 

.020 

.021 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

35 

55 

0.017 

O.OlS 

0.019 

0.020 

0.021 

0.022 

0.023 

0.024 

0.025 

0.025 

0.026 

0.027 

36 

54 

.016 

.Ol6 

.017 

.018 

.019 

.020 

.021 

.021 

.022 

.023 

.024 

.025 

37 

53 

.014 

.015 

.015 

.Ol6 

.017 

.018 

.018 

.OI9 

.020 

.021 

.021 

.022 

38 

52 

.012 

.013 

.014 

.014 

.015 

.OI5 

.Ol6 

.OI7 

.017 

.018 

.019 

.019 

39 

5i 

.on 

.on 

.OI2 

.012 

.013 

.013 

.014 

.014 

.015 

.015 

.016 

.017 

40 

50 

0.009 

0.009 

0.0  10 

O.OIO 

O.OII 

O.OII 

0.012 

0.012 

0.012 

0.013 

0.013 

0.014 

4i 

4Q 

.007 

.007 

.008 

.008 

.009 

.009 

.009 

.010 

.010 

.OIO 

.on 

.Oil 

42 

48 

.005 

.006 

.006 

.006 

.006 

.007 

.007 

.007 

.008 

.008 

.008 

.008 

43 

47 

.004 

.004 

.004 

.004 

.004 

.004 

.005 

.005 

•005 

.005 

.005 

.006 

44 

46 

.002 

.002 

.002 

.OO2 

.002 

.002 

.002 

.002 

.003 

.003 

.003 

.003 

*  "  Smithsonian  Meteorological  Tables,"  p.  58. 


SMITHSONIAN  TABLES. 


122  TABLE  105. 

REDUCTION   OF   BAROMETER   TO   STANDARD   GRAVITY, 

Reduction  to  Latitude  45°.  —Metric  Scale. 

N.  B.  —  From  latitude  o°  to  44°  the  correction  is  to  be  subtracted. 
From  latitude  90°  to  46°  the  correction  is  to  be  added. 


Latitude. 

Height  of  the  barometer  in  millimeters. 

520 

560 

600 

620 

640 

660 

680 

700 

720 

740 

760 

780 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm* 

mm. 

mm. 

mm. 

0° 

90° 

1.38 

1.49 

1.  60 

I.65 

1.70 

I.76 

1.81 

1.86 

1.92 

1.97 

2.02 

2.08 

5 

85 

1.36 

1.47 

r-57 

I.63 

1.68 

i-73 

1.78 

1.84 

1.89 

1.94 

1.99 

2.04 

6 

84 

I.46 

1.56 

1.61 

1.67 

1.72 

1.77 

1.82 

1.87 

J-93 

1.98 

2.03 

7 

83 

i-34 

i-45 

.60 

1.65 

1.70 

1.76 

1.81 

1.86 

1.91 

I.96 

2.OI 

8 

82 

r-33 

143 

i-54 

•59 

1.64 

1.69 

1.74 

1.79 

1.84 

1.89 

1-94 

2.00 

9 

81 

1.32 

1.42 

1.52 

•57 

1.62 

1.67 

1.72 

1.77 

1.82 

1.87 

1.92 

1.97 

10 

80 

1.30 

1.40 

1.50 

•55 

i.  60 

1.65 

1.70 

1-75 

1.80 

1.85 

1.90 

!-95 

ii 

79 

.28 

1.38 

1.48 

•53 

1.58 

1.63 

1.68 

i-73 

1.78 

1.83 

1.88 

I-93 

12 

78 

.26 

1.36 

1.46 

•51 

1.56 

1.  60 

1.65 

1.70 

1.86 

1.85 

1.90 

13 

77 

.24 

i-34 

1.44 

.48 

J-53 

I.58 

1.63 

1.67 

1.72 

1.77 

1.82 

1.87 

14 

76 

.22 

1.32 

1.41 

.46 

1.50 

i-55 

1.60 

1.65 

1.69 

1.74 

1.79 

1.83 

15 

75 

.20 

1.29 

1.38 

i-43 

1.48 

1.52 

T.-57 

1.61 

1.66 

1.71 

I<75 

1.80 

16 

74 

•17 

1.26 

1.40 

1.44 

1.49 

i-54 

1.58 

1.63 

1.67 

1.72 

1.76 

17 

73 

•15 

1.24 

1.32 

•37 

1.41 

i-45 

1.50 

i-54 

*-59 

1.63 

1.68 

1.72 

18 

72 

.12 

1.  21 

1.20 

•34 

1.38 

1.42 

1.46 

i-55 

i-59 

1.64 

1.68 

19 

7i 

.09 

I.I7 

1.26 

•30 

i-34 

1.38 

i-43 

1.47 

i-59 

1.64 

20 

70 

1.06 

I.I4 

1.22 

.26 

I.3I 

•35 

i-39 

1-43 

1.47 

l.5, 

!-55 

J-59 

21 

69 

1.03 

I.  II 

I.I9 

•23 

1.27 

1.38 

1.42 

1.46 

1.50 

i-54 

22 

68 

I.OO 

1.07 

I-I5 

.19 

1.23 

.'26 

1.30 

i-34 

1.38 

1.42 

1.46 

1.49 

23 
24 

67 
66 

0.96 
•93 

1.04 
I.OO 

I.  II 

1.07 

•15 

.10 

I.I4 

.22 
.18 

1.26 

1.  21 

1.29 
1.25 

1:3283 

1.32 

1.41 

1.44 

25 

65 

0.89 

0.96 

1.03 

.06 

I.IO 

!.!, 

1.16 

1.20 

1.23 

1.27 

1.30 

I33 

26 

64 

•85 

.92 

0.98 

.02 

1.05 

I.  Oo 

i.  ii 

I-I5 

1.18 

1.  21 

1.25 

1.28 

27 

^ 

.81 

.88 

•94 

0.97 

I.OO 

1.03 

i.  06 

I.IO 

1.13 

1.16 

1.19 

1.22 

28 

62 

•77 

•83 

.89 

.92 

o-95 

0.98 

I.OI 

1.04 

1.07 

I.IO 

1.16 

29 

61 

•73 

•79 

•85 

.87 

.90 

•93 

0.96 

0.99 

i.  02 

1.04 

1.07 

I.IO 

30 

60 

0.69 

0-75 

0.80 

0.83 

0.85 

0.88 

0.91 

0.94 

0.96 

0.98 

I.OI 

I.O4 

31 

59 

•65 

.70 

•75 

•77 

.80 

.82 

•85 

•87 

.90 

.92 

°-95 

0.97 

32 

58 

.61 

•65 

.70 

•72 

•75 

•77 

•79 

Q 

.84 

.86 

.89 

.91 

33 

57 

.56 

.61 

.65 

.67 

.69 

•74 

•76 

.78 

.80 

.82 

.84 

34 

56 

•52 

.56 

.60 

.62 

.64 

!66 

.68 

.70 

.72 

•74 

•76 

.78 

35 

55 

0.47 

0.51 

0-55 

0.56 

0.58 

0.60 

0.62 

0.64 

0.66 

0.67 

0.69 

0.71 

36 

54 

•43 

.46 

•49 

.51 

•53 

•54 

.56 

.58 

•59 

.61 

•63 

.64 

37 

53 

•38 

.41 

•44 

•45 

•47 

.48 

•50 

•51 

•53 

•54 

.56 

•57 

38 

52 

•33 

•36 

•39 

.40 

.41 

•43 

•45 

.46 

.48 

•49 

•5° 

39 

51 

.29 

•3i 

•33 

•34 

•35 

•37 

•38 

•39 

.40 

.41 

.42 

•43 

40 

50 

0.24 

0.26 

0.28 

0.29 

0.30 

0.31 

0.31 

0.32 

o-33 

0-34 

0-35 

0.36 

41 

4Q 

.19 

.21 

.22 

•23 

.24 

.24 

•25 

.26 

.27 

.27 

.28 

.29 

42 

48 

.14 

.16 

•17 

•17 

.18 

.18 

.19 

.19 

.20 

.21 

.21 

.22 

43 
44 

47 
46 

.10 

•05 

.IO 

.11 
.06 

.12 
.06 

.12 
.06 

.12 
.06 

•'3 

.07 

•13 

.07 

.14 
.07 

.14 

.07 

.14 
.07 

SMITHSONIAN  TABLES. 


'  "  Smithsonian  Meteorological  Tables,"  p.  59. 


TABLES  106-107. 
TABLE  106.  —  Correction  of  the  Barometer  for  Capillarity.* 


123 


i.  METRIC  MEASURE. 

HEIGHT  OF  MENISCUS  IN  MILLIMETERS. 

Diameter 
of  tube 

0.4 

0.6 

0.8 

1.0 

1.2 

1.4 

1.6 

1.8 

in  mm. 

Correction  to  be  added  in  millimeters. 

4 

0.83 

1.22 

i-54 

1.98 

2.37 

_ 

_ 

_ 

•47 

0.65 

0.86 

I.IQ 

i-45 

1.80 

- 

- 

6 

.27 

41 

•56 

0.78 

0.98 

1.  21 

1-43 

— 

7 

.18 

.28 

.40 

•53 

•67 

0.82 

0.97 

i-i3 

8 

— 

.20 

.29 

.38 

.46 

.56 

.65 

0.77 

9 

- 

•15 

.21 

.28 

•33 

•40 

.46 

•52 

10 

- 

- 

•15 

.20 

•25 

.29 

•33 

•37 

ii 

— 

— 

.IO 

.14 

.18 

.21 

.24 

.27 

12 

— 

— 

.07 

.10 

•13 

•IS 

.18 

.19 

13 

.04 

.07 

.10 

.12 

•'3 

.14 

2.  BRITISH  MEASURE. 

HEIGHT  OF  MENISCUS  IN  INCHES. 

Diameter 
of  tube 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

in  inches. 

Correction  to  be  added  in  hundredths  of  an  inch. 

•15 

2.36 

4.70 

6.86 

9-23 

11.56 

_ 

_ 

_ 

.20 

1.  10 

2.20 

3.28 

4-54 

5-94 

7.85 

— 

— 

•25 

o-55 

1.20 

1.92 

2.76 

3-68 

4.72 

5.88 

— 

•30 

•35 
.40 

•36 

0-79 

•51 

40 

1.26 
0.82 
.61 

1.77 
0.8  1 

2.30 
1.49 

1.02 

2.88 
1.85 

1.22 

348 
2.24 
1.42 

4.20 
2.65 
1.62 

•45 

- 

•32 

•5i 

0.68 

0.83 

0.96 

I-I5 

•50 

- 

- 

.20 

•35 

•47 

.56 

.64 

0.71 

•55 

.08 

.20 

•3i 

.40 

•47 

•52 

*  The  first  table  is  from  Kohlrausch  (Experimental  Physics),  and  is  based  on  the  experiments  of  Mendelejeff  and 
Gutkowski  (Jour,  de  Phys.  Chem.  Geo.  Petersburg,  1877,  or  Wied.  Beib.  1877).  The  second  table  has  been  calcu- 
lated from  the  same  data  by  conversion  into  inches  and  graphic  interpolation. 


TABLE  107.  —  Volume  of  Mercury  Meniscus  in  On.  Mm. 


Diameter  of  tube  in  mm. 

Height  of 

meniscus. 

M 

15 

16 

17 

18 

*9 

20 

21 

22 

23 

24 

mm. 

1.6 
•1.8 

1S7 
181 

185 

211 

214 
244 

245 
281 

280 
320 

318 

362 

356 
407 

398 

455 

444 
507 

492 
560 

& 

2.0 
2.2 

206 
233 

240 
271 

278 
313 

319 

358 

362 
406 

409 

459 

46O 

5'5 

5i3 

574 

57i 
637 

631 

704 

694 
776 

2.4 
2.6 

262 
291 

303 
338 

35° 
388 

400 
444 

454 
503 

% 

573 
633 

b39 
706 

708 
782 

781 
862 

859 
948 

Scheel  und  Heuse,  Annalen  der  Physik,  33,  p.  291,  1910. 


SMITHSONIAN  TABLES. 


124 


TABLE  108. 


AERODYNAMICS. 


The  pressure  on  a  plane  surface  normal  to  the  wind  is  for  ordinary  wind  velocities  expressed  by 


where  k  is  a  constant  depending  on  the  units  employed,  w  the  mass  of  unit  volume  of  the  air, 
a  the  area  of  the  surface  and  v  the  velocity  of  the  wind.*  Engineers  generally  use  the  table  of 
values  of  P  given  by  Smeaton  in  1759.  This  table  was  calculated  from  the  formula 

P=.  00492  z/2 

and  gives  the  pressure  in  pounds  per  square  foot  when  v  is  expressed  in  miles  per  hour.  The 
corresponding  formula  when  v  is  expressed  in  feet  per  second  is 

P=.  00228  z/2. 

Later  determinations  do  not  agree  well  together,  but  give  on  the  average  somewhat  lower 
values  for  the  coefficient.  The  value  of  w  depends,  of  course,  on  the  temperature  and  the  baro- 
metric pressure.  Langley's  experiments  give  kw  =  .  00166  at  ordinary  barometric  pressure  and 
10°  C.  temperature. 

For  planes  inclined  at  an  angle  a  less  than  90°  to  the  direction  of  the  wind  the  pressure  may 
be  expressed  as  Pa  =  FaPw 

Table  108,  founded  on  the  experiments  of  Langley,  gives  the  value  of  F*  for  different  values  of 
a.  The  word  aspect,  in  the  headings,  is  used  by  him  to  define  the  position  of  the  plane  relative  to 
the  direction  of  motion.  The  numerical  value  of  the  aspect  is  the  ratio  of  the  linear  dimension 
transverse  to  the  direction  of  motion  to  the  linear  dimension,  a  vertical  plane  through  which  is 
parallel  to  the  direction  of  motion. 


TABLE  108.  -Values  of  Fa  In  Equation  Pa= 


=VM. 


Plane  30  in.  X  4.8  in. 
Aspect  6  (nearly). 

Plane  12  in.  X  12  in. 
Aspect  i. 

Plane  6  in.  X  24  in. 
Aspect  J. 

a 

fa 

a 

K 

a 

fa 

0° 

0.00 

0° 

0.00 

0° 

0.00 

g 

0.28 

5 

0.15 

5 

0.07 

10 

0.44 

10 

0.30 

10 

0.17 

15 

0.55 

J5 

0.44 

15 

0.29 

20 

0.62 

20 

0.57 

20 

0.43 

25 

30 

0.66 
0.69 

25 

30 

0.69 
0.78 

25 

30 

0.58 
0.71 

35 

0.72 

35 

0.84 

40 

0.74 

40 

0.88 

_ 

— 

45 

0.76 

45 

0.91 

- 

- 

50 

0,78 

50 

- 

- 

- 

*  The  following  pressures  in  pounds  per  square  inch  show  roughly  the  influence  of  the  shape  and  size  of  the  resist- 
ing surface  (Dines'  results).     The  wind  velocity  was  20.9  miles  per  hour.     The  flat  plates  were  f  in.  thick. 
Square,  sides  4  in 1.51 


Circle,  same  area 1.51 

Rectangle,  16  in.  by  i 170 

Square,  12  in.  sides 1.57 

Circle,  same  area .  i  55 

Rectangle,  24  in.  by  6 .'  i.5g 

Square,  sides  16  in .  ,.e2 

Plate,  6  in.  diam.  4j  thick i  45 

Ditto,  curved  side  to  wind o  02 

Sphere,  6  in.  diam 0.67 

SMITHSONIAN  TABLES. 


Plate,  6  in.  diam.  90°  cone  at  back 1.49 

Same,  cone  in  front 0.98 

1      sharp  30°  cone  at  back 1.54 

"      cone  in  front 0.60 

5  in.  Robinson  cup  on  8£  in.  of  £  in.  rod    ....  1.68 

Same,  with  back  to  wind 0.73 

9  in.  cup  on  6£  in.  of  f  in.  rod L75 

Same,  with  back  to  wind 0.60 

2i  in.  cup  on  9!  in.  of  \  in.  rod 2.60 

Same,  with  back  to  wind 1.04 


TABLE  109. 


AERODYNAMICS. 

On  the  basis  of  the  results  given  in  Table  108  Langley  states  the  following  condition  for  the 
soaring  of  an  aeroplane  76.2  centimeters  long  and  12.2  centimeters  broad,  weighing  500  grams, 
—  that  is,  a  plane  one  square  foot  in  area,  weighing  i.i  pounds.  It  is  supposed  to  soar  in  a 
horizontal  direction,  with  aspect  6. 

TABLE  109.  -  Data  for  the  Soaring  of  Planes  76.2  X  12.2  cms.  weighing  500  Grams,  Aspect  6. 


Weight  of  planes  of  like 

Inclination 

Soaring  speed  v. 

Work  expended  per  minute 
(activity). 

form,  capable  of  soaring 
at  speed  v  with  the  ex- 
penditure of  one  horse 

to  the  hori- 

power. 

zontal  a. 

Meters  per 
sec. 

Feet  per 
sec. 

Kilogram 
meters. 

Foot 
pounds. 

Kilograms. 

Pounds. 

2° 

20.0 

66 

24 

174 

95-o 

209 

5 

10 

I5.2 
12.4 

5° 
41 

f 

Q  t 

297 
474 

55-5 
34-8 

122 

15 

30 

II.  2 

10.6 

37 
35 

175 

1268 

26.5 
13.0 

29 

45 

II.  2 

37 

336 

2434 

6.8 

In  general,  if  p  = 


Soaring  speed  v=  i/  £.- 
V   k. 


Activity  per  unit  of  weight  =  v  tan  a 

The  following  data  for  curved  surfaces  are  due  to  Wellner  (Zeits.  fiir  Luftschifffahrt,  x.,  Oct. 

1893)- 

Let  the  surface  be  so  curved  that  its  intersection  with  a  vertical  plane  parallel  to  the  line  of 
motion  is  a  parabola  whose  height  is  about  ^  the  subtending  chord,  and  let  the  surface  be 
bounded  by  an  elliptic  outline  symmetrical  with  the  line  of  motion.  Also,  let  the  angle  of  incli- 
nation of  the  chord  of  the  surface  be  a,  and  the  angle  between  the  direction  of  resultant  air 
pressure  and  the  normal  to  the  direction  of  motion  be  0.  Then  /3  <  o,  and  the  soaring  speed  is 

p-— — - — ,  while  the  activity  per  unit  of  weight  =^tan  j3. 

ra  COS  p 

The  following  series  of  values  were  obtained  from  experiments  on  moving  trains  and  in  the 
wind. 

Angle  of  inclination  a  =  —3°  o°        +3°  6°  9°  12° 

Inclination  factor  Fa=    0.20          0.50          0.75          0.90          i.oo          1.05 

tan/3  =    o.oi          0.02          0.03          0.04          o.io          0.17 

Thus  a  curved  surface  shows  finite  soaring  speeds  when  the  angle  of  inclination  a  is  zero  or  even 
slightly  negative.    Above  a=  12°  curved  surfaces  rapidly  lose  any  advantage  they  may  have  for 
small  inclinations. 
SMITHSONIAN  TABLES. 


I 


I26  TABLES  11O-112. 

TABLE  110.  —  Friction. 

The  following  table  of  coefficients  of  friction /and  its  reciprocal  i/f,  together  with  the  angle  of  friction  or  angle  of 
repose  tf>,  is  quoted  from  Rankine's  "Applied  Mechanics.'1  It  was  compiled  by  Rankine  from  the  results  of 
General  Morin  and  other  authorities,  and  is  sufficient  for  all  ordinary  purposes. 


Material. 

/ 

I// 

0 

.21;-.  "50 

4.00-2.00 
5.00 
2.00-1.67 

4-  1  7-3-85 
5-oo 
5.00-4.00 
1.89 
3.00 
3.70-2.86 
1.79 
2.78 

ti} 
6.67-5.00 

3-33 
14.3-12.50 

20.00 
33-3-27-6 

5-oo 
9-35 
3-33~I43 
2.50 
1.67-1.43 

3 

3.00 
4.00-1.00 
2.63-1.33 

1.  00 

3-23 
1.23-0.9 

14.0-26.5 

"•5 
26.5-31.0 

I3-5-M-5 
n-5 
11.5-14.0 

28.0 
18.5 
15.0-19.5 
29-5 

20.0 
13.0 

8-5 
8.5-11-5 
16.5 

4-0-4-5 
3-o 
1.75-2.0 

y-s 

6.1 

16.7-35-° 

22.O 

33-o-35-o 
36-5 
27.0 
18.25 
14.0-45.0 
21.0-37.0 
45-o 
17.0 
39.0-48.0 

.20 

.so-.  60 

.24—  .26 

.20 
.2O-.21J 

•53 

•27--3S 

•56 
•36 
•23 
•15 

.1  C-.2O 

"        "        "       wet                   .... 

«         «         "        oily          

"       "        "       wet                    .... 

.07-.08 

•°5 
.03-.036 

.20 

.107 
•30-70 
About  .40 
.6o--7O 
•74 
•5i 
•33 
.25-1.00 

•38-75 

1.  00 

.81-1.11 

Smooth  surfaces,  occasionally  greased  . 
"            "        continually  greased   . 
u            "        best  results         .... 
Steel  on  agate,  dry  *      
"      «      "       oiled*  

Iron  on  stone         
Wood  on  stone      
Masonry  and  brick  work,  dry        .... 
"         '•      "        "       damp  mortar 
"       on  dry  clay      ...... 

Earth  on  earth       
"       "       "     dry  sand,  clay,  and  mixed  earth   . 
"       "       "      damp  clay     
"       "       "      wet  clay        .         .         .         .    '     . 
"       "       "      shingle  and  gravel 

*  Quoted  from  a  paper  by  Jenkin  and  Ewing,  "  Phil.  Trans.  R.  S."  vol.  167.  In  this  paper  it  is  shown  that  in 
cases  where  "  static  friction  "  exceeds  "  kinetic  friction  "  there  is  a  gradual  increase  of  the  coefficient  of  friction  as  the 
speed  is  reduced  towards  zerot 

TABLE  111.  -  Lubricants. 

The  best  lubricants  are  in  general  the  following:  Low  temperatures,  light  mineral  lubricating 
oils.  Very  great  pressures,  slow  speeds,  graphite,  soapstone  and  other  solid  lubricants.  Heavy 
pressures,  slow  speeds,  ditto  and  lard,  tallow  and  other  greases.  Heavy  pressures  and  high  speeds, 
sperm  oil,  castor  oil,  heavy  mineral  oils.  Light  pressures,  high  speeds,  sperm,  refined  petroleum 
olive,  rape,  cottonseed.  Ordinary  machinery,  lard  oil,  tallow  oil,  heavy  mineral  oils  and  the 
heavier  vegetable  oils.  Steam  cylinders,  heavy  mineral  oils,  lard,  tallow.  Watches  and  delicate 
mechanisms,  clarified  sperm,  neat's-foot,  porpoise,  olive  and  light  mineral  lubricating  oils. 

TABLE  112.  —Lubricants  For  Cutting  Tools. 


Material. 

Turning. 

Chucking. 

Drilling. 

Tapping 
Milling. 

Reaming. 

Tool  Steel, 

dry  or  oil 

oil  or  s.  w. 

oil 

oil 

lard  oil 

Soft  Steel, 

dry  or  soda  water 

soda  water 

oil  or  s.  w. 

oil 

lard  oil 

Wrought  iron 

dry  or  soda  water 

soda  water 

oil  or  s.  w. 

oil 

lard  oil 

Cast  iron,  brass 
Copper 

dry 
dry 

dry 
dry 

dry 
dry 

dry 
dry 

dry 
mixture 

Glass 

turpentine  or  kerosene 

Mixture  =  %  crude  petroleum,  %  lard  oil.     Oil  =  sperm  or  lard. 

Tables  in  and  112  quoted  from  "Friction  and  Lost  Work  in  Machinery  and  Mill  Work,"  Thurston,  Wiley  and  Sons. 
SMITHSONIAN  TABLES. 


TABLE  113. 
VISCOSITY. 


127 


The  coefficient  of  viscosity  is  the  tangential  force  per  unit  area  of  one  face  of  a  plate  of  the 
fluid  which  is  required  to  keep  up  unit  distortion  between  the  faces.  Viscosity  is  thus  measured 
in  terms  of  the  temporary  rigidity  which  it  gives  to  the  fluid.  Solids  may  be  included  in  this 
definition  when  only  that  part  of  the  rigidity  which  is  due  to  varying  distortion  is  considered. 
One  of  the  most  satisfactory  methods  of  measuring  the  viscosity  of  fluids  is  by  the  observation  of 
the  rate  of  flow  of  the  fluid  through  a  capillary  tube,  the  length  of  which  is  great  in  comparison 
with  its  diameter.  Poiseuille*  gave  the  following  formula  for  calculating  the  viscosity  coefficient 

in  this  case  :  /A  =    „      ,  where  h  is  the  pressure  height,  r  the  radius  of  the  tube,  s  the  density  of 

the  fluid,  v  the  quantity  flowing  per  unit  time,  and  /  the  length  of  the  capillary  part  of  the  tube. 
The  liquid  is  supposed  to  flow  from  an  upper  to  a  lower  reservoir  joined  by  the  tube,  hence  h 
and  /  are  different.  The  product  hs  is  the  pressure  under  which  the  flow  takes  place.  Hagen- 
bach  t  pointed  out  that  this  formula  is  in  error  if  the  velocity  of  flow  is  sensible,  and  suggested  a 
correction  which  was  used  in  the  calculation  of  his  results.  The  amount  to  be  subtracted  from 

V* 

the  acceleration  due  to  gravity.    Gartenmeister  J 


h,  according  to  Hagenbach,  is  -\ 


points  out  an  error  in  this  to  which  his  attention  had  been  called  by  Finkener,  and  states  that  the 
quantity  to  be  subtracted  from  h  should  be  simply  —  ;  and  this  formula  is  used  in  the  reduction 

of  his  observations.  Gartenmeister's  formula  is  the  most  accurate,  but  all  of  them  nearly  agree 
if  the  tube  be  long  enough  to  make  the  rate  of  flow  very  small.  None  of  the  formulas  take  into 
account  irregularities  in  the  distortion  of  the  fluid  near  the  ends  of  the  tube,  but  this  is  probably 
negligible  in  all  cases  here  quoted  from,  although  it  probably  renders  the  results  obtained  by  the 
"  viscosimeter  "  commonly  used  for  testing  oils  useless  for  our  purpose. 

The  term  "  specific  viscosity  "  is  sometimes  used  in  the  headings  of  the  tables  ;  it  means  the 
ratio  of  the  viscosity  of  the  fluid  under  consideration  to  the  viscosity  of  water  at  a  specified  tem- 
perature. 

The  friction  of  a  fluid  is  proportional  to  the  size  of  the  rubbing  surface,  to  -^,  where  v  is  the 

velocity  of  motion  in  a  direction  perpendicular  to  the  rubbing  surface,  and  to  a  constant  known 
as  the  viscosity. 


(a)  Variation  of  Viscosity  of  Water,  with  Temperature.    Dynes  per  sq.  cm. 


cL 

Poise  ville. 

Sprung. 

Slotte. 

Thorpe-  Rogers. 

Hosking. 

A 

Slotte. 

Thorpe-Rogers 

Hosking. 

•H 

1846. 

1876. 

1883. 

i894.§ 

igog.ll 

HJ 

1883. 

1894- 

1909.11 

0° 

O.OI7I6 

0.01778 

O.OlSoS 

0.01778 

0.01793 

55° 

0.00510 

0.00506 

.00508 

5 

.01515 

.01510 

.01524 

.01510 

.01522 

60 

.00472 

.00468 

.00469 

10 

.01309 

.01301 

.01314 

.01303 

.01310 

6S 

.00438 

.00436 

.06436 

1  5  . 

.01146 

•OII35 

.01144 

.01134 

.OII42 

70 

.00408 

.00406 

.00406 

20 

3° 

.01008 
.00897 
.00803 

.01003 
.00896 
.00802 

.01008 
.00806 
.00803 

.OIOO2 
.00891 
.00798 

.OIOO6 
.00893 
.00800 

U 

.00382 
.00358 
•00337 

.00380 
.00356 
•00335 

.00380 
.00356 
•00335 

35 

.00721 

•00723 

.00724 

.00720 

.00724 

90 

.00318 

.00316 

.00316 

40 

.00653 

.00657 

.00657 

.00654 

.00657 

9S 

.00301 

.00299 

.00300 

45 

•00595 

.00602 

.00602 

.00597 

.OO6OO 

100 

.00285 

.00283 

.00284! 

5° 

•00553 

•00553 

.00548 

.00550 

153 

~ 

~ 

.OOlSl! 

(b)  Variation  of  Specific  Viscosity  of  Water  with  Temperature,  y 

o°         i.  ooo         25°         0.498         50° 

0.307 

75° 

O.2I2 

100° 

0.158 

5°           -849         30             446         55 

.283 

80 

.199 

124° 

.124! 

10°           .730         35            .404        60 

.262 

85 

.I87 

153° 

15°           .637         40            .367         65 

•243 

.176 

_ 

20°           .561         45            -335         70 

.226 

95 

.167 

~ 

*  "Comptes  rendus,"  vol.  15,  1842;  "Mem.  Serv.  Etr."  1846. 

t  "  Pogs;.  Ann."  vol.  109,  1860. 

f'Zeitschr.  Phys.  Chem."  vol.  6,  1890. 

§  Thorpe  and  Rogers,  "  Philos.  Trans."  i8$A,  p.  397,  1894;  "Proc.  Roy.  Soc."  55,  p.  148,  1894. 

|j  Hosking,  Phil.  Mag.  17,  p.  502,  1909;  18,  p.  260,  1909. 

Tide  Haas,  Diss.  Leiden,  1894. 


SMITHSONIAN  TABLES. 


128 


TABLES  114-116. 


VISCOSITY. 

TABLE  114.  —  Solution  ol  Alcohol  In  Water.* 


Coefficients  of  viscosity,  in  C.  G.  S.  units,  for  solution  of  alcohol  in  water. 


Temp. 

Percentage  by  weight  of  alcohol  in  the  mixture. 

o 

8.21 

16.60 

34.58 

43-99 

53.36 

75-75 

87.45 

99.72 

0° 

O.OlSl 

0.0287 

0.0453 

0.0732 

0.0707 

0.0632 

0.0407 

O.O294 

0.0180 

5 

.0152 

.0234 

•035  I 

•0558 

•0552 

.0502 

•0344 

.0256 

.0163 

10 

.0131 

.0195 

.0281 

•0435 

•0438 

.0405 

.0292 

.0223 

.0148 

15 

20 

.0114 
.0101 

.0165 
.0142 

.0230 
.0193 

•0347 
.0283 

•°353 
.O286 

•0332 
.0276 

.0250 
.0215 

.0195 
.OI72 

.0134 

.0122 

25 

O.OOQO 

0.0123 

0.0163 

0.0234 

O.O24I 

0.0232 

0.0187 

0.0152 

O.OIIO 

3° 

.0081 

.0108 

.0141 

.0196 

.O2O4 

.0198 

.0163 

•OI35 

.0100 

35 

.0073 

.0096 

.OI22 

.0167 

.0174 

.0171 

.0144 

.0120 

.0092 

40 

.0067 

.0086 

.0108 

.0143 

.0150 

.0149 

.0127 

.0107 

.0084 

45 

.006l 

.0077 

.0095 

.0125 

.0131 

.OI3O 

.0113 

.0097 

.0077 

50 

0.0056 

0.0070 

0.0085 

0.0109 

O.OII5 

o.oi  1  5 

0.0102 

0.0088 

O.OO7O 

£ 

.0052 
.0048 

.0063 
.0058 

.0076 
.0069 

.0096 
.0086 

.0102 
.OO9I 

.0102 
.0092 

.0091 

.0083 

.0086 
.0073 

.0065 
.OO6O 

The  following  tables  (115-116)  contain  the  results  of  a  number  of  experiments  in  the  viscosity  of  mineral  oils  derived 
from  petroleum  residues  and  used  for  lubricating  purposes.t 


TABLE  115.  -Mineral  Oils.t 


g 

"51  ^ 

M 

.5  «- 
'c  .g 

Sp.  viscosity.    Water  at 
-      20°  C.  =  i. 

Q 

*& 

pQ& 

20°  C. 

50°  C. 

100°  C. 

•931 

243 

274 

_ 

11.30 

2.9 

.921 
.906 

216 
189 

246 
208 

- 

7-31 
3-45 

2-5 

.921 

163 

IQXD 

_ 

27.80 

2.8 

.917 

132 

168 

- 

- 

2.6 

.904 
.891 
.878 

170 

151 
1  08 

207 
182 
148 

8.65 

4-77  - 
2.94 

2.65 
1.86 
1.48 

1-7 

1-3 

•855 

42 

45 

1.65 

- 

.905 

165 

202 

_ 

3.10 

j  5 

.894 
.866 

139 
90 

270 
224 

7.60 
2.50 

3-6o 
1.50 

t? 

TABLE  116.  -Oils. 


Oil. 

1 

M 
'£  'c 

P 

M 

C  ~ 

'S.S 

Viscosity  at 
19°  C.,  water 
ati9°C.=  i.  ] 

Cylinder  oil  .     . 
Machine  oil  .     . 

.917" 
.914 

227 
213 

260 

IO2 

Wagon  oil     .    . 

.914 

148 

182 

80 

Naphtha  residue 

.911 
.910 

157 
134 

«g 

162 

70 

55 

Oleo-naphtha     . 

.910 

219 

2«>7 

121 

.904 

2OI 

242 

66 

"                    « 

.894 

184 

222 

26 

Oleonid     .    .    . 

.884 

jgr 

217 

28 

best 

quality 

.881 

1  88 

224 

20 

Olive  oil    ... 

.916 

_ 

_ 

22 

Whale  oil      .    . 

.879 

_ 

_ 

g 

•     • 

.875 

8 

*  This  table  was  calculated  from  the  table  of  fluidities  given  by  Noack  (Wied.  Ann.  vol.  27,  p.  217),  and  shows  a 
maximi       tor  a  solution  containing  about  40  per  cent  of  alcohol.     A  similar  result  was  obtained  for  solutions  of  acetic 

t  Table  115  is  from  a  paper  by  Engler  in  Dingler's  "  Poly.  Jour."  vol.  268,  p.  76,  and  Table  116  is  from  a  paper  by 
Lamansky  in  the  same  journal,  vol.  248,  p.  29.     The  very  mixed  composition  of  these  oils  renders  the  viscosity  a  very 
•,  neither  the  density  nor  the  flashing  point  being  a  good  guide  to  viscosity. 
:  erouns  in  this  taV>l»  o»-<»  fmm  ,};«„-«.,    :j 


quantity,  ^  „„„  ^...^.ij,  ,,„,  tllc  Urt5,i,Ug  pomi  uemj 

I  Ihe  different  groups  in  this  table  are  from  different  residues. 


SMITHSONIAN  TABLES. 


TABLE  117. 
VISCOSITY. 


129 


This  table  gives  some  miscellaneous  data  as  to  the  viscosity  of  liquids,  mostly  referring  to  oils  and  paraffins.    The 

viscosities  are  in  C.  G.  S.  units. 


F                                Liquid. 

G.% 

Coefficient 
of 

viscosity. 

Temp. 
Cent.0 

Authority. 

0.0160 

II.Q 

Poiseuille. 

0.0149 

14.  c 

«< 

O.OIII 

2O.O 

Gartenmeister. 

Colophonium          .        . 
Di-ethyl  ether         .... 

3  X  10" 
0.00276 
42.20 

15- 

6.°7 

2.8 

Reiger. 
Thorpe,  Roger. 
Schottner. 

«                                                   X 

2C  18 

8  i 

(( 

1-5  87 

14  7 

« 

« 

(( 

8.30 

A   QA 

X^-J 
20.3 
26.? 

« 
(i 

Glycerine  and  water 
«                    « 

«                    « 
«                    <« 

Glycol      

9446 
80.31 
64.05 
49-79 

7-437 

1.  02  1 
O.222 
0.092 

O  O2  IQ 

8.5 
8.5 
8.5 
8.5 

O  O 

« 
ii 

<« 

M 

Arrhenius 

Menthol,  solid        .... 
"         liquid       .... 

Mercury*        .         .        .        .         . 

M 

209  X  lOW 

0.069 

0.0184 
O.OI7O 
O  OI  ?7 

14.9 

34-9 

—  20 
0.0 
2O  O 

Heydweiller. 

Koch. 
« 

« 

« 
« 

0.0122 
O.OIO'* 

1  00.0 
2OO  O 

M 

«« 

<« 

O  OOQ"? 

-jon  O 

<« 

0.1878 

2O  O 

Garten  meister^ 

Olive  oil          

Paraffins:  Decane 
Dodecane 
Heptane 
Hexadecane  . 
Hexane 
Nonane 

Octane           .        . 
Pentane 
Pentadecane  . 
Tetradecane  . 
Tridecane 
Undecane 

Petroleum  (Caucasian) 
Phenol    

0.9890 

0.0077 
O.OI26 
0.0045 

0.0359 
0.0033 
0.0062 

0.0053 
O.OO26 
O.O28l 
0.0213 
0.0155 
0.0095 

O.OIOXD 
O.I27 

I5.0 

22.3 

23-3 
24.0 
22.2 

23-7 
22-3 

22.2 
2I.O 
22.O 
21.9 

23-3 
22.7 

17-5 

18.1 

Brodmann. 

Bartolli  &  Stracciati. 
««                 « 
<«                 « 
«i 

1C 

« 
«« 

{<                      < 
«                     <« 
«                         «« 
«                         (I 

Petroff. 
Scarpa. 

Rape  oil         

25.7 

o.o 

O.  E.  Meyer. 

«      « 

^.8c 

IO.O 

« 

«      « 

O-"J> 

1.63 

2O.O 

<« 

"   "     

0.96 

3O.O 

«< 

•""Calculated  from  the  formula 
p.  1881). 

SMITHSONIAN  TABLES. 


=  .oi7  —  .oooo66/4~-°00o°o2i/2  —  .oooooooooas/3  (vide  Koch,  Wied.  Ann.  vol.  14, 


1 3o 


TABLE   11 8. 
VISCOSITY. 


This  table  gives  the  viscosity  of  a  number  of  liquids  together  with  their  temperature  variation. 
The  headings  are  temperatures  in  Centigrade  degrees,  and  the  numbers  under  them  the  coeffi- 
cients of  viscosity  in  C.  G.  S.  units.* 


T  J«     U 

Temperature  Centigrade. 

V 

Liquid. 

0° 

10° 

20° 

30° 

40° 

5°° 

70° 

90° 

"oS 

Acetates  :  Methyl 

_ 

.0046 

.0041 

.0036 

.0032 

.0030 

_ 

_ 

I 

Ethyl 

— 

.0051 

.0044 

.0040 

•0035 

.0032 

— 

— 

I 

Propyl 

— 

.0066 

.0059 

.0052 

.0044 

.0039 

— 

— 

I 

Allyl 

- 

.0068 

.0061 

•0054 

.0049 

.0044 

— 

— 

I 

Amyl 

- 

.OIO6 

.0089 

.0077 

.0065 

.0058 

- 

- 

I 

Acids:  Formic 

— 

.02262 

.Ol8O4 

.01465 

.OI224 

.01025 

_ 

— 

2 

Acetic 

_ 

.0150 

.OI26 

.OIO9 

.0094 

.0082 

_ 

— 

I 

Propionic 

- 

.0125 

.0107 

.0092 

.008I 

.0073 

- 

- 

3 

" 

— 

.0139 

.OIl8 

.0101 

.0091 

.0080 

— 

— 

i 

Butyric 

- 

.0196 

.0163 

.0136 

.OIl8 

.0102 

- 

- 

2 

Valeric 

— 

.0271 

.0220 

.0183 

•OI55 

.OI27 

— 

— 

3 

Salicylic 

_ 

.0320 

.0271 

.0222 

.0181 

.0150 

_ 

_ 

3 

Alcohol  :  Methyl 

.00813 

.00686 

.00591 

.00515 

.00450 

.00396 

- 

- 

4 

Ethyl 

.01770 

.01449 

.01192 

.00990 

.00828 

.00698 

.00504 

— 

4 

Propyl 

.03882 

.02917 

.02255 

.01778 

.01403 

.OII28 

•00757 

.00526 

4 

Butyric 

•05185 

.03872 

.02947 

.O2266 

.01780 

.01409 

.00926 

.00633 

4 

Allyl 

.02144 

.01703 

.01361 

.01165 

.00911 

.00760 

.00548 

.00407 

4 

Isopropyl 
Isobutyl 

.04564 
.08038 

•03245 
•05547 

.02369 
.03906 

•01755 
.02863 

.01329 

.O2I2I 

.OIO26 
.01609 

.00642 
•00973 

.00633 

4 
4 

Amyl  (op.-inac.) 

.08532 

.06000 

.04341 

.03206 

.02414 

.01849 

.01147 

•00758 

4 

Aldehyde 

.00267 

.00244 

.OO222 

— 

— 

- 

3 

Aniline 

— 

— 

.0440 

.0319 

.0241 

.0189 

— 

_ 

5 

Benzole 

.00902 

.00759 

.00649 

.00562 

.00492 

.00437 

•00351 

- 

4 

Bromides  :  Ethyl 

.00478 

.00432 

.00392 

•00357 

— 

— 

4 

Propyl 

.00645 

•00575 

.00517 

.00467 

.00425 

.00388 

.00328 

- 

4 

Allyl 
Ethylene 

.00619 
•02435 

•00552 
•02035 

.00496 
.01716 

.00449 
.01470 

.00410 
.01280 

.00374 
.OII24 

.00316 
.00895 

•00733 

4 
4 

Carbon  bisulphide 

.00429 

.00396 

•00367 

.00342 

.00319 

— 

4 

Carbon  dioxide  (liq.) 

.00099 

.00085 

.0007  I 

_ 

_ 

_ 

6 

Chlorides  :  Propyl 

.00436 

.00390 

•00352 

•00319 

,OO29I 

- 

- 

_ 

4 

Allyl 

.00402 

•00358 

.OO322 

.OO292 

— 

— 

_ 

_ 

4 

Ethylene 
Chloroform 

.OII28 
.00700 

.00961 
.00626 

•00833 
.00564 

.00730 
.0051  1 

.00646 
.00466 

.00576 
.00390 

.00470 

— 

4 
4 

Ether 

— 

.0026 

.OO23 

.OO2I 

— 

_ 

_ 

i 

Ethylbenzole 
Ethylsulphide 
Iodides:  Methyl 

.00874 

•00559 
.00594 

.00758 
.00496 
.00536 

.00444 
.00487 

.00592 
.00401 
.00446 

.00529 
.00363 
.00409 

•00477 
.00331 

.00394 
.00279 

.00330 
.00237 
—  i 

4 
4 

Ethyl 

.00719 

.00645 

•00583 

.00530 

.00484 

.00444 

.00378 

_ 

Propyl 

Allyl 

.00938 
.00930 

.00827 
.00819 

.00737 
.00726 

.00662 
.00652 

.00598 
.00588 

•00544 
•00534 

.00456 
.00448 

.00387 
.00381 

4 

4 

Metaxylol 

.00802 

.00698 

.00615 

•00547 

.00491 

.00444 

.00369 

•00313 

4 

Nitrobenzene 

— 

— 

.0203 

.OI7O 

.0144 

.OI24 

i 

Paraffines  :   Pentane 

.00283 

.00256 

.00232 

.00212 

_ 

_ 

_ 

4 

Hexane 

.00396 

•00355 

.OO32O 

.00290 

.00264 

.00241 

.00221 

- 

4 

Heptane 

.00519 

.00460 

.OO4IO 

.00369 

•00334 

.00303 

.00253 

.00214 

4 

Octane 

•00703 

.0061  2 

.00538 

.00478 

.00428 

.00386 

.00318 

.OO266 

4 

Isopentane 

.00273 

.00246 

.00223 

.00204 

- 

— 

— 

— 

4 

Isohexane 

.00371 

•00332 

.OO3OO 

.OO272 

.00247 

.00226 

- 

_ 

4 

Isoheptane 

.00477 

.00423 

.00379 

.00342 

.00309 

.00282 

.00235 

.00200 

4 

Propyl  aldehyde 

— 

.0047 

.0041 

.0036 

•0033 

— 

- 

i 

Toluene 

.00768 

.00668 

.00586 

.00520 

.00466 

.OO42O 

.00348 

.OO292 

4 

i  Pribram-Handl,  Wien.  Ber.  78,  1878,  80,  1879,  84,                1897;    Proc.  Roy.  800.55,  1894,  60,  1896;   Jour. 

1881.                                                                                         Chem.  Soc.  71,  1897;  Chem.  News,  75,  1897. 
2  Gartenmeister,  Zeitschr.  Phys.  Chem.  6,  1890.                5  Wijkander,  Wied.  Beibl.  3,  1879. 

3  Rellstab,  Diss.  Bonn,  1868.                                                6  Warburg-Babo,  Wied.  Ann.  17,  1882. 

4  Thorpe-Roger,  Philos.  Trans.  185  A,  1894,  189  A, 

*  Calculated  from  the  specific  viscosities  given  in  Landolt  &  Bernstein's  Phys.  Chem.  Tab. 

For  inorganic  acids,  see  Solutions. 
SMITHSONIAN  TABLES. 


TABLE  119. 
VISCOSITY  OF  SOLUTIONS. 


This  table  is  intended  to  show  the  effect  of  change  of  concentration  and  change  of  temperature  on  the  viscosity  of 
solutions  of  salts  in  water.  The  specific  viscosity  X  100  is  given  for  two  or  more  densities  and  for  several  tem- 
peratures in  the  case  of  each  solution.  JA  stands  for  specific  viscosity,  and  t  for  temperature  Centigrade. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

t* 

t 

- 

t 

• 

t 

fl 

t 

Authority. 

BaCl2 

7.60 

_ 

77-9 

10 

44-o 

30 

35-2 

50 

_ 

_ 

Sprung. 

" 

15.40 

— 

86.4 

M 

56.0 

u 

39-6 

• 

— 

— 

" 

|| 

24-34 

- 

100.7 

" 

66.2 

" 

47-7 

" 

- 

- 

" 

Ba(N03)2 

2.98 
5-24 

1.027 
1.051 

62.0 
68.1 

tf 

54-2 

25 

42.4 
44.1 

345 

34-8 
36-9 

45 

Wagner. 

CaCl2 

I5-I7 

_ 

110.9 

IO 

7i-3 

30 

5°-3 

So 

_ 

_ 

Sprung. 

" 

31.60 

— 

272.5 

" 

177.0 

" 

124.0 

" 

— 

— 

u 

" 

39-75 

- 

670.0 

" 

379-o 

M 

245-5 

" 

- 

- 

" 

" 

44.09 

- 

- 

- 

593-1 

U 

363-2 

" 

- 

- 

M 

Ca(N03)2 

J7-55 

I.I7I 

93-8 

15 

74-6 

25 

60.0 

345 

49-9 

45 

Wagner. 

II 
M 

30.10 
40.13 

1.274 
1.386 

144.1 
242.6 

« 

112.7 
217.1 

H 

« 

90.7 
156-5 

« 

128.1 

« 

(( 

u 

CdCl2 

11.09 

1.109 

77-5 

15 

60.5 

25 

49.1 

35 

40.7 

45 

« 

M 

16.30 

I.lSl 

88.9 

70-5 

M 

47-2 

H 

" 

24.79 

1.320 

104.0 

" 

80.4 

M 

64.6 

u 

53-6 

" 

" 

Cd(N03)2 

7.81 

1.074 

61.9 

15 

50.1 

25 

41.1 

35 

34-o 

45 

« 

" 

15.71 

I-I59 

71.8 

« 

58.7 

48.8 

« 

41.3 

|| 

" 

22.36 

1.241 

85.1 

u 

69.0 

" 

57-3 

H 

47-5 

M 

" 

CdS04 

7.14 

1.068 

78.9 

15 

61.8 

25 

49-9 

35 

41-3 

45 

tt 

** 

14.66 

1-1  59 

96.2 

72-4 

58.1 

M 

48.8 

a 

" 

" 

22.OI 

1.268 

120.8 

** 

91.8 

" 

73-5 

H 

60.1 

" 

" 

CoCl2 

7-97 

1.081 

83.0 

15 

65.1 

25 

53-6 

35 

44-9 

45 

« 

* 

14-86 

1.161 

1  1  1.  6 

85.1 

73-7 

«< 

58.8 

" 

M 

22.27 

1.264 

161.6 

M 

126.6 

" 

101.6 

" 

S5.6 

" 

" 

Co(N03)2 

8.28 

1-073 

74-7 

15 

§9 

25 

48.7 

35 

39-8 

45 

« 

M 

15.96 

1.144 

87.0 

2 

55-4 

44-9 

M 

" 

" 

24-53 

1.229 

110.4 

U 

0 

" 

M 

59-  1 

" 

" 

CoS04 

7-24 

1.086 

86.7 

15 

68.7 

25 

55-o 

35 

45-i 

45 

it 

" 

14.16 

I-I59 

117.8 

M 

95-5 

76.0 

« 

61.7 

" 

" 

21.17 

1.240 

193.6 

" 

146.2 

" 

113.0 

H 

89.9 

" 

* 

CuCl2 

I2.OI 

1.104 

87.2 

15 

67.8 

25 

55.1 

35 

45-6 

45 

« 

M 

21-35 

1.215 

121.5 

95-8 

U 

77-o 

63-2 

" 

" 

33-03 

I-33I 

178.4 

II 

137.2 

(( 

107.6 

u 

87.1 

" 

U 

Cu(N03)2 

M 

18.99 
26.68 

1.177 
1.264 

97-3 
126.2 

IS 

76.0 
98.8 

V 

61.5 

80.9 

35 

5<;3 

1.5 

H 

tt 

46.71 

382.9 

" 

283.8 

" 

215-3 

" 

172.2 

" 

" 

CuS04 

6.79 

1-055 

79-6 

15 

61.8 

25 

49-8 

35 

41.4 

45 

« 

M 

12.57 
17.49 

1.115 
1.163 

98.2 
124.5 

|| 

74-o 
96.8 

It 

59-7 
75-9 

H 
|| 

52.0 
61.8 

M 

it 

H 

HC1 

M 

8.14 

16.12 

23.04 

1.084 
1.114 

71.0 
80.0 
91.8 

15 

II 

79-9 

15 

48-3 
56-4 
65-9 

35 

40.1 
48.1 
56.4 

I5 

« 

HgCl2 

0.23 

i.  002 

_ 

_ 

58-5 

20 

46.8 

3° 

38-3 

40 

« 

" 

3-55 

'•033 

76.75 

10 

59-2 

H 

46.6 

u 

38-3 

SMITHSONIAN  TABLES. 


132 


TABLE  119  (continued). 
VISCOSITY  OF   SOLUTIONS. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

- 

• 

> 

• 

- 

t 

> 

' 

Authority. 

HNO8 

8-37 

1.067 

66.4 

15 

54-8 

25 

45-4 

35 

37-6 

45 

Wagner. 

« 

12.20 

1.116 

69.5 

" 

57-3 

" 

47-9 

" 

40.7 

" 

" 

" 

28.31 

1.178 

80.3 

u 

65.5 

" 

54-9 

" 

46.2 

M 

" 

H2S04 

7.87 

1.065 
1.130 

77-8 
95-1 

y 

61.0 
75-o 

25 

50.0 
60.5 

35 

41.7 

49-8 

45 

" 

u 

23-43 

I.2OO 

122.7 

tt 

95-5 

« 

77-5 

" 

64-3 

" 

« 

KC1 

IO.23 

_ 

70.0 

10 

46.1 

3p 

33-i 

5p 

- 

- 

Sprung. 

u 

22.21 

- 

70.0 

" 

48.6 

M 

— 

— 

" 

KBr 

I4.O2 

_ 

67.6 

10 

44-8 

3p 

32.1 

5° 

_ 

_ 

« 

H 

23.16 

— 

66.2 

" 

44-7 

33-2 

" 

— 

— 

" 

" 

34-64 

- 

66.6 

" 

47.0 

" 

35-7 

" 

— 

— 

" 

KI 

8.42 

_ 

69.5 

10 

44-o 

30 

3i.3 

50 

- 

_ 

« 

** 

17.01 

— 

65-3 

" 

42.9 

u 

31.4 

" 

— 

— 

" 

" 

33-03 

- 

61.8 

* 

42-9 

" 

32-4 

* 

- 

- 

" 

« 

45-98 
54-00 

- 

63.0 
68.8 

H 

II 

« 

« 

35-3 
37-6 

H 

- 

- 

u 

KC103 

3-51 

- 

71.7 

10 

44-7 

3p 

31.5 

50 

- 

- 

« 

" 

5-69 

— 

— 

M 

45-° 

314 

<( 

— 

— 

* 

KNO8 

6.32 

_ 

70.8 

10 

44-6 

3p 

31-8 

5p 

- 

- 

" 

" 

12.19 

— 

68.7 

" 

44.8 

32-3 

— 

— 

" 

u 

17.60 

- 

68.8 

" 

46.0 

" 

334 

" 

- 

- 

M 

K2S04 

5-T7 

_ 

77-4 

IO 

48.6 

3p 

34-3 

5p 

_ 

_ 

« 

" 

9-77 

— 

81.0 

* 

52-0 

36-9 

— 

— 

" 

K2Cr04 

"•93 

_ 

75-8 

10 

62.5 

3p 

41.0 

40 

_ 

_ 

M 

" 

19.61 

- 

85-3 

" 

68.7 

47-9 

M 

- 

- 

" 

" 

24.26 

!-233 

97-8 

" 

H 

H 

— 

— 

Slotte. 

" 

32.78 

109.5 

M 

88.9 

" 

62.6 

" 

— 

- 

Sprung. 

K2Cr207 

4.71 

1.032 

72.6 

10 

55-9 

20 

45-3 

3p 

37-5 

40 

Slotte. 

" 

6.97 

1.049 

73-1 

" 

56-4 

" 

45-5 

37-7 

" 

H 

LiCl 

7.76 

_ 

96.1 

10 

59-7 

3p 

41.2 

5° 

_ 

_ 

Sprung. 

«« 

I3-9I 
26.93 

- 

121.3 
229.4 

« 

75-9 
142.1 

52.6 
98.0 

« 

- 

- 

M 

Mg(N08)2 

18.62 

1.  102 

99-8 

15 

81.3 

25 

66.5 

35 

56.2 

45 

Wagner. 

M 

34-19 

I.2OO 

213-3 

164.4 

H 

132.4 

u 

109.9 

" 

" 

39-77 

1.430 

S^-o 

" 

250.0 

" 

191.4 

" 

158.1 

" 

MgS04 

4.98 

_ 

96.2 

IO 

59-o 

30 

40.9 

5p 

_ 

_ 

Sprung. 

I 

9-50 
19.32 

- 

130.9 
302.2 

« 

,83 

M 

« 

53-o 
1  06.0 

it 

- 

- 

- 

MgCrO4 

12.31 

.089 

111.3 

IO 

84.8 

2O 

67.4 

3° 

55-o 

40 

Slotte. 

« 

21.86 
27.71 

.164 
.217 

167.1 
232.2 

II 

125.3 
172.6 

H 

99-o 
133-9 

M 
U 

794 
106.6 

« 

« 

MnCl2 

8.01 

.096 

92.8 

15 

71.1 

25 

57-5 

35 

48.! 

45 

Wagner. 

" 

J5-65 

.!96 

130.9 

104.2 

84.0 

M 

68.7 

" 

" 

30.33 

•337 

256-3 

M 

193.2 

" 

155.0 

(1 

123.7 

" 

H 

40.13 

•453 

537-3 

393-4 

300.4 

246.5 

H 

SMITHSONIAN  TABLES. 


TABLE  1 1 9  (continued). 
VISCOSITY  OF   SOLUTIONS. 


133 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

ft 

t 

c- 

' 

* 

< 

- 

t 

Authority. 

Mn(NO3)2 

18.31 
29.60 

1.148 

96.0 

167-5 

15 

76.4 

126.0 

25 

64.5 

104.6 

35 

in 

1.5 

Wagner. 

" 

49-3  r 

1.506 

396.8 

" 

301.1 

221.0 

" 

188.8 

* 

" 

MnSO4 

"45 

I.I47 

129.4 

15 

98.6 

25 

78.3 

35 

634 

45 

« 

" 

18.80 

1.251 

228.6 

172.2 

I37-I 

107.4 

*' 

" 

22.08 

1.306 

661.8 

" 

474-3 

" 

347-9 

" 

266.8 

" 

M 

NaCl 

7-95 
I4-31 

- 

82.4 

94-8 

10 

£? 

30 

31.8 
36-9 

5° 

- 

- 

Sprung. 

c« 

23.22 

- 

128.3 

79-4 

" 

474 

(« 

— 

— 

" 

NaBr 

9-77 

_ 

75-6 

10 

48.7 

3? 

344 

5f. 

- 

_ 

« 

M 

18.58 

— 

82.6 

" 

53-5 

38-2 

— 

— 

u 

" 

27.27 

- 

95-9 

* 

61.7 

" 

43-8 

" 

— 

- 

* 

Nal 

8.83 

_ 

73-J 

10 

46.0 

30 

324 

50 

- 

_ 

14 

" 

17.15 

— 

73-8 

" 

47-4 

" 

33-7 

M 

— 

— 

" 

M 

35-69 

— 

86.0 

" 

M 

40.6 

" 

— 

— 

II 

" 

55-47 

- 

157-2 

" 

96.4 

M. 

66.9 

" 

- 

- 

" 

NaClO8 

11.50 

_ 

78.7 

IO 

50-0 

30 

35-3 

50 

- 

- 

« 

" 

20.59 

— 

88.9 

* 

56.8 

M 

40.4 

— 

— 

M 

" 

33-54 

— 

I2I.O 

" 

75-7 

|| 

53-o 

" 

— 

— 

" 

NaNOs 

7-25 

- 

75-6 

10 

47-9 

30 

33-8 

5° 

- 

_ 

M 

M 

I2-35 

— 

81.2 

" 

51.0 

" 

36-1 

— 

— 

" 

" 

18.20 

- 

87.0 

" 

55-9 

ll 

39-3 

" 

- 

- 

" 

" 

31-55 

— 

121.  2 

« 

76.2 

M 

53-4 

" 

— 

- 

" 

Na2S04 

4-98 

- 

96.2 

10 

59-o 

30 

40.9 

5f 

- 

_ 

II 

" 

9-50 

- 

130.9 

" 

77-7 

U 

53-o 

- 

- 

** 

" 

14.03 

— 

187.9 

u 

107.4 

* 

71.1 

" 

— 

— 

" 

" 

19.32 

- 

302.2 

(( 

166.4 

" 

1  06.0 

" 

— 

- 

" 

Na2CrO4 

5-76 

1.058 

85.8 

IO 

66.6 

20 

534 

3f 

43-8 

40 

Slotte. 

" 

10.62 

1.  112 

103-3 

" 

79-3 

" 

63-5 

52-3 

u 

" 

" 

14.81 

1.164 

127-5 

" 

97.1 

" 

77-3 

" 

63.0 

" 

" 

NH4C1 

3-67 

- 

71-5 

10 

45-° 

30 

31.9 

5f 

- 

- 

Sprung. 

« 

8.67 
15.68 

_ 

69.1 

« 

45-3 
46.2 

« 

32.6 
34-o 

« 

_ 

_ 

« 

M 

23-37 

— 

67.4 

" 

47-7 

" 

36-1 

" 

— 

— 

" 

NH4Br 

15-97 

._. 

65-2 

10 

43-2 

30 

31-5 

50 

- 

- 

« 

« 

25.33 

x-   OO 

36.88 

- 

62.6 
62.4 

« 

44-6 

32.2 
34-3 

M 

- 

- 

H 

NH4NO3 

5-97 

_ 

69.6 

10 

44-3 

3f 

31.6 

5f 

_ 

_ 

« 

" 

12.19 

— 

66.8 

" 

44-3 

3*-9 

— 

— 

" 

« 

27.08 

- 

67.0 

" 

47-7 

N 

349 

« 

- 

- 

" 

« 

37-22 

— 

71.7 

M 

51.2 

M 

38.8 

" 

— 

— 

" 

« 

49-83 

- 

81.1 

" 

63-3 

" 

48.9 

" 

- 

- 

" 

(NH4)2S04 

8.10 

- 

107.9 

IO 

52.3 

30 

37-o 

50 

- 

_ 

« 

" 

!5-94 

— 

1  20.  2 

" 

60.4 

it 

43-2 

" 

— 

— 

H 

25-5I 

148.4 

M 

74.8 

it 

M 

SMITHSONIAN  TABLES. 


134 


TABLE  119  (continued). 

VISCOSITY   OF   SOLUTIONS. 


Salt. 

Percentage 
by  weight 
of  salt  in 
solution. 

Density. 

M 

/ 

M 

t 

M 

t 

M 

t 

Authority. 

(NH4)2Cr04 

10.52 

1.063 

79-3 

10 

62.4 

20 

_ 

_ 

42.4 

40 

Slotte. 

« 

19.75 

I.I2O 

88.2 

a 

7O.O 

« 

57-8 

30 

48.4 

— 

u 

" 

28.04 

I-I73 

IOI.I 

it 

80-7 

" 

60.8 

56.4 

- 

« 

(NH4)2Cr207 

6.85 

1.039 

72-5 

IO 

56.3 

2O 

45-8 

3° 

38.0 

40 

u 

" 

13.00 

1.078 

72.6 

(I 

57-2 

M 

46.8 

II 

39-i 

" 

" 

« 

19-93 

I.I26 

77-6 

" 

58.8 

« 

48.7 

II 

40.9 

M 

<« 

NiCl2 

"45 

I.I09 

90.4 

15 

70.0 

25 

57<5 

35 

48.2 

45 

Wagner. 

M 

22.69 

1.226 

140.2 

" 

109.7 

" 

87.8 

" 

72.7 

" 

<« 

u 

30.40 

1-337 

229.5 

« 

171.8 

|| 

139.2 

111.9 

«< 

M 

Ni(N03)2 

M 

16.49 
30.01 
40.95 

1.136 

1.278 
1.388 

90.7 
135-6 

222.6 

tf 

70.1 
105.9 
169.7 

*$ 

« 

57-4 
83-5 
128.2 

35 

U 

48.9 
70.7 
152.4 

445 
u 

« 

«< 

NiSO4 

10.62 

1.092 

94.6 

«s 

73-5 

25 

60.  i 

35 

49-8 

45 

<« 

" 

18.19 

1.198 

154-9 

f| 

119.9 

U 

99-5 

u 

75-7 

" 

" 

" 

25-35 

I.3H 

298.5 

« 

224.9 

|| 

i73-o 

« 

152.4 

tt 

" 

Pb(N03)2 

J7-93 

1.179 

74-o 

15 

59-i 

25 

48-5 

35 

40-3 

45 

|| 

M 

32.22 

1.362 

91.8 

u 

72-5 

59-6 

50.6 

M 

<« 

Sr(N03)2 

10.29 

i.  088 

69-3 

15 

56.0 

25 

45-9 

35 

39-i 

45 

M 

« 

21.19 

1.124 

87.3 

69.2 

57-8 

48.1 

M 

« 

32.61 

1.307 

116.9 

« 

93-3 

(( 

76.7 

«« 

62.3 

« 

<( 

ZnCl2 

15-33 

1.146 

93-6 

15 

I2;l 

25 

57-8 

35 

48.2 

45 

«« 

u 

23-49 

1.229 

111.5 

M 

86.6 

M 

69.8 

" 

57-5 

" 

«( 

" 

3378 

1-343 

IS1-? 

« 

117.9 

" 

90.0 

« 

72-6 

« 

M 

Zn(N03)2 

15-95 

1.115 

80.7 

IS 

64-3 

25 

52.6 

35 

43-8 

45 

« 

" 

3°-23 

1.229 

104.7 

85.7 

« 

69.5 

57-7 

" 

M 

44-50 

1-437 

167.9 

(( 

130.6 

«( 

105.4 

<« 

87.9 

« 

N 

ZnSO4 

7.12 

1.106 

97.1 

15 

79-3 

25 

62.7 

35 

5T-5 

45 

<« 

M 
M 

16.64 
23.09 

I-I95 
1.281 

156.0 
232.8 

« 

« 

118.6 
1774 

« 

n 

94.2 
135-2 

73-5 
108.1 

M 
U 

« 
« 

SMITHSONIAN  TABLES. 


TABLE  1 20. 
SPECIFIC   VISCOSITY.* 


135 


Normal  solution. 

J  normal. 

J  normal. 

\  normal. 

Dissolved  salt. 

>, 

0   >• 

>, 

0    >> 

>, 

<u  rr 

£, 

£~ 

Authority. 

'$ 

1 

tC  ."£ 

"u  o 

$J 

°w 

<L> 

Q 

11 

C0-g 

1 

S'35 

aw 
ws 

i 

Q 

11 
Jj 

Acids  :  C]2O3      .     . 

1.0562 

I.OI2 

1.0283 

I.OO3 

1.0143 

.000 

1.0074 

0.999 

Reyher. 

HC1  .     .    . 

1.0177 

1.067 

1.0092 

•034 

1.0045 

.017 

1.0025 

.009 

" 

HC1O3   .     . 

1.0485 

1.052 

1.0244 

•025 

I.OI26 

.014 

1.0064 

.006 

*' 

HNO3    .     . 

1.0332 

1.027 

1.0168 

.Ol  I 

1.0086 

.005 

1.0044 

.003 

M 

H2SO4    .     . 

1.0303 

1.090 

1.0154 

.043 

1.0074 

.022 

1.0035 

.OO8 

Wagner. 

Aluminium  sulphate 

1-0550 

1.406 

1.0278 

.178 

1.0138 

.082 

1.0068 

.038 

«( 

Barium  chloride  .     . 

1.0884 

1.123 

1.0441 

•057 

1.0226 

.026 

I.OII4 

.013 

« 

"        nitrate     .     . 

— 

1.0518 

1.044 

1.0259 

.021 

1.0130 

.008 

a 

Calcium  chloride      . 

1.0446 

1.156 

1.0218 

1.076 

I.OIO5 

.036 

1.0050 

.017 

*' 

"        nitrate  .     . 

1.0596 

1.117 

1.0300 

1-053 

1.0151 

I.  O2  2 

1.0076 

1.  008 

M 

Cadmium  chloride  . 

1.0779 

1.134 

1.0394 

1.063 

I.OI97 

I.03I 

1.0098 

I.O2O 

« 

"          nitrate 

1.0954 

1.165 

1.0479 

1.074 

1.0249 

1.038 

I.OII9 

I.OI8 

M 

"         sulphate  . 

1.0973 

1.348 

1.0487 

I.I57 

1.0244 

1.078 

I.OI2O 

1-033 

" 

Cobalt  chloride   .     . 

1.0571 

1.204 

1.0286 

1.097 

1.0144 

1.048 

1.0058 

1.023 

fj 

"      nitrate      .     . 

1.0728 

1.166 

1.0369 

1.075 

1.0184 

1.032 

1.0094 

1.018 

« 

"      sulphate  .     . 

1.0750 

1-354 

1.0383 

1.160 

1.0193 

1.077 

I.OIIO 

1.040 

« 

Copper  chloride  .     . 

1.0624 

1.205 

1-0313 

1.098 

1.0158 

1.047 

1.0077 

1.027 

« 

"        nitrate     .     . 

I  -07SS 

1.179 

1.0372 

1.080 

1.0185 

I.O4O 

1.0092 

1.018 

M 

"        sulphate 

1.0790 

1.358 

1  .0402 

1.160 

I.O2O5 

1.080 

1.0103 

1.038 

« 

Lead  nitrate    .     .     . 

1.1380 

I.IOI 

0.0699 

1.042 

L035I 

I.OI7 

1.0175 

1.007 

ft 

Lithium  chloride 

1.0243 

1.142 

1.0129 

i.  066 

1  .0062 

I.O3I 

1.0030 

I.OI2 

(t 

"        sulphate 

1-0453 

1.290 

1.0234 

I-I37 

I.OII5 

1.065 

1.0057 

I.O32 

« 

Magnesium  chloride 

I-I375 

I.2OI 

i.  oi  88 

1.094 

1.0091 

1.044 

1.0043 

1.  02  1 

u 

"           nitrate  . 

1.0512 

I.I7I 

1.0259 

1.082 

1.0130 

I.O4O 

1.  0066 

I.O2O 

u 

"           sulphate 

1.0584 

1.367 

1.0297 

1.164 

1.0152 

1.078 

1.0076 

1.032 

(( 

Manganese  chloride 

1-0513 

1.209 

1.0259 

1.098 

I.OI25 

1.048 

1.0063 

1.023 

n 

"           nitrate   . 

1.0690 

1.183 

1-0349 

1.087 

1.0174 

1.043 

1.0093 

1.023 

il 

"           sulphate 

1.0728 

1.364 

1-0365 

1.169 

I.OI79 

1.076 

1.0087 

1.037 

« 

Nickel  chloride   .     . 

1.0591 

1.205 

1.0308 

1.097 

.0144 

1.044 

1  .0067 

1.  02  1 

H 

"       nitrate.     .     . 

I-075S 

I.lSo 

1.0381 

1.084 

.0192 

1.042 

1  .0096 

I.OI9 

M 

"       sulphate  .     . 

1-0773 

1.361 

1.0391 

1.161 

.0198 

1-075 

1.0017 

1.032 

" 

Potassium  chloride  . 

1.0466 

0.987 

1.0235 

0.987 

.0117 

0.990 

1.0059 

0-993 

M 

"          chromate 

J.o935 

I.II3 

1-0475 

L053 

.0241 

I.O22 

I.OI2I 

I.OI2 

ft 

"          nitrate    . 
"          sulphate 

1.0605 
1.0664 

0-975 
I.IO5 

1-0305 
1-0338 

0.982 
1.049 

.Ol6l 
.0170 

0.987 
1.  02  1 

1.0075 
1.0084 

0.992 
1.008 

U 
U 

Sodium  chloride  .     . 

1.0401 

1.097 

1.0208 

1.047 

.OIO7 

I.O24 

.0056 

I.OI3 

Reyher. 

"        bromide  . 

1.0786 

1.064 

1.0396 

1.030 

.0190 

I.OI5 

.OIOO 

1.008 

« 

"        chlorate 

1.0710 

1.090 

I-0359 

1.042 

.Ol8o 

1.022 

.0092 

I.OI2 

u 

"        nitrate    ..    . 

1-0554 

1.065 

1.0281 

1.026 

1.0141 

1.  01  2 

.0071 

I.OO7 

(I 

Silver  nitrate  .     .    . 

1.1386 

1.058 

1.0692 

i.  020 

1  .0348 

I.  OO6 

.0173 

I.OOO 

Wagner. 

Strontium  chloride  . 

1.0676 

I.I4I 

1.0336 

1.067 

.0171 

.034 

.0084 

1.014 

u 

"          nitrate    . 

1.0822 

I.II5 

1.0419 

1.049 

.0208 

.024 

.OIO4 

I.  OH 

n 

Zinc  chloride  .     .     . 

1.0590 

1.189 

1.0302 

1.096 

.0152 

•053 

1.0077 

1.024 

" 

"     nitrate     .     .     . 

1.0758 

1.164 

1.0404 

1.086 

.0191 

•°39 

1.0096 

1.019 

« 

"     sulphate.     .     . 

1.0792 

I-367 

1.0402 

i.i73 

.0198 

.082 

1.0094 

1.036 

« 

*  In  the  case  of  solutions  of  salts  it  has  been  found  (vide  Arrhennius,  Zeits.  fur  Phys.  Chem.  vol.  i,  p.  285)  that 
the  specific  viscosity  can,  in  many  cases,  be  nearly  expressed  by  the  equation  /u.  =  /u.1™,  where  /xt  is  the  specific  viscosity 
for  a  normal  solution  referred  to  the  solvent  at  the  same  temperature,  and  n  the  number  of  gramme  molecules  in  the 
solution  under  consideration.  The  same  rule  may  of  course  be  applied  to  solutions  stated  in  percentages  instead  of 
gramme  molecules.  The  table  here  given  has  been  compiled  from  the  results  of  Reyher  (Zeits.  fur  Phys.  Chem.  vol.  2, 
p.  749)  and  of  Wagner  (Zeits.  fiir  Phys.  Chem.  vol.  5,  p.  31)  and  illustrates  this  rule.  The  numbers  are  all  for  25°  C. 

SMITHSONIAN  TABLES. 


136  TABLES  121-122. 

TABLE  121  .-VISCOSITY  OF  GASES  AND  VAPORS. 

The  values  of  p  given  in  the  table  are  io6  times  the  coefficients  of  viscosity  in  C.  G.  S.  units. 


Substance. 

Temp. 

* 

Refer- 
ence. 

Substance. 

Temp. 
°C 

* 

Refer- 
ence. 

Acetone 

1  8.0 

78. 

, 

Chloroform 

0.0 

95-9 

I 

Air                 ... 

-21.4 

163.9 

2 

" 

17.4 

102.9 

it 

ii 

0.0 

173-3 

it 

41       . 

61.2 

189.0 

3 

"                  ... 

15.0 

180.7 

u 

Ether 

0.0 

68.9 

i 

.        . 

99.1 

220.3 

ii 

ii 

16.1 

73-2 

" 

"                  ... 

182.4 

255-9 

u 

"           .        . 

36.5 

79-3 

ii 

ii 
Alcohol  :  Methyl     . 

302.0 

66.8 

299-3 
'35- 

3 

Ethyl  iodide      . 
Helium 

72-3 

0.0 

216.0 
189.1 

3 

5 

Ethyl       . 

78.4 

142. 

"           .        . 

J5-3 

196.9 

"        Propyl,  norm. 

97-4 

142. 

ii 

" 

66  6 

234.8 

<• 

"         Isopropyl 
"        Butyl,  norm.    . 

82.8 
116.9 

162. 
143- 

u 

Hydrogen  . 

184.6 

-20.6 

269.9 
81.9 

2 

"        Isobutyl  . 

108.4 

144. 

ii 

"         .        . 

15.0 

88.9 

ii 

"        Tert.  butyl      . 

82.9  " 

100. 

ii 

" 

99-2 

105.9 

it 

Ammonia 

0.0 

96. 

4 

"         . 

182.4 

121.5 

" 

"              .        • 

20.0 

108. 

" 

" 

302.0 

139.2 

ii 

Argon    .... 

0.0 

210.4 

5 

Mercury    . 

270.0 

489* 

8 

"        •        •        .        . 

14.7 

220.8 

"           .        .' 

300.0 

532.* 

" 

"        .        .        .        . 

17.9 

224.1 

" 

. 

330.0 

582.* 

it 

"        .        .        .        . 

99-7 

273-3 

" 

. 

360.0 

627.* 

* 

ii 

183-7 

322.1 

" 

" 

390.0 

671.* 

ii 

Benzole  .... 

19.0 

79- 

6 

Methane    . 

2O.O 

1  20.  i 

4 

M 

Carbon  bisulphide 

IOO.O 

16.9 

118. 
92.4 

i 

Methyl  iodide   . 
"      chloride 

44-0 
I5.0 

232. 
105.2 

3 

2 

dioxide 

-20.7 

129.4 

2 

u            u 

302.0 

213.9 

" 

. 

15.0 

M5-7 

ii 

Nitrogen  . 

-21.5 

156-3 

7 

. 

99.1 

1  86.  i 

" 

"          .        . 

10-9 

170.7 

" 

. 

182.4 

222.1 

ii 

" 

53-5 

189.4 

" 

" 

302.0 

268.2 

• 

Oxygen     . 

15-4 

195-7 

" 

"       monoxide 

o.o 

163.0 

4 

" 

53-5 

215.9 

" 

"             " 

20.0 

184.0 

it 

Water  vapor     . 

0.0 

90.4 

i 

Chlorine 

0.0 

128.7 

" 

u          it 

16.7 

96.7 

" 

. 

2O.O 

147.0 

K 

. 

IOO.O 

132.0 

9 

i  Puluj,  Wien.  Ber.  69,  (2),  1874.                        6  Schumann,  Wied.  Ann.  23,  1884. 

2  Breitenbach,  Ann.  Phys.  5,  1901.                      7  Obermayer,  Wien.  Ber.  71,  (2a),  1875. 

3  Steudel,  Wied.  Ann.  16,  1882.                          8  Koch,  Wied.  Ann.  14,  1881,  19,  1883. 

4  Graham,  Philos.  Trans.  Lond.  1846,  III.         9  Meyer-Schumann,  Wied.  Ann.  13,  1881. 
5  Schultze,  Ann.  Phys.  (4),  5,  6,  1901. 

*  The  values  here  given  were  calculated  from  Koch's  table  (Wied.  Ann.  vol.  19,  p.  869)  by  the  formula  y.  =  489  [i  -f- 
746  (*— 270)]. 


TABLE  122.- VISCOSITY  OF  AIR.    2O.2°C. 


Markowski,  ditto.  1904 
Tanzler,  Ver.  D.  Phys.  G.  1906 
Tomlinson,  Phil.  Trans.  1886 


Hogg,  Am.  Acad.  Proc.  1905 
Gilchrist 


1.835 
1.836 
1.811 
1.812 
1.812 

1. 808 

1.812 


Holman,  Phil.  Mag.  1886  1.810  X  io— *     Markowski,  ditto.  1904  1.835X10' 

Fischer,  Phys.  Rev.  1909  1.807 
Grindlay,  Gibson,  Pr.  Roy.  Soc. 

1908  1.809 

Rankine,  ditto.  1910  1.814 

Rapp,  unpublished  1.810 

Breitenbach,  Wied.  Ann.  1899  1.833 

Schultze,  Ann.  der  Phys.  1901  1.837 

The  viscosity  of  air  at  20.2°  may  be  taken  as  1.812  X  io— *  within  a  probable  error  of  less  than 
0.2  per  cent.  Its  variation  with  the  temperature  may  be  obtained  from  Holman's  formula 
=  1715.50 X  io— 7  (i  +0.00275*  —  0.00000034/2).  See  Phys.  Rev.  1913,  p.  124,  where  full  refer- 
ences may  be  obtained. 

SMITHSONIAN  TABLES. 


TABLE  123.  137 

COEFFICIENT  OF  VISCOSITY  OF  GASES. 

Temperature  Coefficients. 

If  ^=the  viscosity  at  t°  C*,  juo  =  the  vicosity  at  o°,  a  =  the  coefficient  of  expansion,  ft  7,  and 
n  =  coefficients  independent  of  /,  then 

(I)  ^=^0(1+ o/X     (Meyer,  Obermayer,  Puluj,  Breitenbach,) 
(II)      =/io(i+#).     (Meyer,  Obermayer.) 
(Ill)     =jio(i+a/)*(i+7/)2.    (Schumann.) 


(IV) 


-^.     (Sutherland.) 


Gas. 

/U.0IO7. 

a. 

Constants. 

Range  °  C. 

Refer- 
ence. 

Air* 

_ 

0.003665 

«  =  0.77 

O-IOO 

I 

tt 

'733-1 

.003665 

(7=119.4 

- 

2 

M 

1811. 

— 

n—  0.767  5 

15.0-99.7 

3 

H 

2208. 

— 

»  =  0.7  544 

99.7-182.9 

tt 

« 

_ 

— 

n  =0.7  54;  C=m.3 

4 

Argon 

_ 

— 

«=O.8i5;   (7=150.2 

15-100 

4 

t< 

2208. 

- 

^=0.8227,  C==  169.9 

14.7-99.7 

3 

M 

2733- 

— 

«=o.8ii9 

99.7-183.7 

3 

Benzole 

698.4 

.004 

7=0.00185 

18.7-100 

Carbon  dioxide 

1  387-9 

— 

(7=239.7 

— 

6 

«            « 

1497.2 

.003701 

7=0.000889 

I2.8-IOO 

5 

«            « 
"       monoxide 

1382.1 
1625.2 

.OO37OI 
.003665 

j8=  0.00348;  72=0.941 
0=  0.00269;  72=0.738 

—21.5-53.5 
17.5-53.5 

7 

Ether  . 

689. 

.004158 

w=o-94 

0-36.5 

8 

Ethylene 

961.3 

- 

£-=225.9 

6 

« 
"        chloride 

922.2 
889.03 

.003665 
.003900 

£=0.00350;  72=0.958 
/8=o.oo38i  ;  7z=o  9772 

—21.5-53.5 
15.6-157.3 

7 

Helium 

_ 

— 

«=o.68i  ;  ^=72.2 

0-15.0 

4 

« 

1969. 

2348. 

— 

n  =0.6852;  (7=80.3 
72=0.6771 

1  5.3-99.6 

99.6-184.6 

3 
3 

Hydrogen    . 

8574 

.00366 

<7=7r.7 

- 

2 

" 

— 

— 

»=o.68i;  (7=72.2 

— 

4 

Mercury 
Nitrogen 

1620. 
1658.6 

.003665 
.003665 

7/=I.6 

)8  =  0.00269  >  »  ==  0.738 

273-380 
—21.5-53.5 

10 

7 

Nitrous  oxide 

1353-3 

.003719 

/3=  0.00345;  72=0.929 

—  21.5-100.3 

H 

Oxygen 

~ 

n  =0.782;  (7=128.2 

— 

4 

i  Holman,  Proc.  Amer.  Acad.  12,  1876;  21,           5  Schumann,  Wied.  Ann.  23,  1884. 

1885;  Philos.  Mag.  (5)  3,  1877;  21,  1886.           6  Breitenbach,  Ann.  Phys.  5,  1901. 

2  Breitenbach,  Wied.  Ann.  5,  1901.                         7  Obermaver,  Wien.  Ber.  73  (2A),  1876. 

3  Schultze,  Ann.  Phys.  (4)  5,  1901.                          8  Puluj,  Wien.  Ber.  78  (2),  1878. 
4  Rayleigh,  Proc.  Roy.  Soc.  62,   1897  ;  66,           9  Schultze,  Ann   Phys.  (4)  6,  1901. 
1900;  67,  1900.                                                 10  Koch,  Wied.  Ann.  19,  1883. 

*  See  Table  122  for  viscosity  of  air. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


A) 


* 


138  TABLE  124. 

DIFFUSION  OF  AN  AQUEOUS  SOLUTION  INTO  PURE  WATER. 

If  k  is  the  coefficient  of  diffusion,  dS  the  amount  of  the  substance  which  passes  in  the  time  dtt 
at  the  place  x,  through  q  sq.  cm.  of  a  diffusion  cylinder  under  the  influence  of  a  drop  of  concen- 
tration dc  I '  dx,  then  » 

dS  =  -kq  $£  dt. 
ax 

k  depends  on  the  temperature  and  the  concentration. 
The  unit  of  time  is  a  day. 


c  gives  the  gram-molecules  per  liter. 


Substance. 

c 

to 

k 

Ii 

Substance. 

C 

,. 

k 

is 

-_>  c 

Bromine  . 

O.I 

12. 

0.8 

I 

Calcium  chloride     . 

0.864 

8.5 

0.70 

4 

Chlorine  . 

12. 

1.22 

" 

"             "   . 

1.22 

9- 

0.72 

Copper  sulphate 

" 

17- 

o-39 

2 

"             "  . 

O.O6O 

9- 

0.64 

" 

Glycerine 
Hydrochloric  acid   . 

u 

IO.I4 
19.2 

o-357 

2.21 

3 

2 

Copper  sulphate 

0.047 

9- 
17- 

0.68 
0.23 

2 

Iodine 

M 

12. 

(0-5) 

I 

"            " 

o-95 

17- 

0.26 

u 

Nitric  acid 

" 

19-S 

2.07 

2 

"            " 

0.30 

17- 

o-33 

" 

Potassium  chloride  . 

M 

I.38 

2 

"            "    . 

0.005 

0.47 

U 

hydrate  . 

U 

J3-5 

1.72 

2 

Glycerine 

2/8 

10.14 

o.354 

3 

Silver  nitrate    . 

" 

12. 

0.985 

2 

"... 

6/8 

10.14 

o-345 

Sodium  chloride 

" 

15.0 

0.94 

2 

"... 

10/8 

10.14 

0.329 

u 

Urea 

" 

14.8 

0.97 

3 

"... 

14/8 

10.14 

0.300 

" 

Acetic  acid 

0.2 

13-5 

o-77 

4 

Hydrochloric  acid    . 

4.52 

n-5 

2-93 

4 

Barium  chloride 

u 

8. 

0.66 

4 

«              « 

3.16 

n. 

2.67 

Glycerine 

" 

IO.I 

3-55 

3 

««              u 

0-945 

n. 

2.12 

" 

Sodium  actetate 

" 

12. 

0.67 

5 

U                             « 

0.387 

n. 

2.02 

" 

"      chloride 

u 

15.0 

o-94 

2 

"              " 

0.250 

u. 

1.84 

» 

Urea 

u 

I4.8 

0.969 

3 

Magnesium  sulphate 

2.18 

5-5 

0.28 

4 

Acetic  acid       .         . 

I.O 

12. 

0.74 

6 

«               « 

0.541 

5-5 

0.32 

" 

Ammonia         . 

tt 

I5-23 

i-54 

7 

«               « 

3-23 

10. 

0.27 

" 

Formic  acid 

" 

12. 

0.97 

7 

"               « 

0.402 

10. 

0-34 

|4 

Glycerine 
Hydrochloric  acid    . 

u 

10.14 
12. 

0-339 
2.09 

Potassium  hydrate  . 

0.75 
o-49 

12. 
12. 

-72 
.70 

6 

Magnesium  sulphate 

" 

7- 

0.30 

4 

« 

o-375 

12. 

.70 

" 

Potassium  bromide  . 

(i 

10. 

8 

nitrate    . 

3-9 

I7.6 

0.89 

2 

hydrate  . 

" 

12. 

1.72 

6 

" 

1.4 

I7.6 

.10 

M 

Sodium  chloride 

« 

J5° 

o-94 

2 

" 

o-3 

17-6 

.26 

M 

U                      « 

" 

14-3 

0.964 

3 

M 

0.02 

I7.6 

.28 

" 

"        hydrate 

" 

12. 

i.  ii 

2 

sulphate 

o-95 

19.6 

0-79 

" 

"        iodide 

» 

10. 

0.80 

8 

M 

0.28 

19.6 

0.86 

«« 

Sugar        . 
Sulphuric  acid 

fl 

12. 
12. 

0.254 

1.  12 

6 
6 

«      ; 

0.05 

O.O2 

19.6 
19.6 

0.97 

I.OI 

It 

Zinc  sulphate  . 

" 

14.8 

0.236 

9 

Silver  nitrate    . 

3-9 

12. 

o-535 

" 

Acetic  acid 

2.O 

12. 

0.69 

6 

"           " 

0.9 

12. 

0.88 

«' 

Calcium  chloride 

«« 

IO. 

O.Oo 

8 

«           « 

O.O2 

12. 

1.035 

« 

Cadmium  sulphate  . 
Hydrochloric  acid    . 

M 

19.04 
12. 

0.246 

2.21 

I 

Sodium  chloride 

2/8 

4/8 

14-33 

J4-33 

1.013 

0.996 

3 

Sodium  iodide 

" 

10. 

O.9O 

8 

"            "     . 

6/8 

14-33 

0.980 

2 

Sulphuric  acid 

" 

12. 

1.16 

6 

"            " 

10/8 

M-33 

0.948 

" 

Zinc  acetate     . 

" 

18.05 

0.210 

9 

"            " 

14/8 

z4-33 

0.917 

•* 

"         "           .        . 

U 

0.04 

O.I  2O 

9 

Sulphuric  acid 

9-85 

18. 

2.36 

2 

Acetic  acid 

3-° 

12. 

0.68 

u                    « 

4-85 

18. 

.90 

«' 

Potassium  carbonate 

IO. 

0.60 

8 

«                    «     [ 

2.85 

18. 

.60 

« 

hydrate  . 

" 

12. 

1.89 

6 

"                    " 

0.85 

1  8. 

•34 

" 

Acetic  acid      . 

4.0 

12. 

0.66 

6 

"                    " 

°-35 

18. 

.32 

'< 

Potassium  chloride  . 

10. 

1.27 

8 

«                    «t 

0.005 

18. 

•30 

M 

i  Euler,  Wied.  Ann.  63,  1897.                                5  Kawalki,  Wied.  Ann.  52,  1894;  59,  1896. 
2  Thovert,  C.  R.  133,  1901  ;   134,  1902.                  6  Arrhenius,  Zeitschr.  Phys.  Chem.  10,  1892. 
3  Heimbrodt,  Diss.  Leipzig,  1903.                          7  Abegg,  Zeitschr.  Phys.  Chem.  ii,  1893. 
4  Scheffer,  Chem.  Ber.  iq,   1882;    16,   1883;      8  Schuhmeister,  Wien.  Ber.  79  (2),  1879. 
Zeitschr.  Phys  Chem.~2,  1888.                          9  Seitz,  Wied.  Ann.  64,  1898. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  125. 
DIFFUSION  OF  VAPORS. 


139 


Coefficients  of  diffusion  of  vapors  in  C.  G.  S.  units.    The  coefficients  are  for  the  temperatures  given  in  the  table  and 
a  pressure  of  76  centimeters  of  mercury.* 


Vapor. 

Temp.  C. 

0 

7ft  for  vapor 
diffusing  into 
hydrogen. 

Jet  for  vapor 
diffusing  into 
air. 

fee  for  vapor 
diffusing  into 
carbon  dioxide. 

Acids  :  Formic         .... 

O.O 

o-S^1 

0-13*5 

0.0879 

a 

65-4 

0.7873 

0.2035 

0.1343 

"                  .... 

84.9 

0.8830 

0.2244 

0.1519 

Acetic          .... 

O.O 

0.4040 

0.1061 

0.0713 

« 

65.5 

O.62II 

0.1578 

0.1048 

« 

98.5 

0.7481 

0.1965 

0.1321 

Isovaleric    .        . 

0.0 

0.21  18 

0-0555 

0.0375 

.... 

98.0 

0-3934 

0.1031 

0.0696 

Alcohols:  Methyl    .... 

O.O 

0.5001 

0.1325 

0.0880 

« 
M 

25.6 

49.6 

0.6015 
0.6738 

0.1620 
0.1809 

0.1046 
0.1234 

Ethyl       '.         1 

0.0 

0.3806 

0.0994 

0.0693 

H 

40.4 

0.5030 

0.1372 

0.0898 

« 

66.9 

0.543° 

0.1475 

0.1026 

Propyl     .... 

0.0 

o.3iS3 

0.0803 

0.0577 

"          .... 

66.9 

0.4832 

0.1237 

0.0901 

« 

83-5 

0-5434 

0.1379 

0.0976 

Butyl       .... 

0.0 

0.2716 

0.068  1 

0.0476 

M 

99.0 

0.5045 

0.1265 

0.0884 

Amyl       .... 

O.O 

0.2351 

0.0589 

O.O422 

« 

99.1 

0.4362 

0.1094 

0.0784 

Hexyl      .        .        '.        . 

0.0 

0.1998 

0.0499 

0.0351 

« 

99.0 

0.3712 

0.0927 

0.0651 

O.O 

0.2940 

0.0751 

0.0527 

« 

IQ.Q 

0.3409 

0.0877 

0.0609 

« 

S    7 

4.C.O 

OT^    ;7 

o.^ocn 

O.IOII 

O.O7  1  5 

Carbon  disulphide    .... 

tj'w 
0.0 

OssO 

0.3690 

0.0883 

/          J 

0.0629 

«              « 

19.9 

0.4255 

0.1015 

O.O726 

«<             « 

32-8 

0.4626 

O.I  120 

0.0789 

Esters  :  Methyl  acetate    . 

O.O 

0.3277 

0.0840 

0-0557 

"            " 

20.3 

0.3928 

O.IOI3 

0.0679 

Ethyl         "         '.        .        . 

0.0 

0.2373 

0.0630 

0.0450 

"             " 

46.1 

0.3729 

O.O97O 

0.0666 

Methyl  butyrate  . 

<<                 u 

O.O 

92.1 

0.2422 
0.4308 

0.0640 
O.II39 

0.0438 
0.0809 

Ethyl                             !         ! 

0.0 

0.2238 

0.0573 

0.0406 

"              "... 

96.5 

0.4112 

0.1064 

0.0756 

"      valerate     . 

O.O 

0.2050 

0.0505 

0.0366 

«          « 

97.6 

0.3784 

0.0932 

0.0676 

Ether        .        .        .        •        • 

O.O 

0.2960 

0.0775 

0.0552 

IQ.Q 

O.'UIO 

0.0893 

0.0636 

y  y 
O.O 

*•  Of 

0.6870 

O.TOSo 

O.I3IO 

4Q.C 

I.OOOO 

f^ 

0.2827 

O.I5II 

4< 

*T;7  j 
Q2.4 

1.1794 

0.3451 

0.2384 

y     ^ 

*  Taken  from  Winkelmann's  papers  (Wied.  Ann.  vols.  22,  23,  and  26).  The  coefficients  for  o°  were  calculated 
by  Winkelmann  on  the  assumption  that  the  rate  of  diffusion  is  proportional  to  the  absolute  temperature.  According 
to  the  investigations  of  Loschmidt  and  of  Obermeyer  the  coefficient  of  diffusion  of  a  gas,  or  vapor,  at  o°  C.  and  a 
pressure  of  76  centimetres  of  mercury  may  be  calculated  from  the  observed  coefficient  at  another  temperature  and 
pressure  by  the  formula  k0  =  kT(^n7—,  where  T  is  temperature  absolute  and  p  the  pressure  of  the  gas.  The 

exponent  «  is  found  to  be  about  1.75  for  the  permanent  gases  and  about  2  for  condensible  gases.    The  following 
are  examples:   Air  — CO2,  n=  1.968;   CO,— N2O,  «  =  2.oS;  CO2— H,  «=i.742;  CO  — O,  »  =  1.785;  H  — O, 
«=  1.755;  O  —  N,  «==  1.792.    Winkelmann's  results,  as  given  in  the  above  table,  seem  to  give  about  2  for  vapors 
diffusing  into  air,  hydrogen  or  carbon  dioxide. 
SMITHSONIAN  TABLES. 


140 


TABLES  126-127. 

DIFFUSION   OF  GASES,  VAPORS,  AND   METALS. 
TABLE  126.  —  Coefficients  of  Diffusion  for  Various  Gases  and  Vapors. 


Gas  or  Vapor  diffusing. 

Gas  or  Vapor  diffused  into. 

Temp. 

°c. 

Coefficient 
of  Diffusion. 

Authority. 

Air                                    .     . 

0 

o 
o 

0 
0 

o 

0 
0 

o 
o 

0 
0 

o 

0 
0 

o 

0 
0 
0 
0 
0 
0 
0 
0 

o 

0 

o 

0 
0 

o 

0 

8 
18 
18 

0.661 

0.1775 
0.1423 
0.1360 
0.1405 
0.1314 

0.5437 
0.1465 
0.0983 

o.i  802 

0.0995 
0.1314 
O.IOI 

0.6422 

O.I  802 

0.1872 
0.0827 

0.3054 
0.6340 

o-5384 
0.6488 

0-4593 
0.4863 
0.6254 

0-5347 
0.6788 
0.1787 

o.i357 
0.7217 
0.1710 
0.4828 
0.2390 
0.2475 
0.8710 

Schulze. 
Obermayer. 
Loschmidt. 
Waitz. 
Loschmidt. 
Obermayer. 

tt 

Loschmidt. 

Stefan. 
Obermayer. 

M 

Loschmidt. 

Obermayer. 
Stefan. 

Obermayer. 

« 
(i 

M 

« 
ft 
n 

« 
« 

Loschmidt. 
Obermayer. 
Loschmidt. 
Guglilemo. 

« 

Carbon  dioxide    .         .    . 
«            tt 
.<            « 
«            <« 
«            «< 
«            « 
«            « 

KM 

Carbon  disulphide         .     . 

Carbon  monoxide          .    . 
«              i« 

«              << 
««              «< 
<«              « 

Ether                

(« 

Carbon  monoxide      .    . 

«             « 

Hydrogen     .         ,     .     . 

Nitrous  oxide    .... 

Air  

Carbon  dioxide     .    .     . 

Air  

M 

Carbon  dioxide      .     .     . 
"       monoxide      .    . 
Ethane     

«« 

« 

(( 

(« 

«« 

Nitrous  oxide   .... 

« 

Nitrogen          

Carbon  dioxide     .    .     . 

« 

Sulphur  dioxide   .... 
Water              . 

n 

« 

*  Compiled  for  the  most  part  from  a  similar  table  in  Landolt  &  Bornstein's  Phys.  Chem.  Tab. 


TABLE  127.  —  Diffusion  of  Metals  into  Metals. 


do 

dt 


,d^v     where  x  is  the  distance  in  direction  of  diffusion;  v,  the  degree  of  concentration  of 
'dxi'   the  diffusing  metal;  /,  the  time;  A,  the  diffusion  constant  =  the  quantity  of  metal 
in  grams  diffusing  through  a  sq.  cm.    in  a  day  when  unit  difference  of  concentra- 
tion (gr.  per  cu.  cm.)  is  maintained  between  two  sides  of  a  layer  one  cm.  thick. 


Diffusing  Metal. 

Dissolving 
Metal. 

Tempera- 
ture °  C. 

k. 

Diffusing  Metal. 

Dissolving 
Metal. 

Tempera- 
ture °  C. 

k. 

Gold 

Lead     . 

555 

3-*9 

Platinum 

Lead     . 

492 

1.69 

« 

«« 

492 

3.00 

Lead    . 

Tin  .    . 

555 

3.18 

« 

H 

25i 

0.03 

Rhodium 

Lead     . 

55° 

3-°4 

« 

« 

200 

0.008 

Tin      . 

Mercury 

15 

1.22* 

« 

165 

0.004 

Lead    . 

15 

1.0* 

tt 

« 

IOO 

0.00002 

Zinc     . 

15 

1.0* 

« 

« 

Bismuth 
Tin  .    . 

555 
555 

4-52 
4.65 

Sodium 
Potassium 

• 

15 
15 

o-45* 
0.40* 

Silver       . 

41 

555 

4.14 

Gold     .    . 

• 

15 

0.72* 

From  Roberts- Austen,  Philosophical  Transactions,  i87A,  p.  383,  1896. 
*  These  values  are  from  Guthrie. 


SMITHSONIAN  TABLES. 


TABLE  128. 

SOLUBILITY  OF  INORGANIC  SALTS   IN  WATER;  VARIATION  WITH 
THE    TEMPERATURE. 

The  numbers  give  the  number  of  grams  of  the  anhydrous  salt  soluble  in  1000  grams  of  water  at 

the  given  temperatures. 


Salt. 

Temperature  Centigrade. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

zoo0 

AgN03  

A12(S04)3    .... 
A12K2(S04)4    .     .     . 
A12(NH4)2(S04)4      . 
B2O3  

1150 
3U 

le 

II 
316 

50 

595 
405 
1614 

93 
1671 
818 
149 

744 
156 

43 
540 
1050 
285 

5° 
225 
1279 

133 

970 

7 
74 

i 

260 
408 
297 
119 

'$ 

795 

7i 
204 

356 
820 

3T7 
1630 
69 
25 
1590 
73° 

1600 
335 

45 
15 

333 

6£ 

45° 
1747 
149 

J731 

819 

208 
66 

312 

*S° 
609 

85 
277 
1361 
209 
1030 

9 
92 
127 

535 
309 
422 

333 
159 

73° 

8?l 

126 

263 

357 
890 
502 
1700 
82 

*39 
1690 

805 

2I5O 
362 

66 

22 

357 
92 

745 
500 
1865 
230 
1787 
1250 

685 
918 
264 

74 
650 

343 
7i 
629 

J31 
332 
1442 
3^6 
1  1  20 
ii 
in 
128 

545 
356 
439 
372 

2IO 

754 
903 

214 
3^ 

990 
900 
l800 
96 

93 

1790 
880 

2700 
404 
84 
91 

3~82 
116 

IOIO 

565 
1973 
339 
1841 

255 

330 
84 

1140 
373 

101 

650 

390 

1523 
458 

14 
130 
129 

409 

453 
414 
270 
2418 
780 

39 

409 

$ 

1970 
in 
241 
1900 
962 

3350 

457 

124 
40 
408 
142 

"53 
650 
2080 
472 
1899 
1598 
295 

402 

?6 
760 

1170 
401 

i45 
670 

292 

453 
1600 

639 
1360 
18 
148 
130 
575 
456 

4~S8 

2970 
810 
1058 

(laq) 
363 

1235 
960 

2  2OO 
I27 

639 
2050 
1049 

4OOO 
521 

159 

436 
171 

935 

2185 
644 
1949 

336 

820 

3151 

486 

"3 

1210 

429 
I97 
690 

522 

T855 
1400 

22 
I65 
133 

504 
504 

3540? 
844 

1160 
105 

475 
367 

1050 
2480 
145 

2280 
1140 

4700 

59i 
248 

211 
62 
464 

.$ 

940 
2290 
838 
I999 
1791 
390 

550 
139 
860 
1270 

455 
260 
710 

5°5 
600 
1760 
1099 
1460 
26 
182 
'38 
610 

550 

552 

4300? 
880 
1170 

200 

464 

371 
1470 
1150 
2830 
164 

2570 
1246 

270 

494 
236 
1417 
950 

2395 
1070 
2050 

457 

560 
173 

'& 

325 

73° 

1840 
1380 
1510 

£ 

144 

596 
602 

513°? 
916 

244 

458 
375 

3230 
949 
1360 

6500 
73i 

352 
95 
524 
270 
1470 
960 
2500 
J34Q 
2103 
2078 

535 
1040 

5258 
506 

243 
955 
1400 

5io 
396 
751 
730 

1920 
1690 
1590 
38 
214 

& 

642 
656 

5800 

953 
1185 

3H 

$ 

'75° 
1240 
3860 

2950 
1480 

7600 
808 

5~56 
306 

1527 

2601 
1630 
2149 

6~27 
1050 

43° 
37i 

1470 
538 
475 
771 

2010 

2040 

1680 

& 

689 
713 

7400 
992 

408 

452 

385 

1610 

9IOO 
89I 
1540 

342 
1590 
1030 
2705 
1970 
2203 

735 
1060 

5357 

540 
1050 
1560 

566 
560 
791 

1020 

2090 
2460 
1780 

52 
241 

175 

730 

7~38 
773 

8710 

1033 
1205 

523 

452 
39i 
2040 
1260 
4330 

988 
3020 
1755 

BaCl2  
Ba(NO3)2  .... 
CaCl2  
CoCl2  

CsCl  .  . 

CsNO3  
Cs2SO4  

Cu(NO3)2  .... 
CuSO4  .  ... 

FeCl2  .  . 

Fe2Cl6  

FeSO4  .... 

HgCl2  
KBr  .  . 

K2CO8  
KC1  

KC1O3  
K2CrO4  
K2Cr2O7  .... 
KHCO3  . 

KI  .  .  . 

KNO3 

KOH  

K2PtCl6  .  .  . 

K2SO4  .  . 

LiOH  

MgCl2  

MgS04    .     .      (7aq) 
.    .      (6aq) 
NH4C1    
NH4HC03.     .    .    . 
NH4NO3     .... 
(NH4)2S04.     .     .     . 
NaBr  

Na2B4O7      .... 
Na2CO3  .     .     (roaq) 
.     .      (;aq) 
NaCl 

NaClO3  

Na2CrO4  .... 
Na2Cr207  .... 
NaHC03  .... 
Na2HPO4  .... 
Nal  

NaNO3  .  .  .  . 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


142  TABLES  128  (concluded}'  130. 

SOLUBILITY   OF   SALTS   AND   CASES    IN   WATER. 

TABLE  128  (concluded)  —  Solubility  of  Inorganic  Salts  in  Water  ;  Variation  with  the  Temperature. 

The  numbers  give  the  number  of  grams  of  the  anhydrous  salt  soluble  in  1000  grams  of  water  at 

the  given  temperatures. 


Salt. 

Temperature  Centigrade. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

•    100° 

NaOH      
Na4P2O7  
Na2SO8    .     .     .   -.     . 

420 

32 
141 

5° 
196 

525 
272 

361 

770 

'95 

364 
442 

395 

7 

2 

39 
27 
442 
948 

5'5 
39 

90 

f5 
610 
600 

6 

444 
844 

33° 
426 

483 
549 

10 

2 
62 

37 

1090 
62 
287 
194 

447 
700 
640 

8 

523 
911 

$ 

539 

10 

708 
14 

~936 
49 

1190 
99 

400 

847 
680 

425 

12 
607 
976 
813 

535 

12 
876 
20 

5 

'43 
62 

1290 
135 
495 
[482 

1026 
720 

l\ 

1035 
1167 

$ 

14 
9^3 

30 

46 

76 

2069 
700 

H5° 
174 

468 

1697 
760 
502 
2O 

787 
1093 

IS56 

63I 

744 
17 
926 

5i 

25 

3°4 
92 

7~68 

1740 

220 

455 
2067 
810 
548 
24 
880 
"55 

2OOO 
674 

831 
21 
940 

16 

10 

462 
109 

104 

255 

445 

594 

28 

977 
1214 
2510 

7H 
896 
25 
956 

ii 
435 

127 

72 

8*90 

3130 
3OO 

437 
2488 

6~32 

1076 

1272 
3090 
750 
924 

3° 
972 

16 

IIIO 

146 
69 

860 

429 

2542 

688 

1174 
i33i 

3750 
787 
962 

34 
990 

20 

2000 

? 

92O 

330 
427 
2660 

776 
48 

1270 

1389 

4520 

818 
1019 
40 
ion 

4140 
47 
7~85 

Na2SO4    .     .     (ioaq) 
.     .       (7aq) 
Na2S2O3  
NiCl2                 .     .     . 

NiSO4               .     .     . 

PbBr2  

Pb(NOg)a     .... 
RbCl 

RbNO3    

RboSCXt 

SrCl2                       .     . 

SnI2     
Sr(N03)2      .... 
Th(S04)2      .     .(9aq) 

TIQ'  ,  .  :  :(4.aq! 

T1NO8          .... 

T12S04     
Yb2(S04)3    .... 
Zn(N08)2      .... 
ZnSO4      

TABLE  129.  -Solubility  of  a  Few  Organic  Salts  in  Water;  Variation  with  the  Temperature. 


Salt. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

9o° 

100° 

H2(C02)2  .... 
H2(CH2.CO2)2  .  . 
Tartaric  acid  .  .  . 
Racemic  "  ... 
K(HCO2)  .... 
KH(C4H4O4)  .  .  . 

36 

28 

1150 

92 

2900 
3 

53 
45 
1260 
140 

4 

IO2 
69 

1390 
206 
3350 

6 

1560 
291 

9 

228 
162 
1760 

433 
3810 

13 

32I 
244 
1950 

595 
18 

44  S 
358 

2150 
783 
455° 
24 

635 

5" 

2440 

999 
32 

978 
708 
2730 

1250 
575° 
45 

1200 
3070 

57 

1209 
3430 

1850 
7900 
69 

TABLE  130. -Solubility  of  Gases  In  Water;  Variation  with  the  Temperature. 

The  table  gives  the  weight  in  grams  of  the  gas  which  will  be  absorbed  in  1000  grams  of  water 
when  the  partial  pressure  of  the  gas  plus  the  vapor  pressure  of  the  liquid  at  the  given  tempera- 
ture equals  760  mm. 


Gas. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

02 

H2 

N2 
Br2 

.0705 
.00192 
.0293 
43'- 

•0551 
.00174 
.0230 
248. 

•0443 
.OOl6O 
.0189 
148. 

.0368 
.00147 
.Ol6l 
94. 

.0311 

.00138 
.0139 
62. 

.0263 
.00129 

.0121 
40. 

.0221 
.001  18 
.OIO5 
28. 

.Ol8l 
.00102 
.0089 

1  8. 

•0135 
.00079 
.0069 
ii. 

C12 
C02 

3-35 

9-97 
2.32 

7.29 

& 

4-59 
0.97 

3-93 
0.76 

3-30 
0.58 

2.79 

2.23 

H2S 

7.10 

5-30 

3-98 

_ 

_ 

— 

— 

— 

— 

NH8 
SO2 

ft 

689. 
162. 

535- 

"3- 

M: 

54- 

- 

- 

- 

- 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  131.  143 

CHANCE. OF  SOLUBILITY  PRODUCED  BY  UNIFORM  PRESSURE.* 


CdSO48/3H2Oat25° 

ZnSO4.7H2O  at  25° 

Mannite  at  24.05° 

NaCl  at  24.05° 

Pressure 

Is 

i 

iU  • 

1 

1L 

| 

|fc   . 

1 

in 
atmos- 
pheres. 

•3o£ 

jjgg 

•5 

ft 

2 

JjfJ 

jq 

9 

V 

H 

11* 

lla 

1 

i 

iS 

;^a 

i 

"&§ 

i 

«g,  8 

y^§ 

J6S 

§ 

c3 

1 

6 

(2 

c3 

1 

1 

I 

76.80 

— 

57-95 

— 

20.66 

— 

35-90 

— 

500 

78.01 

+  1.57 

57.87 

0.14 

21.14 

+  2.32 

36-55 

+  1.81 

1000 

78.84 

+  2.68 

57.65 

—  0.52 

21.40 

+  3-57 

37.02 

4-3-12 

1500 

— 

— 

— 



21.64 

+  4.72 

37.36 

+  4.07 

*  E.  Cohen  and  L.  R.  Sinnige,  Z.  physik.  Chem.  67,  p.  432,  1909;  69,  p.  102,  1909.     E.  Cohen,  K. 
C.  Euwen,  ibid.  75,  p.  257,  1911.    These  authors  give  a  critical  resume  of  earlier  work  along  this  line. 


Inouye  and 


SMITHSONIAN  TABLES. 


144 


TABLE  132. 
ABSORPTION  OF  GASES  BY  LIQUIDS. 


ABSORPTION  COEFFICIENTS,  at>  FOR  GASES  IN  WATER. 

Temperature 

Centigrade. 

t 

Carbon 
dioxide. 
C02 

Carbon 
monoxide. 
CO 

Hydrogen. 
H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N2O 

Oxygen. 

O 

1.797 

0.0354 

O.O2IIO 

0.02399 

0.0738 

1.048 

0.04925 

5 

1.4 

SO 

•0315 

.O2O22 

.02134 

.0646 

0.8778 

•04335 

10 

I.I 

8<5 

.0282 

.01944 

.01918 

.0571 

0.7377 

.03852 

IS 

1.002 

.0254 

.Ol875 

.01742 

•0515 

0.6294 

•03456 

20 

0.901 

.0232 

.01809 

.01599 

.0471 

0-5443 

•03137 

25 

0.772 

.0214 

•01745 

.01481 

.0432 

— 

.02874 

3° 

.O2OO 

.Ol6cjO 

•01370 

.0400 

— 

.02646 

40 

0.506 

.0177 

.01644 

.01195 

•0351 

- 

.02316 

5° 

.Ol6l 

.01608 

.01074 

•°3  1  S 

— 

.02080 

100 

0.244 

.0141 

.OI600 

.01011 

.0263 

— 

.01690 

Temperature 
Centigrade. 

t 

Air. 

Ammonia. 
NH3 

Chlorine. 
Cl 

Ethylene. 
C2H4 

Methane. 
CH4 

Hydrogen 
sulphide. 
H2S 

Sulphur 
dioxide. 
S02 

O 

0.02471 

II74.6 

3-036 

0.2563 

0-05473 

4-371 

79-79 

5 

.02179 

971-5 

2.808 

•2I53 

.04889 

3-965 

67.48 

10 

•01953 

840.2 

2-585 

•1837 

.04367 

3-586 

56.65 

15 

•01795 

756.0 

2.388 

.1615 

•03903 

3-233 

47.28 

20 

.01704 

683.1 

2.156 

.1488 

•03499 

2.905 

39-37 

25 

610.8 

1.950 

" 

.02542 

2.604 

32-79 

ABSORPTION  COEFFICIENTS,  at,  FOR  GASES  IN  ALCOHOL,  C2H5OH. 

Centigrade.      Carbon 

f               dioxide. 
C03 

Ethylene. 
C2H4 

Methane.   Hydrogen. 
CH4              H 

Nitrogen. 

Nitric 
oxide. 
NO 

Nitrous 
oxide. 
N20 

Hydrogen    Sulphur 
sulphide,     dioxide. 
H2S            SO2 

o           4.329 

3-595 

0.5226       0.0692 

0.1263 

0.3161 

4.190 

17.89       328.6 

5          3-891 

3-323 

.5086         .0685 

.1241 

.2998 

3-838 

14.78        251.7 

10           3.514 

3.086 

•4953        -0679 

.1228 

.2861 

3-525 

11.99        I90-3 

15           3-199 

2.882 

.4828        .0673 

.1214 

.2748 

3-215 

9-54       144-5 

20                2.946 
25                2.756 

2.713 
2.578 

.4710       .0667 
.4598        .0662 

.1204 
.1196 

.2659 
•2595 

3-015 
2.819 

7.41       114.5 
5.62        99.8 

*  This  table  contains  the  volumes  of  different  gases,  supposed  measured  at  o°  C.  and  76  centimeters'  pressure,  which 
unit  volume  of  the  liquid  named  will  absorb  at  atmospheric  pressure  and  the  temperature  stated  in  the  first  column. 
The  numbers  tabulated  are  commonly  called  the  absorption  coefficients  for  the  gases  in  water,  or  in  alcohol,  at  the 
temperature  t  and  under  one  atmosphere  of  pressure.  The  table  has  been  compiled  from  data  published  by  Bohr  & 
Bock,  Bunsen,  Carius,  Dittmar,  Hamberg,  Henrick,  Pagliano  &  Emo,  Raoult,  Schbnfeld,  Setschenow,  and  Winkler. 
The  numbers  are  in  many  cases  averages  from  several  of  these  authorities. 

NOTB.  —  The  effect  of  increase  of  pressure  is  generally  to  increase  the  absorption  coefficient.  The  following  is 
approximately  the  magnitude  of  the  effect  in  the  case  of  ammonia  in  alcohol  at  a  temperature  of  23°  C. : 

(  P   =45  cms.        50  cms.        55  cms.        60  cms.        65  cms. 

\  0,3  =  69  74  79  84  88 

According  to  Setschenow  the  effect  of  varying  the  pressure  from  45  to  85  centimeters  in  the  case  of  carbonic  acid  in 
water  is  very  small. 
SMITHSONIAN  TABLES. 


TABLES   133-135. 
CAPILLARITY. -SURFACE    TENSION  OF  LIQUIDS.* 


TABLE  133.— Water  and  Alcohol  in  Contact  with  Air. 


TABLE  135.— Solutions  of  Salts  In 
Water,  t 


Surface  tension 
in   dynes    per 

Surface  tension 
in   dynes   per 

Surface 
tension 

Salt  in 
solution. 

Density. 

Temp. 
C° 

Tension 
in  dynes 

centir 

neter. 

centu 

neter. 

per  cm. 

Temp. 
C. 

Temp. 

Temp. 

o. 

timeter. 

Water. 

Ethyl 
alcohol. 

Water. 

Ethyl 
alcohol. 

Water. 

BaCl2 

1.2820 
1.0497 

15-16 
15-16 

8l.8 

77-5 

CaCl2 

1'3511 

!9 

95-o 

0° 

5 

75-6 

74-9 

23-5 
23.1 

40° 

45 

7O.O 
69.3 

2O.O 
!9-5 

80° 

«S 

64-3 
6,3-6 

HC1 

1-2773 
I.II90 

19 

20 

90.2 
73-6 

10 

74.2 

22.6 

5° 

68.6 

I9.I 

90 

62.9 

1  .0007 

2O 

74-5 

15 

20 

73-5 
72.8 

22.2 
21-7 

£ 

67.8 
67.1 

18.6 
18.2 

95 

100 

62.2 
61.5 

KC1 

1.0242 
1.1699 

2O 
15-16 

75-3 
82.8 

25 
3° 
35 

72.1 
71.4 
70.7 

21-3 
20.8 

20.4 

65 
70 

75 

66.4 
65.7 
65.0 

17.8 

'7-3 
16.9 

MgCl2 

« 

I.IOII 

1.0463 

1.2338 
1.1694 

15-16 
15-16 
15-16 
15-16 

80.  i 
78.2 
90.1 
85.2 
*?X  o 

NaCl 

1.1932 

2O 

85.8 

1.1074 

20 

80.5 

" 

1.0360 

2O 

77-6 

NH4C1 

1.0758 

16 

84-3 

TABLE  134. 

-Miscellaneous  Liquids  In  Contact  with  Air. 

SrClo 

1-0535 

1.0281 

16 
16 

81.7 
78.8 

Qc  A 

Liquid. 

Surface 

Authority. 

« 

1-J114 
I.I2O4 

15-16 

79-4 

Temp. 
C° 

tension 
in  dynes 

K2CO8 

1.0567 

1-3575 

15-16 
15-16 

77.8 
90.9 

per  cen 

1.1576 

15-16 

81.8 

timeter 

« 

TMo   CT) 

i  .0400 

15-16 

77-5 

1.1329 

14-15 

79-3 

Aceton    .... 
Acetic  acid  .     .     . 
Amyl  alcohol  .     . 

1  6.8 

17.0 
15.0 

23-3 
30.2 
24.8 

Ramsay-Shields. 
Average  of  various. 

K 

KNO3 

1.0605 
1.0283 
1.1263 

14-15 
14-15 
14 

77-8 
77-2 
78.9 

Benzole  .... 

15.0 

28.8 

« 

" 

1.0466 

H 

77-6 

Butyric  acid     .     . 

15.0 

28.7 

« 

NaNO3 

1.3022 

12 

83-5 

Carbon  disulphide 
Chloroform      .     . 
Ether  

2O.O 
20.0 
2O.O 

30-5 
28.3 
18.4 

Quincke. 

Average  of  various. 
« 

CuSO4 
«( 

1.1311 

I-I775 
1.0276 

12 
15-16 
I5-I6 

80.0 
78.6 
77.0 

Glycerine 

17.0 

•*•"•? 

63.14 

Hall. 

H2SO4 

1.8278 

15 

63.0  ? 

Hexane  .... 

o.o 

21.2 

Schiff. 

1-4453 

'5 

79-7 

» 

68.0 

14.2 

1.2636 

15 

79-7 

Mercury  .... 
Methyl  alcohol     . 
Olive  oil.     .     .     . 

1  8.0 
15.0 

20.0 

520.0 
24.7 
34.7 

Average  of  various. 
« 

K2S04 
« 

MgSO4 

1.0744 
1.0360 
1.2744 

I5-I6 
15-16 
15-16 

78.0 

77-4 
83.2 

Petroleum  .     .     . 
Propyl  alcohol 

2O.O 

S-8 

25-9 
25-9 

Magie. 
Schiff. 

M 

Mn2SO4 

i.  0680 
1.1119 

15-16 
15-16 

77-8 
79.1 

« 

H 

97.1 

18.0 

« 

" 

1.0329 

15-16 

77-3 

Toluol     .... 

15.0 

29.1 

« 

ZnSO4 

1.3981 

I5-l6 

833 

it 

109  8 

18  9 

« 

« 

1.2830 

15-16 

80.7 

Turpentine  .     .     . 

2I.O 

28.5 

Average  of  various. 

1.1039 

15-16 

77-8 

*  This  determination  of  the  capillary  constants  of  liquids  has  been  the  subject  of  many  careful  experiments,  but  the 
results  of  the  different  experimenters,  and  even  of  the  same  observer  when  the  method  of  measurement  is  changed, 
d_o  not  agree  well  together.  The  values  here  quoted  can  only  be  taken  as  approximations  to  the  actual  values  for  the 
liquids  in  a  state  of  purity  in  contact  with  pure  air.  In  the  case  of  water  the  values  given  by  Lord  Rayleigh  from  the 
wave  length  of  ripples  (Phil.  Mag.  1890)  and  by  Hall  from  direct  measurement  of  the  tension  of  a  flat  film  (Phil.  Mag. 
1893)  have  been  preferred,  and  the  temperature  correction  has  been  taken  as  0.141  dyne  per  degree  centigrade.  The 
values  for  alcohol  were  derived  from  the  experiments  of  Hall  above  referred  to  and  the  experiments  on  the  effect  of 
temperature  made  by  Timberg  (Wied.  Ann.  vol.  30). 

The  authority  for  a  few  of  the  other  values  given  is  quoted,  but  they  are  for  the  most  part  average  values  derived 
from  a  large  number  of  results  published  by  different  experimenters. 

t  From  Volkmann  (Wied.  Ann.  vol.  17,  p.  353). 

SMITHSONIAN  TABLES. 


146 


TABLES  136-138. 

TENSION   OF   LIQUIDS. 
TABLE  136.  —Surface  Tension  of  Liquids.' 


•  

Liquid. 

Specific 
gravity. 

Surface  tension  in  dynes  per  cen- 
timeter of  liquid  in  contact  with  — 

Air. 

Water. 

Mercury. 

I.O 

13-543 
1.2687 
1.4878 
0.7906 
0.9136 
0.8867 

•7977 

I.IO 

1.1248 

75-o 

S'3-0 

3°-5 
(31-8) 
(24.1) 
34-6 
28.8 
29.7 

(72.9) 
69.9 

o.o 

392.0 
41.7 
26.8 

18.6 

"•5 

(28.9) 

(392) 
0 

(387) 
(415) 

364 
3*7 
241 
271 

(392) 
429 

Hyposulphite  of  soda  solution      .... 

TABLE  137.  — Surface  Tension  of  Liquids  at  Solidifying  Point,  t 


Substance. 

Tempera- 
ture of 
solidifi- 
cation. 
Cent.0 

Surface 
tension  in 
dynes  per 
centimeter. 

Substance. 

Tempera- 
ture of 
solidifi- 
cation. 
Cent.0 

Surface 
tension  in 
dynes  per 
centimeter. 

Platinum 

2000 

1691 

Antimony 

432 

249 

Gold 

I2OO 

1003 

Borax    .... 

IOOO 

216 

Zinc 

360 

877 

Carbonate  of  soda 

1000 

2IO 

Tin 

230 

Chloride  of  sodium 

- 

116 

Mercury 

—40 

588 

Water   .... 

o 

87-9J 

Lead     . 

33° 

457 

Selenium 

217 

71.8 

Silver    . 

1000 

427 

Sulphur 

III 

42.1 

Bismuth 
Potassium 

263 
5» 

1390 

Phosphorus  .        .        . 
Wax      .... 

^ 

42.0 
34-1 

Sodium 

90 

258 

TABLE  138.  —  Tension  of  Soap  Films. 


Elaborate  measurements  of  the  thickness  of  soap  films  have  been  made  by  Reinold  and 
Rucker.  ||  They  find  that  a  film  of  oleate  of  soda  solution  containing  i  of  soap  to  70  of 
water,  and  having  3  per  cent  of  KNO3  added  to  increase  electrical  conductivity,  breaks  at 
a  thickness  varying  between  7.2  and  14.5  micro-millimeters,  the  average  being  12.1  micro- 
millimeters.  The  film  becomes  black  and  apparently  of  nearly  uniform  thickness  round 
the  point  where  fracture  begins.  Outside  the  black  patch  there  is  the  usual  display  of 
colors,  and  the  thickness  at  these  parts  may  be  estimated  from  the  colors  of  thin  plates 
and  the  refractive  index  of  the  solution  (vide  Newton's  rings,  Table  222). 

When  the  percentage  of  KNO3  is  diminished,  the  thickness  of  the  black  patch  increases. 
For  example,  KNOs  =3  I  0.5  o.o 

Thickness  ==12.4  13.5  14.5  22.1  micro-mm. 

A  similar  variation  was  found  in  the  other  soaps. 

It  was  also  found  that  diminishing  the  proportion  of  soap  in  the  solution,  there  being 
no  KNOs  dissolved,  increased  the  thickness  of  the  film. 

i  part  soap  to  30  of  water  gave  thickness  21.6  micro-mm. 

i  part  soap  to  40  of  water  gave  thickness  22.1  micro-mm. 

i  part  soap  to  60  of  water  gave  thickness  27.7  micro-mm. 

I  part  soap  to  80  of  water  gave  thickness  29.3  micro-mm. 


*  This  table  of  tensions  at  the  surface  separating  the  liquid  named  in  the  first  column  and  air,  water  or  mercury 
as  stated  at  the  head  of  the  last  three  columns,  is  from  Quincke's  experiments  (Pogg.  Ann.  vol.  139,  and  Phil.  Mag. 
1871).  The  numbers  given  are  the  equivalent  in  dynes  per  centimeter  of  those  obtained  by  Worthington  from 
Quincke's  results  (Phil.  Mag.  vol.  20,  1885)  with  the  exception  of  those  in  brackets,  which  were  not  corrected  by 
Worthington ;  they  are  probably  somewhat  too  high,  for  the  reason  stated  by  Worthington.  The  temperature  was 
about  20°  C. 

t  Quincke,  "  Pogg.  Ann."  vol.  135,  p.  661. 

t  It  will  be  observed  that  the  value  here  given  on  the  authority  of  Quincke  is  much  higher  than  his  subsequent 
measurements,  as  quoted  above,  give. 

H  "Proc.  Roy.  Soc."  1877,  and  "  Phil.  Trans.  Roy.  Soc."  1881,  1883,  and  1893. 

NOTE.  —  Quincke  points  out  that  substances  may  be  divided  into  groups  in  each  of  which  the  ratio  of  the  surface 
tension  to  the  density  is  nearly  constant.  Thus,  if  this  ratio  for  mercurv  be  taken  as  unit,  the  ratio  for  the  bromides 
and  iodides  is  about  a  half  :  that  of  the  nitrates,  chlorides,  sugars,  and  fats,  as  well  as  the  metals,  lead,  bismuth,  and 
antimony,  about  i ;  that  of  water,  the  carbonates,  sulphates,  and  probably  phosphates,  and  the  metals  platinum,  goid, 
silver,  cadmium,  tin,  and  copper,  2 ;  that  of  zinc,  iron,  and  palladium,  3;  and  that  of  sodium,  6. 

SMITHSONIAN  TABLES. 


TABLE  139. 
VAPOR    PRESSURES. 


The  vapor  pressures  here  tabulated  have  been  taken,  with  one  exception,  from  Regnault's  results. 
The  vapor  pressure  of  Pictet's  fluid  is  given  on  his  own  authority.  The  pressures  are  in  centimeters  of 
mercury . 


Tem- 
pera- 
ture 
Cent. 

Acetone. 
C3H60 

Benzol. 
C6H6 

Carbon 
bisul- 
phide. 
CS8 

Carbon 
tetra- 
chloride. 
CC14 

Chloro- 
form. 

CHClg 

Ethyl 
alcohol. 
C2H60 

Ethyl 
ether. 
C4H100 

Ethyl 
bromide. 
C2HcBr 

Methyl 
alcohol. 
CH40 

Turpen- 
tine. 
C10H6 

—25° 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

4.41 

.41 

_ 

—  20 

- 

.58 

4-73 

.98 

- 

•33 

6.89 

5-92 

•63 

- 

—15 

- 

.88 

6.16 

'•35 

- 

•5i 

8-93 

7.8l 

•93 

- 

—  IO 

— 

1.29 

7-94 

1.85 

— 

•65 

11.47 

10.15 

1.35 

— 

—5 

— 

1.83 

10.13 

2.48 

- 

.91 

14.61 

13.06 

1.92 

— 

0 

_ 

2-53 

12.79 

3-29 

5-97 

1.27 

18.44 

16.56 

2.68 

.21 

5 

— 

3-42 

16.00 

4-32 

1.76 

23.09 

20.72 

3-69 

— 

10 

15 

; 

4-52 
5.89 

19.85 
24.41 

5.60 
7.17 

10.05 

2.42 
3-30 

28.68 
35-36 

25.74 
31.69 

5.01 
6.71 

.29 

20 

17.96 

7.56 

29.80 

9.10 

16.05 

4-45 

43.28 

38.70 

8.87 

44 

25 

22.63 

9-59 

36.11 

11-43 

20.02 

5-94 

52.59 

46.91 

1  1.  60 

_ 

3° 
35 
40 

28.10 
34-52 
42.01 

I2.O2 

'4-93 
18.36 

43-46 
5*-97 
61-75 

14.23 

17-55 
21.48 

2475 
30.35 
36.93 

7.85 
10.29 
13-37 

63.48 
76.12 
90.70 

56.45 
67.49 
80.19 

15.00 
19.20 
24-35 

.69 

1.08 

45 

50-75 

22.41 

72.95 

26.08 

44.60 

17.22 

107.42 

94-73 

30.61 

— 

50 

62.29 

27.14 

85.71 

3M4 

53-50 

21.99 

126.48 

111.28 

38.17 

1.70 

& 

72.59 
86.05 

32-64 
39.01 

100.16 
116.45 

44-74 

63-77 

75-54 

27.86 
35-02 

148.11 
172.^0 

130.03 
151.19 

47.22 
57-99 

2^5 

65 
70 

101.43 
118.94 

46-34 
5474 

134-75 
1  55-2  1 

52.87 
62.11 

88.97 
104.21 

43-69 
54." 

199.89 
230.49 

174-95 
201.51 

70.73 
85-71 

4.06 

75 

138.76 

64.32 

177.99 

72.57 

121.42 

66.55 

264.54 

231.07 

103.21 

- 

80 

161.10 

203.25 

84-33 

140.76 

81.29 

302.28 

263.86 

123-85 

6.13 

85 
90 

95 

186.18 
214.17 
245-28 

8746 
101.27 
116.75 

231.17 
261.91 
296.63 

97-51 
112.23 
128.69 

162.41 
186.52 
213.28 

98.64 
118.93 
142.51 

343-95 
389^3 
440.18 

300.06 
339-89 
383.55 

147.09 
174.17 
205.17 

9.06 

100 

279.73 

134.01 

332.51 

146.71 

242.85 

I69-75 

495-33 

431-23 

240.51 

13.11 

105 
no 

"5 

317.70 
359-40 
405.00 

153.18 

174.44 
197.82 

372.72 
416.41 
463-74 

166.72 
188.74 
212.91 

275.40 
311.10 

201.04 
236.76 
277-34 

555-62 
621.46 
693-33 

483.12 
539-40 
600.24 

280.63 
325-96 
376.98 

18.60 

1  20 

454.69 

223.54 

514.88 

239-37 

392-57 

323-I7 

771.92 

665.80 

434.18 

25.70 

125 

508.62 

251.71 

569-97 

268.24 

438.66 

374-69 

_ 

736.22 

498.05 

_ 

130 

566.97 

282.43 

629.16 

299.69 

488.51 

432.3° 

— 

811.65 

569-!  3 

34.90 

629.87 

3I5-85 

692.59 

333-86 

542.25 

496.42 

- 

892.19 

647-93 

- 

140 

697-44 

352-07 
391.21 

760.40 
832.69 

370.90 
411.00 

600.02 
661.92 

567.46 
645-80 

- 

977.96 

733-71 
830.89 

46.40 

150 

_ 

433-37 

909.59 

454-31 

728.06 

731.84 

- 

_ 

936-13 

60.50 

155 

- 

478.65 

501.02 

798.53 

825.92 

- 

- 

68.60 

165 

_ 

527-I4 
568.30 

— 

55I-3I 
605.38 

873.42 
952.78 

~ 

_ 

_ 

_ 

77-50 

170 

" 

634.07 

663.44 

SMITHSONIAN  TABLES. 


148 


TABLE   1  39  (continued). 

VAPOR   PRESSURES. 


Tem- 
pera- 
ture, 
Centi- 
grade. 

Ammonia. 
NH3 

Carbon 
dioxide. 
C02 

Ethyl 
chloride. 
C2H5C1 

Ethyl 
iodide. 
C2H5I 

Methyl 
chloride. 

CHgCl 

Methylic 
ether. 
C2H60 

Nitrous 
oxide. 
N20 

Pictet's 
fluid. 
64SO«4- 
44C02"by 
weight 

Sulphur 
dioxide. 
S02 

Hydrogen 
sulphide. 
H2S 

—30° 

86.61 

- 

11.02 

- 

57.90 

57.65 

- 

58.52 

28.75 

- 

—25 

—  20 
—  10 

110.43 
139.21 

I73-65 
214.46 

1300.70 
1514.24 

1758.25 
2034.02 

14.50 

18.75 
23.96 
3O.2I 

- 

71.78 
88.32 
107.92 
130.96 

7I.6l 

88.20 
107.77 
130.66 

1569.49 
1758.66 
1968.43 
22OO.8O 

67.64 

74.48 
89.68 
101.84 

37.38 
47.95 
60.79 
76.25 

374-93 
443-85 
5T9-65 
608.46 

—  5 

264.42 

2344.13 

37.67 

— 

I57.87 

157-25 

2457.92 

121.60 

94.69 

706.60 

0 

318.33 

2690.66 

46.52 

4.19 

189.10 

187.90 

2742.10 

139.08 

116.51 

820.63 

5 

383-03 

3075.38 

56.93 

5-41 

225.11 

222.90 

3055-86 

167.20 

142.11 

949-08 

10 
15 

20 

45740 
543-34 
638.78 

3499.86 
3964.69 
4471.66 

6r.n 
83.26 
99.62 

6.92 
8.76 
II.OO 

266.38 

3I3-4I 
366.69 

262.90 
307.98 
358.60 

3401.91 

3783-17 
4202.79 

193.80 
226.48 
258.40 

171.95 

206.49 
246.20 

1089.63 
1244.79 

25 

747.70 

5020.73 

118.42 

13.69 

426.74 

415.10 

4664.14 

297.92 

291.60 

1601.24 

30 

870.10 

5611.90 

139.90 

16.91 

494.05 

477.8o 

5  1  70.85 

338.20 

343-18 

1803.53 

35 

1007.02 

6244.73 

164.32 

20.71 

569-II 

— 

6335.98 

383.80 

401.48 

2002.43 

40 

"59-53 

6918.44 

191.96 

25-17 

— 

— 

434.72 

467.02 

2258.25 

45 

7631.46 

223.07 

30.38 

— 

— 

— 

478.80 

540.35 

2495-43 

50 

1515.83 

- 

257-94 

36.40 

- 

_ 

_ 

521.36 

622.00 

2781.48 

g 

1721.98 
1948.21 

_ 

266.84 
340.05 

43-32 
51.22 

— 

— 

— 

712.50 
812.38 

3069-07 

3374-02 

65 

2196.51 

- 

387-85 

- 

- 

.     - 

- 

922.14 

3696.15 

70 

2467.55 

-~ 

440.50 

— 

— 

— 

— 

— 

- 

4035-32 

75 

2763.00 

- 

498.27 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

80 

3084.31 

- 

561.41 

- 

- 

- 

- 

- 

- 

_ 

85 

3433-09 

— 

630.16 

— 

— 

— 

— 

— 

_ 

_ 

90 

3810.92 

— 

704.75 

— 

— 

— 

_ 

_ 

_ 

_ 

95 

4219-57 

— 

785.39 

- 

- 

- 

- 

- 

- 

- 

100 

4660.82 

872.28 

- 

- 

- 

- 

- 

- 

- 

SMITHSONIAN  TABLES. 


TABLES  140-141. 
VAPOR   PRESSURE. 


I49 


TABLE  140.  -Vapor  Pressure  oi  Ethyl  Alcohol.* 


Temp.  C. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Vapor  pressure  in  millimeters  of  mercury  at  o°  C. 

0° 

10 
20 
30 

40 

£ 

70 

12.24 

23.78 
44.00 
78.06 

I33-70 
22O.OO 

350-30 
541.20 

13.18 

25-31 
46.66 
82.50 

140-75 
230.80 
366.40 
564-35 

H.I5 

27.94 

49-47 
87.17 

148.10 
242.50 
383-  I0 
588.35 

15.16 
28.67 

52-44 
92.07 

155.80 
253.80 
400.40 
613.20 

16.21 

30.50 
55.56 
97.21 

163.80 
265.90 

418.35 
638.95 

I7-3I 
32-44 
58.86 
I02.6o 

172.20 
278.60 
437-oo 
665.55 

18.46 

34-49 
62.33 
108.24 

181.00 
291.85 

456.35 
693.10 

19.68 
36-67 
65-97 
114.15 

190.10 
305.65 
476.45 
721.55 

20.98 

38.97 
69.80 
120.35 

199.65 
3I9-95 
497-25 
751.00 

22.34 
41.40 

73-83 
126.86 

209.60 

334.85 
518.85 

781.45 

From  the  formula  log/  =  a  -\-  ba*  -\-  c{&  Ramsay  and  Young  obtain  the  following  numbers.t 

Temp.  C. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Vapor  pressure  in  millimeters  of  mercury  at  o°  C. 

0° 

100 
200 

12.24 
1692.3 
22182. 

23-73 

2359-8 
26825. 

43-97 
3223.0 
32196. 

78.11 
4318.7 
38389- 

I33-42 
5686.6 
455I9- 

219.82 
7368.7 

350-21 
9409.9 

540.91 
11858. 

8n.8i 
14764. 

1186.5 
18185. 

TABLE  141.— Vapor  Pressure  of  Methyl  Alcohol. T 


0 

A 
H 

0° 

1° 

2° 

3° 

4° 

6° 

6° 

7° 

8° 

9° 

Vapor  pressure  in  millimeters  of  mercury  at  o°  C. 

0° 

10 
20 

29-97 
53.8 
94-o 

31.6 
57-0 
99-2 

g 

104.7 

35-6 
63-8 
110.4 

37.8 
67-5 
116.5 

40.2 
71.4 
122.7 

42.6 

75-5 
129.3 

45-2 
79.8 
136.2 

47-9 
84-3 
143-4 

50.8 
89.0 
151.0 

30 

40 

£ 

158.9 

259-4 
409.4 

624-3 

167.1 
271.9 
427.7 
650.0 

175-7 
285.0 
446.6 
676.5 

184.7 

298-5 
466.3 
703.8 

194.1 
312.6 
486.6 
732.0 

203.9 
327.3 
5077 
761.1 

214.1 
342.5 
529.5 
791.1 

224.7 

358.3 
352-0 
822.0 

235-8 
374-7 
575-3 

247-4 
39!-7 
599-4 

*  This  table  has  been  compiled  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc.  vol.  47,  and  Phil. 
Trans.  Roy.  Soc.,  1886). 

t  In  this  formula  a  =  5.0720301;  log  &  =  ~2. 6406131]  log  c  =  0.6050854 ;  log  o  =  0.003377538 ;  log /3  =  7.99682424 
(c  is  negative). 

t  Taken  from  a  paper  by  Dittmar  and  Fawsitt  (Trans.  Roy.  Soc.  Edin.  vol.  33). 
SMITHSONIAN  TABLES. 


150 


TABLE  142. 
VAPOR  PRESSURE/ 

Carbon  Bisulphide,  Chlorobenzene,  Bromobenzene,  and  Aniline. 


Temp. 

0° 

1° 

2° 

3° 

4o 

5° 

6° 

7° 

8° 

9° 

(a)  CARBON  DISULPHIDE. 

0° 

127.90 

I33-85 

140.05 

146.45 

^•Jo 

l6o.OO 

167.15 

174-60 

182.25 

190.20 

10 

198.45 

207.00 

215.80 

224.95 

234.40 

244.15 

254-25 

264.65 

275.40 

286.55 

20 

298.05 

309.90 

322.10 

334-70 

347-70 

361.10 

374.95 

389.20 

403.90 

419.00 

30 
40 

434.60 
617.50 

450-65 
638.70 

467-15 
660.50 

484.15 
682.90 

501.65 
705.90 

5J9-65 
729.50 

538-I5 
753-75 

557-15 
778.60 

576.75 
804.10 

596.85 
830.25 

(b)   CHLOROBENZENE. 

20° 

8.65 

9.14 

9.66 

IO.2I 

10.79 

11.40 

12.04 

12.71 

13.42 

14.17 

30 

14.95 

15-77 

16.63 

17.53 

18.47 

1945 

20.48 

21.56 

22.69 

23.87 

40 

25.10 

26.38 

27.72 

29.12 

30.58 

32.10 

33-69 

35-35 

37.08 

38.88 

50 

60 

40.75 

64.20 

42.69 
67.06 

44.72 
70.03 

46.84 
73-H 

49-05 
76.30 

51-35 
79.60 

53-74 
83.02 

56.22 
86.56 

58-79 
90.22 

61.45 
94.00 

70 

97.90 

101.95 

106.10 

IIO.4I 

114.85 

H9-45 

124.20 

129.10 

134.15 

139.40 

80 

144.80 

150.30 

156-05 

I6I.95 

168.00 

174-25 

181.70 

187.30 

194.10 

201.15 

90 

208.35 

215.80 

223.45 

231.30 

239-35 

247.70 

256.20 

265.00 

274.00 

283-25 

100 

292.75 

302.50 

312.50 

322.80 

333-35 

344.15 

355.25 

366.65 

378.30 

390.25 

no 

402.55 

415.10 

427-95 

44LI5 

454.65 

468.50 

482.65 

497.20 

512.05 

527-25 

1  20 

542.80 

558.70 

575-05 

59I.70 

608.75 

626.15 

643-95 

662.15 

680.75 

699.65 

130 

718.95 

738-65 

758.80 

~ 

~ 

~ 

(c)  BROMOBENZENE. 

40° 

- 

- 

- 

- 

- 

12.40 

13.06 

13-75 

14.47 

15-22 

50 

1  6.00 

16.82 

17.68 

18.58 

19.52 

20.50 

21.52 

22.59 

2371 

24.88 

60 

g 

26.10 
41.40 
63.90 

27.36 
43.28 
66.64 

28.68 

45.24 
69.48 

3O.O6 
47.28 
7242 

31.50 
49.40 
7546 

33-oo 
51.60 
78.60 

34.56 
53-88 
81.84 

36.18 
56-25 
85.20 

37-86 
58.71 
88.68 

39-60 
61.26 
92.28 

90 

96.00 

99.84 

103.80 

107.88 

112.08 

116.40 

120.86 

125.46 

130.20 

135.08 

100 

140.10 

145.26 

1  50.57 

1  56.03 

161.64 

167.40 

I73-32 

179.41 

185.67 

192.10 

no 

198.70 

205.48 

212.44 

219.58 

226.90 

234-40 

242.10 

250.00 

258.10 

266.40 

1  20 
130 

274.90 
372-65 

283.65 
38375 

292.60 
395-  To 

3OI-75 
406.70 

311-15 

418.60 

320.80 
430-75 

330-70 
443.20 

340.80 
455-90 

35I-I5 
468.90 

361.80 
482.20 

140 

495.80 

509.70 

523-90 

538-40 

553-20 

568.35 

583-85 

599-65 

6i5.75 

632.25 

150 

649.05 

666.25 

683.80 

701.65 

7I9-95 

738.55 

757-55 

776.95 

796.70 

816.90 

(d)  ANILINE.  . 

80° 

1  8.80 

19.78 

20.79 

21.83 

22.90 

24.00 

25.14 

26.32 

27-54 

28.80 

90 

30.10 

3J-44 

32-83 

34.27 

35-76 

37.30 

38.90 

40.56 

42.28 

44.06 

100 

no 

45-90 
68.50 

47.80 
71.22 

49-78 

74.04 

51.84 
76.96 

53-98 
79.98 

56.20 
83.10 

58.50 
86.32 

60.88 
89.66 

63-34 
93.12 

65.88 
96.70 

1  20 

100.40 

104.22 

108.17 

112.25 

1  1  6.46 

120.80 

125.28 

129.91 

134.69 

139.62 

130 
140 

144.70 
204.60 

149.94 
211.58 

155-34 
218.76 

160.90 
226.14 

166.62 
233-72 

172.50 
241.50 

178.56 
249.50 

184.80 
257.72 

191.22 
266.16 

197.82 
274.82 

150 

160 

!£ 

283.70 
515-60 

292.80 

397.65 
530.20 

302.15 
409.60 
545-20 

3".75 
421.80 

560.45 

321.60 
434-30 
576.10 

33J-7o 
447.10 
592.05 

342.05 
460.20 
608.35 

352-65 
473.6o 
625.05 

363-50 
487.25 
642.05 

374.60 
501.25 
659-45 

1  80 

677-15 

695-30 

71375 

732.65 

75L90 

771.5° 

" 

*  These  tables  of  vapor  pressures  are  quoted  from  results  published  by  Ramsay  and  Young  (Jour.  Chem.  Soc. 
vol.  47).     The  tables  are  intended  to  give  a  series  suitable  for  hot-jacket  purposes. 
SMITHSONIAN  TABLES. 


TABLE    142   (continued). 
VAPOR  PRESSURE. 

Methyl  Sallcylate,  Bromonaphthaline,  and  Mercury. 


Temp. 
C. 

0° 

1° 

2° 

30 

4°' 

6° 

6° 

7° 

8° 

9° 

(e)  METHYL  SALICYLATE. 

70° 

80 
90 

2.40 
4.60 
7.80 

2.58 
4.87 

8.20 

2.77 

S-1S 
8.62 

2.97 
9.06 

5-74 
9-52 

6.05 
9-95 

3.62 

6.37 
10.44 

3-85 
6.70 
10.95 

4.09 

7.05 
11.48 

4-34 
742 
12.03 

100 

12.60 

13.20 

13.82 

14.47 

I5.i5 

15-85 

16.58 

17-34 

18.13 

18.95 

110 

19.80 

20.68 

21.60 

22.55 

23-53 

24-55 

25.61 

26.71 

27.85 

29.03 

1  20 

30-25 

31.52 

32-84 

34.21 

37.10 

38.67 

40.24 

41.84 

43-54 

130 
140 

45-30 
66-55 

47.12 
69.08 

49.01 
71.69 

50.96 
74-38 

52.97 

77.15 

55-05 
80.00 

57.20 
82.94 

5943 
85-97 

61-73 
89.09 

64.10 
92.30 

150 

160 

95.60 
I34-25 

99.00 
138.72 

102.50 

106.10 
148.03 

109.80 
152.88 

113.60 

157.85 

117-  51 
162.95 

121.53 
168.19 

125.66 
I73-56 

129.90 
179.06 

170 

184.70 

190.48 

196.41 

202.49 

208.72 

215.10 

221.65 

228.30 

235-15 

242.15 

1  80 

249-35 

256.70 

264.20 

271.90 

279.75 

287.80 

296.00 

304.48 

3I3-05 

321.85 

190 

330.85 

340.05 

349-45 

359-05 

368.85 

378.90 

389.  !  5 

399.60 

410.30 

421.20 

200 

210 

432.35 
557.50 

443-75 
571-45 

455-35 
585-70 

467.25 
600.25 

479-35 
615-05 

491.70 
630.15 

504.35 
645-55 

661.25 

53040 
677.25 

543-80 
693.60 

220 

710.10 

727.05 

744-35 

761.90 

779-85 

798.10 

(f)  BROMONAPHTHALINE. 

110° 

3-6o 

3-74 

3.89 

4.05 

4.22 

4.40 

4.59 

4-79 

5.00 

C.22 

1  20 

5-45 

5-70 

5-96 

6.23 

6.51 

6.80 

7.10 

7.42 

7-76 

8.12 

130 

8.50 

8.89 

9-29 

9.71 

10.15 

10.60 

11.07 

11.56 

12.07 

1  2.6O 

140 

*3-lS 

1372 

I4-31 

14.92 

15-55 

16.20 

16.87 

17-56 

18.28 

19.03 

150 

19.80 

20.59 

21.41 

22.25 

23.11 

24.00 

24.92 

25.86 

26.83 

27.83 

160 

28.85 

29.90 

30.98 

32.09 

33-23 

3440 

35-60 

36-83 

38.10 

39-41 

170 
1  80 

40-75 
56.45 

42.12 

58-27 

43-53 
60.14 

44-99 
62.04 

46.50 
64.06 

48.05 
66.  i  o 

49-64 
68.19 

51.28 
70-34 

52.96 

72-55 

54-68 
74.82 

190 

77.15 

79-54 

81.99 

84.51 

87.10 

89.75 

9247 

95-26 

98.12 

IOI.O5 

200 

104.05 

107.12 

110.27 

11  3-  5° 

116.81 

120.20 

123.67 

127.22 

130.86 

J34-59 

210 

138.40 

142.30 

146.29 

150-38 

154.57 

158.85 

163-25 

167.70 

172.30 

176-95 

22O 

181.75 

186.65 

191.65 

1  96-7  5 

202.00 

207.35 

212.80 

218.40 

224.15 

230.00 

230 

235-95 

242.05 

248.30 

254-65 

261.20 

267.85 

274.65 

281.60 

288.70 

295-95 

240 

303-35 

310.90 

318.65 

326.50 

334-55 

34275 

351.10 

359.65 

368.40 

377.30 

250 

260 

270 

386.35 
487-35 
608.75 

395-6o 

498.55 
622.10 

405-05 
509.90 
635.70 

414.65 
521-50 
649.50 

424.45 
533-35 
663-55 

434-45 
545-35 
677-85 

444.65 
557-60 
692.40 

570.05 
707.15 

465.60 
582.70 
722.15 

476.35 
595.60 

737-45 

(g)  MERCURY. 

270° 

280 
290 

123.92 

157-35 
198.04 

126.97 
161.07 
202.53 

130.08 
164.86 
207.10 

211.76 

136-50 
172.67 
216.50 

139.81 
176.79 
221.33 

143.18 
180.88 
226.25 

146.61 
185.05 
231-25 

1  50.12 
189.30 
236.34 

I5370 
193-63 
24L53 

300 

246.81 

252.18 

257-65 

263.21 

268.87 

274-63 

280.48 

286.43 

292.49 

298.66 

310 

304-93 

311.30 

317.78 

324-37 

331.08 

337.89 

344.81 

35L85 

359-oo 

366.28 

320 

373-67 

381.18 

388.81 

396.56 

404.43 

412.44 

420.58 

428.83 

437-22 

445-75 

330 
340 

454-41 
548.64 

463.20 

558.87 

472.12 
569-25 

481.19 
57978 

490.40 
590.48 

499-74 
601.33 

509-22 
612.34 

518.85 
623.51 

528.63 
634-85 

646.36 

350 

658.03 

669.86 

681.86 

694.04 

706.40 

718.94 

73I-65 

744-54 

757.6i 

770.87 

36o 

784-31 

SMITHSONIAN  TABLES. 


I  tj  2  TABLE  143. 

VAPOR   PRESSURE   OF  SOLUTIONS    OF   SALTS    IN   WATER.* 

The  first  column  gives  the  chemical  formula  of  the  salt.  The  headings  of  the  other  columns  give  the  number  of 
gram-molecules  of  the  salt  in  a  liter  of  water.  The  numbers  in  these  columns  give  the  lowering  of  the  vapor 
pressure  produced  by  the  salt  at  the  temperature  of  boiling  water  under  76  centimeters  barometric  pressure. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

A12(S04)8    . 

12.8 

36.5 

AlClg    .... 

22.5 

61.0 

179.0 

318.0 

Ba(SO3)2     . 

6.6 

15-4 

34-4 

Ba(OH)2     . 

12.3 

22.5 

39-o 

Ba(N03)2    . 

13-5 

27.0 

Ba(C103)2    .        .        . 

15.8 

33-3 

70-5 

108.2 

BaCl2  .... 

16.4 

36-7 

77.6 

BaBr2  .... 

16.8 

38.8 

91.4 

150.0 

204.7 

Ca(S03)2     . 

9-9 

23-0 

56.0 

1  06.0 

Ca(N03)2    . 

16.4 

34-8 

74-6 

J39-3 

161.7 

205.4 

CaCl2. 

17.0 

39-8 

95-3 

166.6 

241.5 

3I9-5 

CaBr2  .... 

17.7 

44-2 

105.8 

191.0 

283.3 

368.5 

CdS04 

4.1 

18.1 

CdI2    .... 
CdBr2  .... 

7.6 
8.6 

14.8 
17.8 

HI 

52-7 
55-7 

8o.O 

CdCl2. 

^9-6 

18.8 

36-7 

57-o 

77-3 

99-o 

Cd(N03)2    .        .        . 

36.1 

78.0 

122.2 

Cd(C103)2  . 

17.5 

CoSO4 

5-5 

10.7 

22.9 

45-5 

CoCl2. 

15.0 

34-8 

83.0 

136.0 

186.4 

Co(N03)2    .        .        . 

17.3 

39-2 

89.0 

152.0 

218.7 

282.0 

332.0 

FeSO4 
H3B03 

a 

10.7 
12.3 

24.0 
25.1 

42.4 
38.0 

51.0 

H3P04         .        .        . 
H3AsO4       . 

6.6 
7-3 

14.0 
15.0 

28.6 
3°-2 

45.2 
46.4 

62.0 
64.9 

81.5 

103.0 

146.9 

189.5 

H2S04 
KH2PO4      . 
KN03. 
KC1O3 

12.9 

IO.2 
10.3 

10.6 

26.5 
19-5 

21.  1 
21.6 

62.8 

33-3 
40.1 
42.8 

104.0 
47-8 
57-6 
62.1 

148.0 
60.5 

74-5 
80.0 

198.4 

73-1 
88.2 

247.0 
85.2 
102.  1 

343-2 
126.3 

148.0 

KBr08 

10.9 

22.4 

45-o 

KHSO4       . 
KN02 
KC1O4 

10.9 
ii.  i 

21.9 
22.8 
22-3 

43-3 
44-8 

65-3 
67.0 

85.5 
90.0 

107.8 
110.5 

129.2 
130-7 

170.0 
167.0 

198.8 

KC1     .... 
KHCO2       . 

12.2 

n.6 

24.4 
23.6 

48.8 
59-0 

74.1 
77.6 

100.9 
104.2 

128.5 
132.0 

152.2 
1  60.0 

2IO.O 

255-0 

KI 
K2C2O4 
K2WO4       . 
K2C03 
KOH  .... 

12.5 
13.9 

14.4 
15.0 

11:1 
33-0 
31.0 

29-5 

52-2 
59-8 
75-° 

68.3 

64.0 

82.6 
94-2 
123.8 
105-5 
99-2 

1  1  2.2 
I3I.O 

175-4 
I52.O 
140.0 

141-5 

226.4 
209.0 
181.8 

I7I.8 

258.5 
223.0 

225-5 

350.0 
309.5 

278.5 
387.8 

K2CrO4       . 

16.2 

29.5 

60.0 

LiNOa 

12.2 

25-9 

55-7 

88.9 

122.2 

I55-I 

188.0 

2534 

309.2 

LiBr    '. 
Li2S04 

I2.I 
12.2 
13-3 

25.5 
26.2 
28.1 

57-i 
60.0 
56.8 

95-o 
97-o 
89.0 

132.5 
I4O.O 

J75-5 
186.3 

219.5 
241.5 

341-5 

393.5 
438.0 

LiHSO4 
Lil       . 
Li2SiFl6       . 
LiOH  .... 

12.8 
I3.6 
15-4 

27.0 
28.6 
34.0 

•37.4 

fi? 

70.0 
78.1 

93-o 

105.2 
1  06.0 

130.0 
154-5 

1  68.0 
206.0 

264.0 

357-0 

445-0 

Li2CrO4      . 

>u 

o/  T^ 

32.6 

/  *-'*  A 

74-o 

120.0 

I7I.O 

by  Tammann'  "  M6m'  Ac  St-  Petersb."  35,  No.  9,  1887.     See  also  Referate,  "Zeit.  f. 


SMITHSONIAN  TABLES. 


TABLE  1 43  (continued).  1 5  3 

VAPOR    PRESSURE    OF   SOLUTIONS   OF   SALTS    IN    WATER. 


Substance. 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

8.0 

10.0 

MgSO4 

6.5 

12.0 

24-5 

47-5 

MgCl2. 

1  6.8 

39-o 

100.5 

183-3 

277.0 

377-0 

Mg(N03)2  .        .        . 

17.6 

42.0 

IOI.O 

174.8 

MgBr2 

17.9 

44.0 

115.8 

205-3 

298.5 

MgH2(S04)2        .        . 

18.3 

46.0 

116.0' 

MnSO4 

6.0 

10.5 

21.0 

MnCl2. 
NaH2PO4    . 

15.0 
10.5 

34-o 

20.0 

76.0 
36.5 

122.3 

5J-7 

167.0 
66.8 

209.0 
82.0 

96.5 

126.7 

157.1 

NaHS04     . 

10.9 

22.1 

47-3 

75-° 

IOO.2 

126.1 

148.5 

189.7 

231.4 

NaNO3        .        .•       . 

10.6 

22.5 

46.2 

68.1 

90-3 

111.5 

i3I-7 

167.8 

198.8 

NaClO3       . 

10.5 

23.0 

48.4 

73-5 

98.5 

I23-3 

147-5 

196.5 

223.5 

(NaP03)6    • 

1  1.  6 

NaOH 

1  1.8 

22.8 

48.2 

77-3 

107-5 

!39-! 

172-5 

243-3 

314.0 

NaN02 

1  1.6 

24.4 

50.0 

75-o 

98.2 

122.5 

146.5 

189.0 

226.2 

NaHPO4     . 

12.1 

23-5 

43-o 

60.0 

78.7 

99-8 

I22.I 

NaHCO2     . 

12.9 

24.1 

48.2 

77-6 

102.2 

127.8 

I52.O 

198.0 

2394 

NaSO4 

12.6 

25.0 

48.9 

74-2 

NaCl   .... 
NaBrO3 

I2.3 
12.  1 

25.2 
25.0 

52.1 
54-i 

80.0 
81.3 

III.O 

108.8 

143.0 
136.0 

176.5 

NaBr   .... 

12.6 

25-9 

57-o 

89.2 

124.2 

159-5 

197-5 

268.0 

Nal      . 

12.1 

2S.6 

60.2 

99-5 

I36.7 

177-5 

22  1.  0 

301-5 

370.0 

Na4P2O7      . 

13.2 

22.O 

Na2CO3        . 

14-3 

27-3 

53-5 

80.2 

III.O 

Na2C2O4      . 

14-5 

30.0 

65.8 

105.8 

146.0 

Na2W04     . 

I4.8 

33-6 

71.6 

iiS-7 

162.6 

Na3P04       . 

16.5 

30.0 

52-5 

(NaPO3)3    . 

I7.I 

36.5 

NH4N03     . 

12.8 

22.O 

42.1 

62.7 

82.9 

103.8 

I2I.O 

152.2 

180.0 

(NH4)2SiFl6        .        . 

"•5 

25.0 

44-5 

NH4C1 

I2.O 

237 

45-i 

69-3 

94-2 

118.5 

138.2 

179.0 

213.8 

NH4HSO4  . 

"•5 

22.0 

46.8 

71.0 

94-5 

118. 

139.0 

181.2 

2  1  8.0 

(NH4)2S04.        .        . 

1  1.0 

24.0 

46.< 

69.5 

93-o 

117.0 

I4I.8 

NH4Br 

11.9 

23-9 

48.8 

74.1 

99-4 

121.5 

J4S-S 

190.2 

228.5 

NH4I  .... 

12.9 

2S.I 

49.8 

78.5 

104.5 

132-3 

156.0 

2OO.O 

243.5 

NiSO4 

5-o 

IO.2 

21.5 

NiCl2  .... 

16.1 

37-o 

86.7 

147.0 

212.8 

Ni(N08)a    • 

1  6.1 

37-3 

9i-3 

156.2 

235.0 

Pb(N03)2    .        .        . 

12.3 

23-5 

45-o 

63.0 

Sr(S03)2      . 

7.2 

20.3 

47.0 

Sr(N03)2     .        .        . 

15.8 

31.0 

64.0 

974 

1314 

SrCl2  .... 

1  6.8 

38-8 

91.4 

156.8 

223.3 

281.5 

SrBr2  .... 

17-8 

42.0 

IOI.I 

179.0 

267.0 

ZnS04 

4-9 

10.4 

21.5 

42.1 

66.2 

ZnCl2           .        . 
Zn(NO3)2    . 

ill 

18.7 
39-o 

46.2 
93-5 

75-° 
IS7.5 

107.0 
223.8 

153-0 

195.0 

SMITHSONIAN  TABLES. 


154 


TABLES  144-146. 

PRESSURE  OF  SATURATED  AQUEOUS  VAPOR, 

TABLE  144.  —  At  Low  Temperature.    Over  Ice. 

Temperatures  Centigrade. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

-60 

mm. 

0.008 

mm. 
O.OO7 

mm. 

O.OO5 

nun. 

0.004 

mm. 
0.003 

mm. 
0.003 

mm. 

ruin. 

mm. 

mm. 

—50 

.029 

.026 

.023 

.021 

.018 

.016 

0.014 

0.012 

0.0  10 

O.OO9 

—40 

.094 

•083 

.074 

.066 

.059 

.0|2 

.047 

.042 

-037 

•033 

—30 

.280 

.252 

.226 

.203 

.182 

-I63 

.146 

•I3I 

.117 

.105 

—  20 

0.770 

0.699 

0-633 

0.574 

0.519 

0.469 

0.424 

0-383 

-345 

.311 

—10 

1.947 

1.780 

1.627 

1.486 

!-356 

1.237 

I.I27 

1.026 

0-933 

0.848 

—  0 

4-579 

4.215 

3.879 

3.566 

3-277 

3.009 

2.762 

2-533 

2.322 

2.127 

Taken  from  Landolt-Bornstein,  Physikalisch-Chemische  Tabellen,  1912. 
TABLE  145. —At  Low  Temperature.    Over  Water. 


0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

—  10 

mm. 
2.144 

mm. 
1.979 

mm. 
1.826 

mm. 
1.684 

mm. 
I-55I 

mm. 
1.429 

mm. 
I-3I5 

mm. 

mm. 

mm. 

—  0 

+  o 

4-579 
4-579 

4.255 
4.926 

3-952 
5-294 

3.669 
5.685 

3-404 

6.101 

3.158 

6-543 

2.928 
7.014 

2.712 

7.5H 

2.509 
8.046 

2.321 
8.610 

Taken  from  Landolt-Bornstein,  Physikalisch-Chemische  Tabellen,  1912. 

TABLE  146.—  0°  to  60°  0.    Hydrogen  Scale. 

Values  interpolated  between  those  given  by  Scheel  and  Heuse  for  every  degree  between  o°  and 
50°  C.     Annalen  der  Physik.  (4),  31,  p.  731,  1910. 


.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

0° 

4-579 

4.613 

4.647 

4.681 

4-7I5 

4-75° 

4.785 

4.820 

4.855 

4.890 

I. 

4.926 

4.962 

4.998 

5.034 

5-07I 

5-ro7 

5-H4 

5.181 

5.218 

5.256 

2. 

5-294 

5.332 

5-370 

5.408 

5-447 

5.486 

5-525 

5-564 

5.604 

5-644 

3- 

4- 

5.685 
6.101 

5-725 
6.144 

5.766 
6.187 

5.807 
6.230 

5.848 
6.274 

5.889 
6.318 

5-931 
6.363 

5-973 
6.408 

6.015 
6453 

6.058 
6.498 

5- 

6-543 

6.589 

6-635 

6.681 

6,728 

6.775 

6.822 

6.870 

6.918 

6.966 

6. 

7.014 

7.063 

7.II2 

7.171 

7.210 

7.260 

7.310 

7.361 

6.412 

7-463 

8.' 

7-5H 
8.046 

7.566 

8.101 

7.618 
8.156 

7.670 
8.212 

8^268 

7-776 
8.324 

7.829 
8.381 

7.883 
8.438 

7-937 
8-495 

7.991 

8.552 

9- 

8.609 

8.668 

8.727 

8.786 

8.845 

8.905 

8.965 

9.026 

9.087 

9.148 

10. 

9.210 

9.272 

9-334 

9.396 

9-459 

9-522 

9.586 

9-650 

9715 

9.780 

u. 

12. 

9-845 
10.519 

9.911 

10.589 

9-977 
10.659 

10.043 
10.729 

IO.IIO 

10.800 

10.177 
10.871 

10.245 
10.943 

10-313 
11.015 

10.381 
11.087 

10.450 
II.I&3 

13. 

n-233 

11.307 

11.381 

"•455 

IX-530 

11.605 

11.681 

n-757 

11.834 

II.9t2 

I4. 

11.989 

12.067 

12.146 

12.225 

12.304 

12.384 

12.464 

12-545 

12.626 

12.708 

'I* 

12.790 

12.873 

12.956 

13-039 

13-123 

13.207 

13.292 

I3.378 

13.464 

13.550 

1  6. 

13-637 

13-724 

13.812 

13.900 

13.989 

14.078 

14.168 

14.258 

14.35° 

14.441 

17. 

14-533 
15.480 

14.625 
15.578 

14.718 
15-676 

14.811 
15-775 

14.905 
I5-874 

14.999 
15-974 

15.094 
16.074 

15.190 
16.175 

15.286 
16.276 

I5-383 
16.378 

19. 

16.481 

16.584 

16.688 

16.792 

16.897 

17.003 

17.109 

17.216 

17-323 

17430 

20. 

17-539 

17.648 

17-757 

17.867 

17.977 

18.088 

18.200 

18.313 

18.426 

18.540 

21. 

18.655 

18.770 

18.886 

19.002 

19.119 

19.236 

19-354 

19-473 

I9-592 

I97I2 

22. 

19.832 

19-953 

20.075 

20.197 

20.320 

20.444 

20.569 

20.694 

20.820 

20.947 

23- 

21.074 

21.  2O2 

21.330 

21.459 

21.589 

21.720 

21.851 

21-983 

22.116 

22.249 

24. 

22.383 

22.518 

22.654 

22.790 

22.927 

23.065 

23.203 

23-342 

23-482 

23.622 

25- 

23-763 

23-905 

24.048 

24.192 

24.336 

24.481 

24.627 

24-773 

24.920 

25.068 

SMITHSONIAN  TABLES. 


TABLES  146"147  (continued). 

PRESSURE  OF  SATURATED  AQUEOUS  VAPOR. 

TABLE  146  (continued).  —  0°  to  50°  C.    Hydrogen  Scale. 


.0 

.1 

.2 

.3 

A 

.5 

.6 

.7 

.8 

.9 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

26° 

25.217 

25-367 

25.5'7 

25.668 

25.820 

25.972 

26.125 

26.279 

26.434 

26.590 

27. 

26.747 

26.904 

27.062 

27.221 

27.381 

27-542 

27.704 

27.866 

28.029 

28.193 

28. 

28.358 

28.524 

28.690 

28.857 

29.025 

29.194 

29.364 

29-535 

29.707 

29.879 

29. 

30.052 

30.226 

30.401 

30-577 

30.754 

30.932 

31.111 

31.291 

3i.47i 

31-653 

30. 

31-834 

32.017 

32.201 

*    32.386 

32-572 

32-759 

32.947 

33-135 

33-324 

33-5M 

3'- 

33-706 

33.899 

34-093 

34-288 

34-483 

34-679 

34-876 

35-074 

35-273 

35-473 

32. 

35-674 

35-876 

36.079 

36.283 

36.488 

36.694 

36.901 

37.109 

37.3i8 

37-529 

33- 

37-741 

37-953 

38.166 

38.380 

38.595 

38.812 

39.030 

39-249 

39-469 

39.689 

34- 

39-9" 

40.134 

40.358 

40-583 

40.809 

41-036 

41.264 

41-493 

41-723 

4L955 

35- 

42.188 

42.422 

42.657 

42-893 

43-130 

43-368 

43-607 

43.847 

44.089 

44-332 

36. 

44-577 

44-82 

45.06 

45-30 

45-55 

45-So 

46.05 

46.30 

46.56 

46.82 

37- 

47-082 

47-34 

47.60 

47-86 

48.12 

48.38 

48.64 

48.90 

49.17 

49-44 

38. 

49.708 

49.98 

5o-25 

50.52 

50.79 

51.06 

5'  -33 

51.60 

51.88 

52.16 

39- 

52-459 

52-74 

53-02 

53-30 

53.58 

53-87 

54.16 

54-45 

54-75 

55-05 

40. 

55-341 

55.63 

55-93 

56-23 

56.53 

56-83 

57-13 

57-43 

57-74 

58-05 

4i. 

58.36 

58.67 

58.98 

59-29 

59.60 

59-92 

60.24 

60.56 

60.88 

61.20 

42. 

61.52 

61.84 

62.16 

62.49 

62.82 

63-  i  5 

63.48 

63.81 

64.14 

64.48 

43- 

64.82 

65.16 

65.50 

65.84 

66.18 

66.53 

66.88 

67.23 

67.58 

67.93 

44- 

68.28 

68.63 

68.99 

69-35 

69.71 

70.07 

70.43 

70.79 

71.16 

71-53 

45. 

71.90 

72.27 

72.64 

73-Qi 

73.38 

73-76 

74.14 

74-52 

74.90 

75-28 

46. 

75-67 

76.06 

76.45 

76.84 

77-23 

77.62 

78.02 

78.42 

78.82 

79-22 

47- 

79.62 

80.03 

80.43 

80.84 

81.25 

81.66 

82.07 

82.48 

82.90 

83.32 

48. 

83-74 

84.16 

84-59 

85.02 

85-45 

85.88 

86.31 

86.74 

87.17 

87.  6  1 

49- 

88.05 

88.49 

88.93 

89-37 

89.82 

90.27 

90.72 

91.17 

91.62 

92.08 

TABLE  147.      50°  to  374°  C.    Hydrogen  Scale. 


1  

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

mm  . 

50° 

92-54 

97.24 

102.13 

107.24 

112.56 

ii8.ii 

123.89 

129.90 

136.16 

142.68 

60. 

149.46 

156.52 

163.85 

171.47 

179.40 

187.64 

196.19 

205.07 

214.29 

223.86 

70. 

233-79 

244.11 

254-82 

265.91 

277.41 

.289.32 

301.65 

314.42 

327-64 

341-32 

80. 
90. 

355-47 
526.00 

370.11 
546.27 

385-25 
567-19 

400.90 
588.77 

417.08 
611.04 

433-79 
634-01 

451-07 
657.69 

468.91 

682.1! 

487-33 
707.29 

506.36 
733-24 

100. 

760.00 

787-57 

815.9 

845-1 

875.1 

906.1 

937-9 

970.6 

1004.3 

1038.8 

no. 

I074-5 

IIII.  I 

1148.7 

1187.4 

1227.1 

1267.9 

1309-8 

1352.8 

i397-o 

1442.4 

120. 

1488.9 

1536.6 

1585-7 

1636.0 

1687.5 

1740.5 

1794-7 

1850.3 

1907-3 

1965.8 

130. 

2025.6 

2086.9 

2149-8 

2214.0 

2280.0 

2347-5 

2416.5 

2487.3 

2559-7 

2633.8 

140. 

2709.5 

2787.1 

2866.4 

2947-7 

3030.5 

31I5-3 

3202.1 

3290.8 

3381-3 

3474-0 

ISO. 

3568.7 

3665.3 

3764-1 

3864.9 

3968. 

4<>73. 

4181. 

4290. 

4402. 

4517- 

1  60. 

4';33 

4752 

4874 

4998 

5124 

5253 

5384 

5518 

5655 

5794 

170. 

5937 

6081 

6229 

6379 

6533 

6689 

6848 

7010 

7175 

7343 

1  80. 

75H 

7688 

7866 

8046 

8230 

8417 

8608 

8802 

8999 

9200 

190. 

9404 

9612 

9823 

10038 

10256 

10479 

10705 

10934 

11168 

11406 

200. 

11647 

11893 

12143 

«397 

12654 

12916 

13183 

13453 

13728 

14007 

210. 

14291 

14578 

14871 

15167 

15469 

15774 

16085 

16401 

16721 

17046 

220. 

17376 

17710 

18049 

18394 

18743 

19098 

19458 

19823 

20193 

20570 

230. 

20950 

21336 

21728 

22125 

22528 

22936 

23350 

23770 

24195 

24626 

240. 

25064 

25506 

25956 

26412 

26873 

27341 

27815 

28294 

28780 

29272 

250. 

29771 

30276 

30788 

31308 

31833 

32364 

32903 

33448 

34°°  i 

3456i 

200. 

35»27 

35700 

36280 

36868 

37463 

38065 

38675 

39291 

39915 

40547 

270. 

41186 

41832 

42487 

43150 

43820 

44498 

45184 

45879 

46580 

47290 

280. 

48011 

48738 

49474 

50219 

50972 

51734 

52506 

53288 

54079 

54878 

290. 

5568o 

56500 

57330 

58170 

59010 

59860 

60730 

61610 

62490 

63390 

300. 

64290 

65200 

66120 

67060 

68000 

68950 

69910 

70890 

71870 

72860 

310. 

7386o 

74880 

75900 

76940 

77980 

79040 

80110 

81180 

82270 

83370 

320. 

84480 

85610 

86750 

87900 

89050 

90220 

91400 

92600 

93820 

95040 

330. 

06270 

97510 

98770 

100040 

101320 

102610 

103930 

105250 

106580 

107930 

340. 

109300 

110670 

112050 

"3450 

114870 

116300 

117750 

119210 

120680 

122160 

35°- 

123660 

125170 

126690 

128230 

129790 

131370 

132960 

134560 

136180 

137820 

360. 

139480 

141150 

142850 

144560 

146300 

148100 

149900 

151700 

153500 

155300 

370. 

157200 

159100 

161000 

163000 

164900 

Taken  from  Landolt-Bbrnstein  Tables  and  based  upon  the  following  data :  50-70°,  Nernst,  Verh.  d.  D.  Phys.  Ges.  12, 
p.  565,  1910:  70-100°,  Regnault,  computed  by  Broch,  1881,  improved  by  Wiebe,  ZS.  fur  Instrum.  13,  p.  329,  1893,  also 
Tafein  fur  die  Spannkraft  des  Wasserdampfes,  Braunschweig,  1903  ;  100-374°,  Holborn,  Henning,  Baumann,  Atmalen 
der  Physik,  26,  p.  833,  1908,  31,  p.  945,  1910. 

SMITHSONIAN  TABLES. 


156 


TABLES   148-149. 


TABLE  148.  —  Weight  in  Grains  of  the  Aqueous  Vapor  contained  in  a  Cubic  Foot  of  Saturated  Air.* 


Temp. 

«F: 

0.0 

1.0 

2.0 

3.0 

4.0 

6.0 

6.0 

7.0 

8.0 

9.0 

—10 

—  o 

0.285 

0.481 

0.270 
0-457 

0.257 
0-434 

0.243 
0.411 

0.231 
0-389 

0.218 
0.370 

0.207 
0-350 

0.196 

0.332 

0.184 
0.316 

0.174 
0.300 

+o 

10 

0.481 
0.776 

0.8  1  6 

0.529 
0.856 

0-554 

0.582 
0.941 

0.610 
0.985 

0.639 
1.032 

0.671 
1.079 

0.704 
1.128 

0-739 
1.181 

20 

T-235 

1.294 

1-355 

1.418 

1.483 

i-55i 

1.623 

1.697 

1-773 

I.853 

3° 

J-935 

2.O22 

2.113 

2.194 

2.279 

2.366 

2-457 

2-550 

2.646 

2.746 

40 

2.849 

2-955 

3.064 

3-177 

3-294 

3414 

3-539 

3-667 

3.800 

3.936 

50 

4.076 

4.222 

4-372 

4.526 

4-685 

4.849 

5.018 

5-T9i 

5-370 

5-555 

60 

5-745 

5-941 

6.142 

6-349 

6-563 

6.782 

7.009 

7.241 

7.480 

7.726 

70 

7.980 

8.240 

8.508 

8.782 

9.066 

9.356 

9-655 

9.962 

10.277 

10.601 

80 
90 

10.934 
14.790 

11.275 
15.234 

11.626 
15.689 

11.987 
16.155 

'2-356 
16.634 

12.736 
17.124 

13.127 
17.626 

13.526 
18.142 

1  3-937 
18.671 

M-359 
19.212 

100 

no 

19.766 
26.112 

20-335 
26.832 

20.917 
27.570 

21.514 

28.325 

22.125 
29.096 

22.750 
29.887 

23-392 

24.048 

24.720 

25.408 

*  See  "  Smithsonian  Meteorological  Tables,"  pp   132-133. 
TABLE  149.  —  Weight  in  Grams  of  the  Aqueous  Vapor  contained  in  a  Cubic  Meter  of  Saturated  Air. 


Temp. 
°C. 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

7.0 

8.0 

9.0 

—20 

0.892 

0.8  10 

0-737 

0-673 

0.613 

0-557 

0-505 

0-457 

0.413 

0-373 

—  10 

2.154 

1.978 

1.811 

1.658 

I-5I9 

1-395 

1.282 

1.177 

1.079 

0.982 

—0 

4.835 

4.468 

4.130 

3.8I3 

3-5I8 

3-244 

2.988 

2-752 

2-537 

2.340 

+0 

4.835 

5.!76 

5.538 

5.922 

6-330 

6.761 

7.219 

7-703 

8.2IC 

8-757 

IO 
20 

9-33° 
17.118 

9-935 
18.143 

10.574 
19.222 

11.249 

20-355 

11.961 
21.546 

12.712 
22.796 

13.505 
24.109 

H-339 

25.487 

15.218 
26.933 

16.144 
28.450 

30 

30.039 

3  '-704 

33-449 

35-275 

37.187 

39-J87 

41.279 

43465 

45-751 

48.138 

SMITHSONIAN  TABLES. 


TABLE   150. 
PRESSURE    OF   AQUEOUS    VAPOR    IN    THE    ATMOSPHERE. 


157 


This  table  gives  the  vapor  pressure  corresponding  to  various  values  of  the  difference  t  —  t±  between  the  readings  of 
dry  and  wet  bulb  thermometers  and  the  temperature  t±  of  the  wet  bulb  thermometer.  The  differences  t  —  t\  are 
given  by  two-degree  steps  in  the  top  line,  and  t\  by  degrees  in  the  first  column.  Temperatures  in  Centigrade 
degrees  and  Regnault's  vapor  pressures  in  millimeters  of  mercury  are  used  throughout  the  table.  The  table  was 
calculated  for  barometric  pressure  B  equal  to  76  centimeters,  and  a  correction  is  given  for  each  centimeter  at  the 
top  of  the  columns.*  V  entilating  velocity  of  wet  thermometer  about  3  meters  per  second. 


«1 

'=£ 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

Difference  per 
i°of*-.f, 

Corrections  for 
B  per  centi- 
meter, t 

.013 

.026 

.040 

•°53 

.066 

.079 

.092 

.106 

.119 

.132 

—10 

1.96 

0.96 

0.100 

—9 

2.14 

1.14 

0.14 

O.I  00 

—8 

2-33 

J-33 

o-33 

O.IOO 

—7 

2-53 

J-53 

o-53 

Example. 

O.IOO 

—6 

2.76 

1.76 

0.76 

t-t^-  7.2 

O.IOO 

—  5 

/!  =  10.0 

3.01 

2.01 

I.OO 

.5=74.5 

O.IOO 

—4 

3.28 

2.28 

I>2£ 

0.27 

Tabular  number—  6.12  —  6  X.  101=  5.51 

O.IOO 

—3 

3-57 

2-57 

oo 

1.56 

0.56 

Correction  for  B^=.  1.5  X  .048  .  .  =     .07 

O.IOO 

—2 

3.88 

2.88 

1.87 

0.87 

Hence  we  get/  .  .  .  =  5.58 

O.IOO 

—  I 

4.22 

3-22 

2.21 

1.  21 

0.21 

O.IOO 

0 

4.60 

3.60 

2-59 

i-59 

o-59 

O.IOO 

I 

4.94 

3-93 

2.92 

1.92 

0.92 

O.IOO 

2 

5-3° 

4.29 

3.29 

2.28 

1.28 

0.27  ( 

O.IOO 

3 

5.69 

4.68 

3.68 

2.67 

1.66 

0.66 

O.IOI 

4 

6.10 

5-09 

4.09 

3.08 

2.07 

1.  06 

0.05 

O.IOI 

5 

6-53 

5-52 

4-51 

3-50 

2.49 

1.48 

0.48 

O.IOI 

6 

7.00 

4.98 

3-97 

2.96 

i-95 

0.94 

O.IOI 

7 

749 

6.48 

5-47 

4-45 

3-44 

2-43 

1.42 

0.41 

O.IOI 

8 

8.02 

7.01 

5-99 

4.98 

3-97 

2.96 

1.94 

0.93 

O.IOI 

9 

8.57 

7-56 

6.54 

5-53 

4-51 

3-5° 

2-49 

1.48 

0.46 

O.IOI 

10 

9.17 

8.16 

7.14 

6.12 

5-11 

4.09 

3.08 

2.07 

1.  06 

0.05 

O.IOI 

ii 

9-79 

8.77 

7.76 

6.74 

5-73 

4.71 

3-69 

2.68 

1.66 

0.64 

O.IO2 

12 
13 

10.46 
ii.  16 

9-44 
10.14 

8-43 
9.12 

7.41 
8.10 

6-39 
7.09 

5-37 
6.07 

4.36 
5-05 

3-34 
4-03 

2.32 
3-oi 

I.30 
1.99 

0.28 
0.97 

0.102 
O.I  O2 

14 

11.91 

10.89 

9.87 

8.85 

7-83 

6.81 

5-79 

4-77 

3-7i 

2.69 

1.67 

O.I  O2 

15 

16 
17 

12.70 

13-54 
14.42 

11.68 

12.52 
13.40 

10.66 
11.50 
12.37 

9.64 
10.47 
"•35 

8.62 
9-45 
10.33 

7.60 
8.43 
9-3i 

6.58 
7.41 
8.28 

5.56 

6.39 

7.26 

4-54 
5-37 
6.24 

3-52 

4-35 
5.22 

2.50 

3-33 
4.20 

0.102 

O.I  O2 
O.IO2 

18 

J5-36 

14-34 

i3-3i 

12.29 

11.26 

10.24 

9.21 

8.19 

7.17 

6.15 

5-J3 

0.102 

T9 

16.35 

15-33 

14.30 

13.27 

12.25 

11.22 

10.20 

9.17 

8.15 

7-13 

6.ii 

0.102 

20 

21 

17-39 

18.50 

16.37 
17.47 

15-34 
16.45 

M-31 

15.42 

13.28 
14-39 

12.26 
I3-36 

11.23 

12-33 

IO.2I 
II-3I 

9.18 
10.28 

8.15 
9-25 

7.12 

8.22 

0.103 

0.103 

22 
23 

19.66 
20.89 

18.63 
19.86 

17.60 
18.83 

16.57 
17.80 

15-54 
16.77 

I4-51 
15.74 

13.48 
14.71 

12.46 
13.68 

ii-43 
12.66 

10.40 
11.63 

9-37 
1  0.60 

0.103 
0.103 

24 

22.18 

21.15 

20.  1  2 

19.09 

18.05 

17.02 

!5-99 

14.96 

J3-94 

12.91 

11.88 

0.103 

25 

26 

23-55 
24.99 

22.52 
23.96 

21.49 
22.92 

20.45 
21.89 

19-43 
20.86 

1839 
19.82 

17-36 
18.79 

16.33 
17.76 

15.30 
16.73 

14.27 
I5-70 

13.24 
14.67 

0.103 

0.103 

27 

26.51 

25.48 

24.44 

23.40 

22.37 

21.34 

20.30 

19.27 

18.24 

17.21 

16.18 

0.103 

28 

28.10 

27.07 

26.03 

24.99 

23.96 

22.92 

21.89 

20.85 

19.82 

18.79 

17.76 

0.103 

29 

29.78 

28.75 

27.71 

26.67 

25-63 

24-59 

23-56 

22.52 

21.49 

20.46 

!9-43 

0.103 

30 

31-55 

30-51 

29.47 

28.43 

27.40 

26.36 

25-32 

24.29 

23-25 

22.22 

21.  18 

0.104 

31 

33-4i 

32-37 

31-33 

30.29 

29-25 

28.22 

27.18 

26.14 

25.10 

24.07 

23-03 

0.104 

32 

35-36 

34-32 

33-28 

32.24 

31.21 

30.17 

29.13 

28.09 

27.05 

26.OI 

2497 

0.104 

33 

374i 

36-37 

35-33 

34-29 

33-25 

32.22 

31.18 

30.14 

29.10 

28.06 

27.02 

0.104 

34 

39-57 

38.53 

37-48 

36-44 

35-40 

34.36 

33-32 

32.28 

31.24 

3O.2O 

29.16 

0.104 

35 

41.83 

40.79 

39-74 

38.70 

37-66 

36.62 

35.58 

34-54 

33.50 

32.46 

31-42 

0.104 

36 

44.20 

43.16 

42.11 

41.07 

40.03 

38.99 

37-95 

36.90 

3<.86 

34.82 

33-78 

0.104 

46.69 
49-30 

45-65 
48.26 

44.60 
47.21 

43-56 
46.17 

42.52 
45-J3 

41.48 
44.08 

40.44 
43-°4 

39-39 
41.99 

3».35 
40.95 

37.31 
39-91 

36.27 
38.87 

0.104 
0.104 

39 

52.04 

51.00 

49-95 

48.91 

47-86 

46.82 

45-77 

4473 

43-68 

42.64 

41.59 

0.105 

*  The  table  was  calculated  from  the  formula  ^=/1  — 0.00066 ^(i—^)  (i  +0.00115^)  (Ferrel,  Annual  Report 
U.  S.  Chief  Signal  Officer,  1886,  App.  24). 

t  When  B  is  less  than  76  the  correction  is  to  be  added,  and  when  B  is  greater  than  76  it  is  to  be  subtracted. 

SMITHSONIAN  TABLES. 


158 


TABLE  151. 


DEW- 


The  first  column  of  this  table  gives  the  temperatures  of  the  wet-bulb  thermometer,  and  the  top  line  the  difference 
the  table.  The  dew-points  were  computed  for  a  barometric  pressure  of  76  centimeters.  When  the  barometer  differs 
and  the  resulting  number  added  to  or  subtracted  from  the  tabular  number  according  as  the  barometer  is  below  or 


f! 

«-*=! 

2 

3 

4 

5 

6 

7 

8 

Dew-points  corresponding  to  the  difference  of  temperature  given  in  the  above  line  and  the 
wet-bulb  thermometer  reading  given  in  first  column. 

57755= 

.04 

.11 

.22 

49 

-10 

—  13.2 

—  17.9 

—  9 

12.0 

1  6.0 

—  22.O 

—  8 

10.7 

14-3 

194 

—  7 

9-5 

12.7 

I7.I 

—  24.0 

—  6 

8-3 

II.  2 

14.9 

20.3 

57755  = 

•03 

.06 

.11 

.18 

•31 

43 

—  5 

—  7-1 

—  9-7 

—  12.9 

—  17-5 

—  24-5 

—  4 

6.0 

8-3 

II.  I 

14.8 

20.1 

—  3 

4.8 

6.9 

94 

12.6 

16.8 

—  23.4 

2 

3-6 

5-5 

7.8 

10.5 

13-9 

18.9 

—  I 

2-5 

4.2 

6.2 

8.5 

11.5 

154 

—  2I.O 

57755  = 

.02 

.04 

.07 

.10 

.14 

.19 

.26 

•38 

0 

—  1-3 

—  2.9 

-4-8 

—  6.8 

-9-3 

—  12.3 

—  16.5 

—  22.9 

I 

O-3 

1.7 

3-5 

5-3 

7.6 

10.2 

'3-5 

18.3 

2 

+  0.6 

0.7 

2.2 

3-9 

6.1 

8-3 

ii.  I 

14.7 

3 

+  0.2 

1.0 

2.6 

4.6 

6.4 

8.9 

11.9 

57755  = 

2.8 
.02 

1.4 
•03 

0.0 

•05 

.07 

.09 

4-7 
.11 

6.9 
.14 

94 
.18 

5 

3-8 

2.6 

+  1.2 

—  O.I 

—  1.6 

—  3-2 

*ti 

6 

4-9 

3-7 

2-5 

+  1.1 

0.2 

3-3 

5-2 

7 

6.0 

4.9 

3.7 

2.4 

+  I.I 

o-3 

34 

8 

7-0 

6.0 

4.9 

3-7 

2-5 

+  1.1 

0.3 

1.8 

9 
57755  = 

8.1 

.01 

.02 

6.1 
.03 

5-° 
•05 

2.6 

.08 

+  1.2 
.10 

O.I 
.12 

10 

9.1 

8-3 

7-3 

6-3 

5'2 

4.1 

2.8 

ii 

IO.2 

9-3 

8.4 

6.5 

5-5 

4-3 

3-1 

12 

II.  2 

10.4 

9.6 

8.7 

7.8 

6.8 

5-8 

4-7 

*3 

12-3 

ii.S 

10.7 

9.9 

9.1 

8.2 

7-2 

6.2 

57755  = 

13-3 
.01 

12.6 
.02 

11.9 

.03 

n.  i 
.04 

10.3 
.05 

9.0 
.06 

8.6 
.07 

7.6 
.08 

15 

144 

13-7 

13.0 

12.3 

10.8 

9.9 

9.1 

16 

17 
18 

57755  = 
20 

154 
16.4 
17-5 

•005 

19.5 

14.8 
15.8 
16.9 

18.0 

.01 

19.0 

14.1 

\ll 

17.4 
.015 
18.5 

'3-5 

14.6 

16.9 

.02 

18.0 

12.7 
13.9 

III 

.027 

17.4 

I2.O 

14.5 
15-7 
.033 
16.9 

"•3 

12.6 

13.8 

.04 

16.3 

10.5 
1  1.8 

14.4 

15-7 

21 

20.| 

20.1 

19.6 

19.1 

18.6 

18.1 

17.0 

22 

21.6 

21.  1 

20.7 

20.2 

19.7 

19.2 

187 

18.2 

23 
24 
57755  = 

25 

^ 

22.6 
23.6 
.005 
24.6 

22.2 
23.2 
.OI 

24.2 

21.7 

22.8 
•015 

23-9 

21.3 
22-4 
.02 

23-5 

20.8 
22.0 
.025 
23.1 

20.4 
21.5 
•03 

19.9 

21.  1 

•035 

22.2 

194 

2O.6 

.04 

21.8 

26 

27 

_o 

25.6 
26.7 

26.3 

24-9 
26.0 

24-5 
25.6 

24.2 
25-3 

24.9 

234 

24-5 

230 
24.1 

28 
29 

27.7 
28.7 

270 
28.4 

27.0 
28.1 

26.7 
27.8 

26.4 
27.4 

26.0 
27.1 

Hi 

26.4 

5  7/55  = 

.003 

.006 

.01 

.013 

.017 

.019 

.022 

.026 

30 

29.7 

29.4 

29.1 

28.8 

28.5 

28.2 

27.9 

27.6 

31 

30.7 

30-5 

30.2 

29.9 

29.6 

29-3 

29.0 

28.7 

32 

3T-7 

3I<5 

31.2 

3°-9 

30-7 

304 

30.1 

29.8 

33 
57755  = 

32.8 
33-8 
.003 

32-5 
33-5 
005 

32.2 

33-3 
.008 

32.0 
.010 

3J-7 
32-8 
.013 

3*5 
.016 

31.2 

32-3 
.019 

30.9 
32.0 

.021 

35 

36 

39 

34-8 
35-8 
36.8 
37-8 
38.8 

34-5 

11 

34-3 

35-3 
364 
374 
384 

35-1 
36.2 

37-2 
38-2 

33-8 
34-9 
36.0 
37-o 
38.0 

33.6 
34.6 

tf 

37-9 

334 
344 
35-5 
36.6 

37-6 

34-2 
35-3 
364 
37-S 

SMITHSONIAN  TABLES. 

TABLE   151  (continued). 
POINTS. 

between  the  dry  and  the  wet  bulb,  when  the  dew-point  has  the  values  given  at  corresponding  points  in  the  body  of 
from  76  centimeters  the  corresponding  numbers  in  the  lines  marked  ST/SB  are  to  be  multiplied  by  the  difference, 
above  76.  See  examples.  Thermometer  ventilated  at  about  3  meters  per  sec. 


% 

«-*  =  . 

10 

11 

12 

13 

14 

15 

Dew-points  corresponding  to  the  difference  of  temperature  given  in  the  above  line  and  the 
wet-bulb  thermometer  reading  given  in  first  column. 

1 

EXAMPLES. 

(i)  Given  £=72,  ^  =  10,  t  —  ^  =  5. 

Then  tabular  number  for  t-,  —  10  and  /  —  /t  —  5  is  5.2 
Also  76  —  72  =  4  and  ST/$B=.o6. 

*   Correction  —  o  06  X  4  —                 •                 *        24 

Hence  the  dew-point  is      •        •        •        •             5  44 

(2)  Given  .5  =  71.  5,  ^  =  7,*—  ^  =  8. 
Then,  as  above,  tabulated  number  =         .        .     3.4 

ST/& 

j?_.I»-t-.I2 

=  •15 

Dew-point  =      4.07 

57785  = 

•45 

.67 

0 

i 

2 

—  20.0 

3 

I5.8 

—  22.2 

4 

12.4 

1  6.8 

57755  = 

•23 

.29 

•37 

•44 

•54 

.66 

.72 

5 

—  19.8 

—  I3-I 

—  17.7 

6 

7-4 

IO.I 

13-4 

—  18.1 

7 

1    5-3 

7.6 

IO.I 

13-5 

-18.3 

8 

3-3 

5-2 

7-4 

IO.I 

13-5 

—  18.3 

9 

1.6 

3-2 

5-1 

7-2 

9-9 

I3<1 

—  17.2 

57755  = 

.14 

•17 

.20 

.22 

•25 

.29 

•36 

10 

o.o 

—  3-° 

—  4-7 

—  6.8 

—  9.4 

—  12.5 

ii 

+  1.8 

+  0.3 

I.O 

2.6 

4-3 

6-3 

8.8 

12 

3-5 

2.2 

+  0.8 

0.6 

2.1 

3-7 

5-7 

*3 

3-9 

2-7 

+  1.3 

O.I 

1.6 

14 

6.7 

5.6 

4-5 

3-3 

+  1.9 

+  0.5 

0.9 

57755  = 

.09 

.11 

.12 

.14 

.16 

.18 

.20 

15 

8.2 

7-2 

6.2 

5-1 

3-9 

2.7 

_|_    J.-5 

16 

9.6 

8.7 

7-8 

6.8 

5-8 

4-7 

3-5 

17 

II.O 

IO.2 

9.4 

8.5 

7-5 

6.5 

5-5 

18 

12.4 

1-1.7 

10.9 

IO.I 

9.2 

8-3 

7-4 

'9 

13.8 

I3-I 

12.4 

1  1.6 

10.8 

1  0.0 

9.1 

57755  = 

.06 

.07 

.08 

.09 

.10 

.11 

•13 

20 

21 

III 

14-5 
15.8 

\3'l 

14-5 

12.4 
13-9 

1  1.6 
13.2 

10.8 
•12.5 

22 

17.6 

17.1 

16.5 

lS-3 

14.7 

14.0 

23 

18.9 

18.4 

17.9 

17.3 

1  6.8 

16.2 

15-7 

24 

20.1 

19.6 

19.2 

18.7 

18.1 

17.6 

17.0 

57755  = 

•045 

.05 

06 

.06 

.07 

.08 

.09 

25 

21-4 

20.9 

20.4 

20.0 

19-5 

19.0 

18.5 

26 

22.6 

22.1 

21.7 

21-3 

20.8 

20.3 

19.9 

27 

23-7 

234 

22.9 

22.3 

22.1 

21.7 

21.2 

28 

24.9 

24-5 

24.2 

23-8 

23-4 

23.0 

22.6 

29 

26.1 

25-7 

25.4 

25.0 

24.6 

24.2 

23-9 

57755  = 

.031 

•035 

.041 

.047 

•053 

.06 

.07 

30 

31 

27.2 
28.4 

26.9 
28.1 

26.6 
27.8 

26.2 
27.4 

25-9 
27.1 

25-3 
26.8 

26.4 

32 

29-5 

29.2 

28.9 

28.6 

28.3 

28.0 

27.7 

33 

30-7 

3°-4 

30.1 

29.8 

29.5 

29.2 

28.9 

34 

31.8 

31.5 

31.2 

3°-9 

30-7 

3°-4 

3O.I 

57755  = 

.024 

.027 

.029 

.032 

•037 

•037 

.04 

35 

32-9 

32.6 

32-4 

32.1 

31.8 

31-6 

31-4 

36 

34-0 

33-7 

33-5 

33-3 

33-o 

32.8 

32-5 

37 

35.1 

34-9 

34-6 

34-4 

34-2 

33-9 

33-7 

38 
39 

36.2 
37-3 

35-9 

III 

35-3 
36-4 

34-8 
36.0 

SMITHSONIAN  TABLES. 


i6o 


TABLE  1 52. 
RELATIVE    HUMIDITY.* 


This  table  gives  the  humidity  of  the  air,  for  temperature  t  and  dew-point  d  in  Centigrade  degrees,  expressed 
in  percentages  of  the  saturation  value  for  the  temperature  t. 


Depression  of 
the  dew-point. 
t  —  d 

Dew-point  (d). 

Depression  of 
the  dew-point. 
t  —  d 

Dew-point  (d). 

10 

0 

+  10 

+  20 

+  30 

10 

o 

+  10 

+  20 

+  30 

C. 

C. 

o°.o 

IOO 

IOO 

IOO 

IOO 

IOO 

8°.0 

54 

57 

60 

62 

64 

0.2 

98 

99 

99 

99 

99 

8.2 

54 

56 

59 

61 

63 

0.4 
0.6 

97 
95 

97 
96 

97 
96 

96 

97 

8.4 
8.6 

53 

52 

56 

55 

58 
57 

60 
60 

63 
62 

0.8 

94 

94 

95 

95 

96 

8.8 

54 

57 

59 

61 

1.0 

92 

93 

94 

94 

94 

9.0 

51 

53 

56 

58 

61 

1.2 

91 

92 

92 

93 

93 

9.2 

5° 

53 

55 

58 

60 

M 

90 

91 

92 

92 

9-4 

49 

52 

55 

57 

59 

1.6 

88 

90 

91 

91 

9.6 

48 

54 

56 

59 

1.8 

87 

89 

90 

90 

9-8 

48 

5i 

53 

56 

p 

2.0 

86 

87 

88 

88 

89 

10.0 

47 

50 

53 

55 

57 

2.2 

84 

85 

86 

87 

88 

10.5 

45 

48 

51 

54 

2.4 

83 

84 

85 

86 

87 

II.O 

44 

47 

49 

52 

2.6 

82 

83 

84 

85 

86 

"•5 

42 

45 

48 

51 

2.8 

80 

82 

83 

84 

85 

12.0 

44 

47 

49 

3.0 

79 

81 

82 

83 

84 

12.0 

39 

42 

45 

48 

3-2 

78 

80 

81 

82 

83 

13.0 

38 

44 

46 

3-4 

77 

79 

80 

81 

82 

37 

40 

43 

45 

3-6 

76 

77 

79 

80 

82 

14.0 

35 

38 

44 

3-8 

75 

76 

78 

79 

81 

14-5 

34 

37 

40 

43 

4.0 

73 

75 

77 

78 

80 

15.0 

33 

36 

39 

42 

4.2 

72 

74 

76 

77 

79 

'5-5 

32 

35 

38 

40 

4-4 

71 

73 

75 

77 

78 

1  6.0 

31 

34 

37 

39 

4.6 

70 

72 

74 

76 

77 

16.5 

30 

33 

36 

38 

4.8 

69 

7i 

73 

75 

76 

17.0 

29 

32 

35 

37 

5.0 

68 

70 

72 

74 

75 

17.5 

28 

31 

34 

36 

5-2 

67 

69 

71 

73 

75 

1  8.0 

27 

30 

33 

35 

5-4 
5-6 

66 
65 

67 

7° 
69 

72 

74 
73 

18.5 
19.0 

26 

25 

3 

32 
31 

34 
33 

5.8 

64 

66 

69 

70 

72 

19-5 

24 

27 

30 

33 

6.0 

63 

66 

68 

70 

7i 

20.0 

24 

26 

29 

32 

6.2 

62 

65 

67 

71 

21.0 

22 

25 

27 

6.4 

61 

64 

66 

68 

7° 

22.0 

21 

23 

26 

6.6 

60 

63 

65 

67 

23.0 

J9 

22 

24 

6.8 

60 

62 

64 

66 

68 

24.0 

18 

21 

23 

7.0 

59 

61 

63 

66 

68 

25.0 

17 

19 

22 

7.2 

58 

60 

63 

65 

67 

26.0 

16 

18 

21 

7-4 

57 

60 

62 

64 

66 

27.0 

15 

17 

20 

7.6 

56 

59 

61 

63 

65 

28.0 

14 

16 

19 

7.8 

55 

58 

60 

63 

65 

29.0 

13 

15 

18 

8.0 

54 

57 

60 

62 

64 

30.0 

12 

14 

17 

*  Abridged  from  Table  45  of  "  Smithsonian  Meteorological  Tables." 
SMITHSONIAN  TABLES. 


TABLE   153. 
VALUES   OF   0.3780.* 


161 


This  table  gives  the  humidity  term  0.378*?,  which  occurs  in  the  equation  5  =  80  ~f~  =  80  — 
for  the  calculation  of  the  density  of  air  containing  aqueous  vapor  at  pressure  e  ;  $Q  is  the  density 
of  dry  air  at  normal  temperature  and  barometric  pressure,  B  the  observed  barometric  pressure, 
and  h  =  B  —  0.378^,  the  pressure  corrected  for  humidity.   For  values  of -7- see  Table  154. 
Temperatures  are  in  degrees  Centigrade,  and  pressures  in  millimeters  of  mercury. 


Dew 

Point. 

Vapor 
Pressure 
(ice). 

0.378*. 

Dew 

Point. 

Vapor 
Pressure 
(water). 

0.378*. 

Dew 

Point. 

Vapor 
Pressure 
(water). 

0.378*. 

—50 

0.034 

O.OI 

0 

4-579 

i-73 

+30 

31-555 

11-93 

45 

.061 

.02 

+  1 

4.921 

1.86 

31 

33-4I6 

12.63 

40 

.105 

.04 

2 

5.286 

2.00 

32 

35-372 

13.37 

35 

•173 

.07 

3 

5-675 

2.15 

33 

37-427 

14-15 

30 

.292 

.11 

4 

6.088 

2.30 

34 

39-586 

14.96 

—25 

0.484 

0.18 

5 

6.528 

2-47 

35 

4I-853 

15.82 

24 

•534 

.20 

6 

6-997 

2.65 

36 

44-23 

16.72 

23 

.589 

.22 

7 

7-494 

2.83 

37 

46.73 

17.66 

22 

.648 

•24 

8 

8.023 

3-03 

38 

49-35 

18.65 

21 

.714 

.27 

9 

8.584 

3-24 

39 

52.09 

19.69 

—  2O 

0.787 

0.30 

10 

9.179 

3-47 

40 

54-97 

20.78 

19 

18 

•955 

•33 
-36 

ii 

12 

9.810 
10.479 

3$ 

42 

57.98 
61.13 

21.92 
23.12 

17 

1.048 

.40 

13 

11.187 

4-23 

43 

6443 

24.35 

16 

1.148 

•44 

14 

11.936 

44 

67.89 

25-66 

—15 
14 

•257 
•375 

0.48 
•52 

15 

12.728 
I3-565 

4.81 

8 

71.50 
75-28 

27.02 
28.46 

13 

.506 

•57 

17 

14.450 

546 

47 

79-23 

29-95 

12 
II 

.650 
.806 

.62 
.68 

18 
19 

16.367 

5.82 
6.19 

48 
49 

83-36 
87.67 

3I-51 
33-14 

—  10 

1.974 

0-75 

20 

17.406 

6.58 

5° 

92-17 

34-84 

9 

2.154 

.81 

21 

18.503 

6-99 

96-87 

36.62 

8 

2-347 

.89 

22 

19.661 

7-43 

52 

101.77 

38.47 

7 

2-557 

•97 

23 

20.883 

7-90 

53 

106.88 

40.40 

6 

2.785 

1.05 

24 

22.178 

8.38 

54 

112.21 

42.42 

—5 
4 

3-99 

1.25 

11 

23.546 
24.987 

8.90 
9-45 

t 

II777 
123.56 

44-52 
46.71 

3 

3.586 

1.36 

27 

26.505 

IO.O2 

57 

129.59 

48.98 

2 

3.894 

1.47 

28 

28.103 

10.62 

58 

J35-87 

51  36 

I 

4.223 

i.  60 

29 

29.785 

11.26 

59 

142.41 

53-83 

0 

4-579 

'•73 

30 

31-555 

"•93 

60 

149.21 

56.40 

*  This  table  is  quoted  from  "  Smithsonian  Meteorological  Tables,' 
SMITHSONIAN  TABLES. 


P.  225. 


TABLES   154-155. 

RELATIVE    DENSITY  OF   MOIST   AIR    FOR    DIFFERENT   PRESSURES 

AND    HUMIDITIES. 


TABLE  154.  —  Values  of  =^-  from  h  =  1  to  h  =  9,  for  the  Computation  of  Different  Values  of  the  Ratio 

/OU 

of  Actual  to  Normal  Barometric  Pressure. 

This  gives  the  density  of  moist  air  at  pressure  h  in  terms  of  the  density  of  the  same  air  at  normal  atmosphere  pressure. 
When  air  contains  moisture,  as  is  usually  the  case  with  the  atmosphere,  we  have  the  following  equation  for  pressure 
term  :  h  —  B — 0.378*,  where  e  is  the  vapor  pressure,  and  B  the  corrected  barometric  pressure.  When  the  neces- 
sary psychrometric  observations  are  made  the  value  of  e  may  be  taken  from  Table  150,  and  then  0.378*?  from  Table 
153,  or  the  dew-point  may  be  found  and  the  value  of  0.378*  taken  from  Table  153. 


h 

h 
760 

1 

2 

3 

0.0013158 
.0026316 
.0039474 

4 

I 

0.0052632 
.0065789 
.0078947 

7 

8 
9 

0.0092105 
.0105263 
.0118421 

EXAMPLES  OF  USE  OF  THE  TABLE. 

To  find  the  value  of  —  when  h  —  754.3 
760 

h  =  700  gives  .92105 

50       '  .065789 

4  .005263 

.3    "  .000395 


754-3 


.992497 


To  find  the  value  of  —  when  h  —  5.73 
760 

h  •=.  5  gives  .0065789 
.7  ' '  .0009210 
.03  "  .0000395 


5-73 


.0075394 


TABLE  155.  —Values  of  the  logarithms  of  -g-  for  values  of  h  between  80  and  340. 

Values  from  8  to  80  may  be  got  by  subtracting  i  from  the  characteristic,  and  from  0.8  to  8  by  subtracting  2  from  the 

characteristic,  and  so  on. 


h 

Values  of  log  —. 
760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

80 

T.O2228 

7.02767 

1.03300 

1.03826 

1.04347 

1.04861 

7.05368 

7.05871 

7.06367 

7.06838 

90 

•07343 

.07823 

.08297 

.08767 

.09231 

.09691 

.10146 

.10596 

.11041 

.11482 

100 

1.11919 

1-12351 

1.12779 

1.13202 

1.13622 

1.14038 

7.14449 

7.14857 

7.15261 

7.15661 

no 

.16058 

.16451 

.16840 

.17226 

.17609 

.17988 

.18364 

•18737 

.19107 

•19473 

120 

.19837 

.20197 

•20555 

.20909 

.21261 

.21611 

.21956 

.22299 

.22640 

.22978 

130 

140 

•233I3 
•26531 

.23646 
.26841 

.23976 
.27147 

.24304 
.27452 

.24629 
•27755 

.24952 
.28055 

•2^273 
•28354 

•25591 
.28650 

.25907 
.28945 

.26220 
.29237 

150 

1.29528 

1.29816 

1.30103 

1.30388 

1.30671 

7.30952 

7.31231 

7.31509 

7.31784 

7.32058 

160 

.32331 

.32601 

.32870 

.33137 

.33403 

.33667 

•33929 

.34190 

.34450 

•34707 

170 

.34964 

.35218 

•35471 

.35723 

•35974 

.36222 

.36470 

.36716 

.36961 

.37204 

180 

.37446 

.37686 

.37926 

.38164 

.38400 

.38636 

.38870 

.39128 

•39334 

•39565 

190 

•39794 

.40022 

.40249 

.40474 

.40699 

.40922 

.41144 

•41365 

.41585 

.41804 

200 

1.42022 

1.42238 

1.42454 

T.42668 

1.42882 

1.43094 

7.43305 

7.435J6 

7.43725 

7-43933 

210 

.44141 

44347 

•44552 

•44757 

.44960 

.45162 

.45364 

•45565 

•45764 

•45963 

22O 

.46161 

•46358 

•46554 

.46749 

•46943 

•47137 

.47329 

•47521 

.47712 

.47902 

230 

.48091 

.48280 

.48467 

.48654 

.48840 

.49025 

.49210 

•49393 

•49576 

•4975s 

240 

.49940 

.50120 

.50300 

.50479 

.50658 

•50835 

.51012 

.51188 

•5I364 

•5*539 

250 

7.5I7I3 

1.51886 

1.52059 

1.52231 

1.52402 

7-52573 

7.52743 

7.52912 

7.53081 

7.53249 

260 

.53416 

.53583 

•53749 

•539M 

•54079 

•54243 

.54407 

•54570 

.54732 

•54894 

270 

•55055 

•55216 

•55376 

•55535 

•55694 

•55852 

.56010 

.56167 

•56323 

•56479 

280 

.56634 

.56789 

.56944 

•57097 

•57250 

•57403 

•57555 

.57707 

•57858 

.58008 

290 

.58158 

.58308 

•58457 

.58605 

•58753 

.58901 

.59048 

•59J94 

.59340 

.59486 

300 

7.59631 

^•59775 

1.59919 

1.60063 

7.60206 

7.60349 

7.60491 

7.60632 

7.60774 

7.60914 

310 

•61055 

.61195 

•61334 

•6i473 

.61611 

.61750 

.61887 

.6202  c 

.62161 

.62298 

320 
330 
340 

.62434 
•63770 
.65067 

.62569 
.63901 
.65194 

.62704 
.64032 
•65321 

.62839 
.64163 
.65448 

•62973 
.64293 

•65574 

.63107 

.64423 
.65701 

.63240 

•64553 
.65826 

.63373 
.64682 

•65952 

.63506 
.64810 
.66077 

-63638 

•64939 
.66201 

SMITHSONIAN  TABLES. 


TABLE  1  55  (continued). 

DENSITY   OF  AIR. 


I63 


Values  of  logarithms  of  —  for  values  of  h  between  350  and  800. 


h 

Values  of  log  A. 
6  760 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

350 

T.66325 

1.66449 

7.66573 

1.66696 

1.66819 

1.66941 

1.67064 

7.67185 

7.67307 

1.67428 

360 

•67549 

.67669 

.67790 

.67909 

.68029 

.68148 

.68267 

.68385 

.68503 

.68621 

370 

.68739 

.68856 

•68973 

.69090 

.69206 

.69322 

•69437 

.69553 

.69668 

.69783 

380 

.69897 

.70011 

.70125 

•70239 

•70352 

.70465 

.70577 

.70690 

.70802 

.70914 

390 

.71025 

.71136 

.71247 

.71358 

.71468 

.71578 

.71688 

.71798 

.71907 

.72016 

400 

T.72I25 

1.72233 

1.72341 

1.72449 

7.72557 

1.72664 

1.72771 

1.72878 

7.72985 

1.73091 

410 

.73197 

•73303 

.73408 

•735I4 

•73619 

.73723 

.73828 

73932 

.74036 

.74140 

420 

.74244 

•74347 

•7445° 

•74553 

.74655 

•74758 

.74860 

.74961 

.75063 

•75l64 

43° 

.75265 

.75366 

•75467 

•75567 

.7566g 

.75768 

.75867 

.75967 

.76066 

-76165 

440 

.76264 

•76362 

.76461 

•76559 

.76657 

.76755 

•76852 

.76949 

.77046 

•77M3 

450 

1.77240 

i"-77336 

7.77432 

1.77528 

1.77624 

1.77720 

7.77815 

1.77910 

1.78005 

1.78100 

460 

.78194 

.78289 

•78383 

•78477 

•78570 

.78664 

.78757 

.78850 

•78943 

.79036 

470 

.79128 

.79221 

•793!3 

•79405 

•79496 

•79588 

.79679 

.79770 

.79861 

.79952 

480 

.80043 

•80133 

.80223 

•80313 

.80403 

•80493 

.80582 

.80672 

.80761 

.80850 

490 

.80938 

.81027 

.81115 

.81203 

.81291 

.81379 

.81467 

.81554 

.81642 

.81729 

500 

T.8i8i6 

1.81902 

1.81989 

1.82075 

1.82162 

1.82248 

7.82334 

1.82419 

1.82505 

1.82590 

510 

.82676 

.82761 

.82846 

.82930 

•83015 

.83099 

.83184 

.83268 

•83352 

•83435 

520 

•835J9 

.83602 

.83686 

.83769 

.83852 

•83935 

.84017 

.84100 

.84182 

ft      •y*' 

.84264 

53° 

.84346 

.84428 

.84510 

.84591 

.84673 

.84754 

•84835 

.84916 

.84997 

.85076 

540 

.85158 

•85238 

•85319 

•85399 

.85479 

.85558 

.85638 

.85717 

•85797 

•85876 

550 

7.85955 

1.86034 

F.86n3 

1.86191 

1.86270 

1.86348 

1.86426 

1.86504 

1.86582 

1.86660 

560 

•86737 

.86815 

.86892 

.86969 

.87047 

.87123 

.87200 

.87277 

.87353 

.87430 

570 

.87506 

•87582 

.87658 

•87734 

.87810 

.87885 

.87961 

.88036 

.88111 

.88186 

580 

.88261 

•88336 

.88411 

.88486 

.88560 

.88634 

.88708 

.88782 

.88856 

.88930 

590 

.89004 

•89077 

.89151 

.89224 

.89297 

.89370 

.89443 

.89516 

.89589 

.89661 

600 

1.89734 

1.89806 

1.89878 

1.89950 

1.90022 

1.90094 

1.90166 

1.90238 

7.90309 

1.90380 

610 

.90452 

•90523 

.90594 

.90665 

•90735 

.90806 

.90877 

.90947 

.91017 

.91088 

620 

.91158 

.91228 

.91298 

.91367 

'•9*437 

•9I5°7 

.91576 

.91645 

•9I7I5 

.91784 

630 

•91853 

.91922 

.91990 

.92059 

.92128 

.92196 

.92264 

•92333 

.92401 

.92469 

640 

•92537 

.92604 

.92672 

.92740 

.92807 

•92875 

.92942 

•93009 

.93076 

•93M3 

650 

1.93210 

1.93277 

7-93343 

1.93410 

1.93476 

7-93543 

7.93609 

7.93675 

7.93741 

7.93807 

660 

•93873 

•93939 

.94004 

.94070 

•94135 

.94201 

.94266 

•94331 

•94396 

.94461 

670 

.94526 

•94591 

.94656 

.94720 

.94785 

.94849 

•949T3 

•94978 

.95042 

.95106 

680 
690 

•95170 
.95804 

•95233 
.95866 

•95297 
.95929 

•95361 
.95992 

•95424 
.96055 

.95488 
.96117 

•95551 
.96180 

.95614 
.96242 

•95677 
.96304 

•95741 
.96366 

700 

1.96428 

1.96490 

7-96552 

1.96614 

1.96676 

7.96738 

7.96799 

1.96861 

1.96922 

7.96983 

710 

.97044 

.97106 

.97167 

.97228 

.97288 

•97349 

.97410 

•97471 

-97531 

•97592 

720 

.97652 

.97712 

•97772 

.97832 

.97892 

•97951 

.98012 

.98072 

.98132 

.98191 

73° 

•98251 

.98310 

.98370 

.98429 

.98488 

.98547 

•  .98606 

.98665 

.98724 

.98783 

740 

.98842 

.98900 

.98959 

.99018 

.99076 

.99134 

•99193 

.99251 

.99309 

•99367 

750 

1.99425 

1.99483 

1.99540 

1.99598 

1.99656 

7.99713 

7.99771 

1.99828 

7.99886 

7-99942 

760 

0.00000 

0.00057 

0.00114 

0.00171 

0.00228 

0.00285 

0.00342 

0.00398 

0.00455 

0.00511 

770 

.00568 

.00624 

.00680 

.00737 

.00793 

.00849 

.00905 

.00961 

.01017 

.01072 

780 

.01128 

.01184 

.01239 

.01295 

.01350 

.01406 

.01461 

.01516 

.01571 

.01626 

790 

-01681 

.01736 

.01791 

.01846 

.01901 

.01955 

.02010 

.02064 

.02119 

•02173 

SMITHSONIAN  TABLES. 


1 64 


TABLE   156. 
VOLUME   OF   CASES. 


Values  of  1  +  .00367  t. 

The  quantity  i  -f-  .00367  t  gives  for  a  gas  the  volume  at  t°  when  the  pressure  is  kept 
constant,  or  the  pressure  at  t°  when  the  volume  is  kept  constant,  in  terms  of  the 
volume  or  the  pressure  at  o°. 

(a)  This  part  of  the  table  gives  the  values  of  i +  .00367  /  for  values  of  /  between  o° 
and  10°  C.  by  tenths  of  a  degree. 

(b)  This  part  gives  the  values  of  i  +  .00367 1  for  values  of  /  between  — 90°  and  +  1990° 
C.  by  10°  steps. 

These  two  parts  serve  to  give  any  intermediate  value  to  one  tenth  of  a  degree  by  a  sim- 
ple computation  as  follows  :  —  In  the  (b)  table  find  the  number  corresponding  to 
the  nearest  lower  temperature,  and  to  this  number  add  the  decimal  part  of  the 
number  in  the  (a)  table  which  corresponds  to  the  difference  between  the  nearest 
temperature  in  the  (b)  table  and  the  actual  temperature.  For  example,  let  the 
temperature  be  682°.  2  : 

We  have  for  680  in  table  (3)  the  number  ....     3.49560 

And  for  2.2  in  table  (a)  the  decimal .00807 

Hence  the  number  for  682.2  is 3-5°367 

(C)  This  part  gives  the  logarithms  of  i  +  . 00367^  for  values  of  t  between — 49°  and 

+  399°  C.  by  degrees. 

(d)  This  part  gives  the  logarithms  of  i  -f  -00367 1  for  values  of  t  between  400°  and  1990° 
C.  by  10°  steps. 

(a)  Values  of  1  +  .00367 1  for  Values  of  t  between  0°  and  10°  C.  by  Tenths 
of  a  Degree. 


* 

0.0 

0.1 

0.2 

0.3 

0.4 

0 

1.  00000 

1.00037 

1.00073 

1.  001  10 

1.00147 

I 

.00367 

.00404 

.00440 

.00477 

.00^14 

2 

•00734 

.00771 

.00807 

.00844 

.00881 

3 

.01101 

.01138 

.01174 

.01211 

.01248 

4 

.01468 

.01505 

.01541 

.01578 

.01615 

5 

1.01835 

1.01872 

1.01908 

I.OI945 

1.01982 

6 

.02202 

.02239 

•02275 

.02312 

.02349 

I 

.02569 
.02936 

.02606 
.02973 

.02642 
.03009 

.02679 
.03046 

.02716 
.03083 

9 

•03303 

.03340 

.03376 

•03413 

•0345° 

I 

0.5 

0.6 

0.7 

0.8 

0.9 

0 

1.00184 

I.OO22O 

1.00257 

1.00294 

1.00330 

i 

.00550 

.00587 

.00624 

.00661 

.00697 

2 

.00918 

.00954 

.00991 

.01028 

.01064 

3 
4 

.01284 
.01652 

.01321 
.01688 

.01358 
.01725 

•01395 
.01762 

.01431 
.01798 

5 

1.02018 

1.02055 

1.02092 

1.02129 

1.02165 

6 

.02386 

.O2422 

.02459 

.02496 

.02532 

7 

.02752 

.02789 

.02826 

.02863 

.02899 

9 

.03120 
.03486 

.03156 

•03193 
.03560 

.03290 
•03597 

.03266 
•03633 

SMITHSONIAN  TABLES. 


TABLE  156  (continued). 
VOLUME  OF   GASES. 


165 


(b)  Values  oi  1 4- .00367*  lor  Values  of  *  between  —90°  and  + 1990°  0.  by 
10°  Steps. 


t 

00 

10 

20 

30 

40 

—000 

1.  00000 

0.96330 

0.92660 

0.88990 

0.85320 

4  ooo 

IOO 
200 
300 
4OO 

1.  00000 

1.36700 
1.73400 

2.IOIOO 

2.46800 

1.03670 
1.40370 
1.77070 
2.13770 
2.50470 

1.07340 
1.44040 
1.80740 
2.17440 
2.54140 

I.IIOIO 

1.47710 
1.84410 

2.2IIIO 
2.57810 

1.14680 
1.51380 
1.88080 
2.24780 
2.61480 

500 

600 
700 
800 
900 

2.83500 
3.20200 

3.56900 
3.93600 
4.30300 

2.87170 

3.23870 
3.60570 
3.97270 
4-33970 

2.90840 
3-27540 
3.64240 
4.00940 
4.37640 

2.94510 
3.3I2IO 
3.67910 
4.04610 
44I3IO 

2.98180 
3.34880 
3-7I580 
4.08280 
4.44980 

1000 

IIOO 
1200 

1300 
1400 

4.67000 
5.03700 
5.40400 
5.77100 
6.13800 

4.70670 
5-07370 
5.44070 
5.80770 
6.17470 

4-74340 
5.11040 
5-47740 
5.84440 
6.21140 

478010 
5.I47IO 

5-5MIO 
5.88110 
6.24810 

4.81680 
5.18380 
5.55080 

6.28480 

1500 

1600 
1700 
1800 
1900 

6.50500 
6.87200 

7.23900 

7.60600 
7.97300 

6.54170 

6.90870 

7.27570 
7.64270 

8.00970 

6.57840 
6.94540 
7.31240 
7.67940 
8.04640 

6.61510 
6.98210 
7.34910 
7.71610 
8.08310 

6.65180 

7.01880 
7.38580 
7.75280 
8.11980 

2000 

8.34000 

8.37670 

8.41340 

8.45010 

8.48680 

* 

50 

60 

70 

80 

90 

—000 

0.81650 

0.77980 

0.74310 

0.70640 

0.66970 

+000 

IOO 
200 

300 
400 

1.18350 

Jt-SSoS0 

1.91750 

2.28450 
2.65150 

I.22O2O 
1.58720 
1.95420 
2.32I2O 
2.68820 

1.25690 
1.62390 
1.99090 
2-35790 
2.72490 

1.29360 
1.66060 
2.02760 
2.39460 
2.76160 

I-33030 
1.69730 
2.06430 
2.43130 
2.79830 

500 

600 
700 
800 
900 

3.01850 

3-38550 
3-7525° 
4.11950 
4.48650 

3-°5520 
3.42220 
3.78920 
4.15620 
4.52320 

3.09190 
3-45890 
3.82590 
4.19290 
4-55990 

3.12860 
3-49560 
3.86260 
4.22960 
4.59660 

3-I6530 
3-53230 
3-89930 
4.26630 

4-63330 

1000 

IIOO 
1200 

1300 
1400 

4-85350 

5.22050 

5-58750 
5-95450 
6.32150 

4.89020 
5.25720 
5.62420 
5.99120 
6.35820 

4.92690 
5-29390 
5.66090 
6.02790 
6.39490 

4.96360 
5-33060 
5.69760 
6.06460 
6.43160 

5.00030 
5-36730 
5-73430 
6.10130 
6.46830 

1500 

1600 
1700 
1800 
1900 

6.68850 

7-05550 
7.42250 
7.78950 

8.15650 

6.72520 
7.09220 
7.45920 
7.82620 
8.19320 

6.76190 
7.12890 
7-49590 
7.86290 
8.22990 

6.79860 
7.16560 
7-53260 

dfe 

6.83530 
7.20230 
7.56930 
7-93630 
8.3033° 

2000 

8.52350 

8.56020 

8.59690 

8.63360 

8.67030 

SMITHSONIAN  TABLES. 


i66 


TABLE  156  (continued). 

VOLUME   OF 

(c)  Logarithms  of  1  -f  .00367  t  lor  Values 


* 

0 

1 

2 

3 

4 

Mean  diff. 
per  degree. 

—  40 

1931051 

1.929179 

1.927299 

1.925410 

T.9235I3 

1884 

—  30 

—  20 

•949341 
.966892 

.947546 
.965169 

•945744 
.963438 

-943934 
.961701 

.942117 
•959957 

1805 

—  10 

.983762 

.982104 

.980440 

.978769 

•977092 

1667 

—  O 

o.oooooo 

.998403 

.996801 

.995192 

•993577 

1605 

+  0 

0.000000 

0.001591 

0.003176 

0.004755 

0.006329 

1582 

10 

•015653 

.017188 

.018717 

.020241 

.021760 

1526 

20 

3° 

.030762 

.045362 

.032244 
.046796 

.033721 
.048224 

•035193 
.049648 

.036661 
.051068 

1474 
1426 

40 

.059488 

.060875 

.062259 

•063637 

.065012 

1381 

50 

0.073168 

0.074513 

0-075853 

0.077190 

0.078522 

1335 

60 

.086431 

.087735 

.089036 

.090332 

.091624 

1299 

70 

.099301 

.100567 

.101829 

.103088 

.104344 

80 

.111800 

.113030 

.114257 

.115481 

.116701 

1226 

90 

.123950 

.125146 

.126339 

.127529 

.128716 

1191 

100 

0.135768 

0-136933 

0.138094 

0.139252 

0.140408 

1158 

no 

.147274 

.248408 

-1  49  539 

.150667 

•I5I793 

1129 

1  20 

.158483 

.159588 

.160691 

.161790 

.162887 

IIOI 

130 

.169410 

.170488 

•171563 

.172635 

.173705 

1074 

140 

.180068 

.181120 

.182169 

.183216 

.184260 

1048 

150 

0.190472 

0.191498 

0.192523 

0.193545 

0.194564 

1023 

1  60 

.200632 

•201635 

•202635 

.203634 

.204630 

IOOO 

170 

.210559 

.211540 

.212518 

•213494 

.214468 

976 

1  80 

.220265 

.221224 

.222180 

.223135 

.224087 

956 

190 

.229759 

•230697 

•231633 

•232567 

•233499 

935 

200 

0.239049 

0.239967 

0.240884 

0.241798 

0.242710 

916 

210 

.248145 

.249044 

.249942 

.250837 

•25173* 

897 

220 

•257054 

•257935 

.258814 

.259692 

.260567 

878 

230 

•265784 

.266648 

.267510 

.268370 

.269228 

861 

240 

•274343 

.275189 

•276034 

.276877 

.277719 

844 

250 

0.282735 

0.283566 

0.284395 

0.285222 

0.286048 

828 

260 

.290969 

.291784 

.292597 

.293409 

.294219 

813 

270 
280 
290 

.299049 
.306982 
•314773 

•299849 
.307768 

•3J5544 

.300648 
•308552 

.301445 
•309334 
•3  17083 

.302240 

•3IOII5 
•3*7850 

798 

8 

300 

0.322426 

0.323184 

0.323941 

0.324696 

0.325450 

756 

310 

•329947 

.330692 

.331435 

•332178 

•3329I9 

743 

320 
330 

•337339 
.344608 

.338072 
•345329 

.338803 
.346048 

•339533 
.346766 

.340262 
.347482 

730 
719 

340 

•35!758 

.352466 

•353174 

.353880 

•354585 

707 

350 

360 

0-358791 
•365713 

0.359488 
.366399 

0.360184 
.367084 

0.360879 
.367768 

0.361573 
.368451 

696 

684 

370 
380 
390 

•372525 
.379233 
•385439 

.373201 
.379898 
.386494 

.373875 
.380562 
.387148 

•374549 
.381225 
.387801 

•375221 
.381887 

•388453 

674 
664 
654 

SMITHSONIAN  TABLES. 


TABLE  156  (continued). 
CASES. 
of  <  between  -49°  and  +399°  0.  by  Degrees. 


i67 


t 

6 

6 

7 

8 

9 

Mean  diff. 
per  degree. 

—  40 

1.921608 

1.919695 

1.917773 

1.915843 

1.913904 

1926 

—  30 

—  20 

.940292 
.958205 

•938460 
•956447 

.936619 
.954681 

.934771 
.952909 

•93291  5 
.951129 

1845 
1771 

—  10 

•975409 

•973719 

.972022 

.970319 

.968609 

1699 

—  O 

•99*957 

.990330 

.988697 

.987058 

•985413 

+  0 

0.007897 

0.009459 

0.011016 

0.012567 

0.014113 

1554 

10 

.023273 

.024781 

.026284 

.027782 

.029274 

1500 

20 

.038123 

.039581 

.041034 

.042481 

•043924 

1450 

30 
40 

.052482 
.066382 

•053893 
.067748 

.055298 
.069109 

.056699 
.070466 

.058096 
.071819 

1402 
1359 

50 

0.079847 

0.081174 

0.082495 

0.083811 

0.085123 

1315 

60 

.092914 

.094198 

.095486 

.096765 

.098031 

I28l 

70 

•I05595 

.106843 

.108088 

.109329 

.110566 

1243 

80 

.117917 

.119130 

.120340 

.121547 

.122750 

12IO 

90 

.129899 

.131079 

.132256 

.133430 

.134601 

1175 

100 

0.141559 

0.142708 

0.143854 

0.144997 

0.146137 

1144 

no 

.152915 

•154034 

•I55I5I 

.156264 

-1  57375 

IIT5 

120 

.163981 

.164072 

.166161 

.167246 

.168330 

1087 

130 

.174772 

.175836 

.176898 

.177958 

.179014 

1060 

I4O 

.185301 

.186340 

.*87377 

.188411 

.189443 

1035 

150 

0.195581 

0.196596 

0.197608 

0.198619 

0.199626 

IOII 

1  60 

.205624 

.206615 

.207605 

.208592 

.209577 

988 

170 

•215439 

.216409 

.217376 

.218341 

.219304 

966 

1  80 

.225038 

.225986 

.226932 

.227876 

.228819 

946 

190 

•234429 

•235357 

.236283 

.237207 

.238129 

925 

200 

0.243621 

0.244529 

0.245436 

0.246341 

0.247244 

906 

210 
2  2O 

.252623 
.261441 

•253512 
•262313 

.254400 
.263184 

•255287 
.264052 

.256172 
.264919 

887 
870 

230 
240 

.270085 
•278559 

.270940 
.279398 

.271793 
.280234 

.272644 
.281070 

.273494 
.281903 

853 
836 

250 

260 

0.286872 
.295028 

0.287694 
•295835 

0.288515 
.296640 

0.289326 
.297445 

0.290153 
.298248 

820 

805 

270 

.303034 

.303827 

.304618 

.305407 

.306196 

790 

280 
290 

.310895 
.318616 

•3Il673 
•3  T  938  1 

.312450 
.320144 

.313226 
.320906 

.314000 
.321667 

776 
763 

300 

0.326203 

0.326954 

0.327704 

0.328453 

0.329201 

750 

310 

.333659 

•334397 

•335*35 

•335871 

.336606 

737 

320 

.340989 

.341715 

.342441 

•343  r  64 

.343887 

724 

330 

•348198 

.348912 

.349624 

•350337 

.351048 

713 

340 

.355289 

•355991 

•356693 

•357394 

.358093 

701 

350 

0.362266 

0.362957 

0.363648 

0.364337 

0.365025 

690 

360 
370 

.369132 

.375892 

.369813 
.376562 

.370493 
•377232 

.377900 

.371849 
•378567 

678 
668 

380 

•382548 

.383208 

.383868 

•384525 

.385183 

658 

390 

.389104 

.389754 

.390403 

.391052 

.391699 

648 

SMITHSONIAN  TABLES. 


1 68  TABLE   156  (continued). 

VOLUME   OF  GASES. 

(d)  Logarithms  of  1  +  .00367  *  for  Values  oi  t  between  400°  and  1990°  0.  by  10°  Steps. 


t 

00 

10 

20 

30 

40 

400 

0.392345 

0.398756 

0.405073 

0.411300 

0.417439 

500 

0.452553 

0.458139 

0.463654 

0.469100 

0.474479 

600 

.505421 

•5I037i 

.515264 

.520103 

•524889 

700 

•552547 

.556990 

.561388 

•565742 

.570052 

800 
900 

•595055 
•633771 

.637460 

.603079 
.641117 

•607037 
.644744 

.610958 
.648341 

1000 

IIOO 

0.669317 
.702172 

0.672717 
•705325 

0.676090 
.708455 

0.679437 
•7  1  ^63 

0.682759 
.714648 

1200 

•732715 

•735655 

•738575 

•74M75 

•744356 

I3OO 

.761251 

.764004 

.766740 

•769459 

.772160 

I4OO 

.788027 

.790616 

.793190 

•795748 

.798292 

1500 

0.813247 

0.815691 

0.818120 

0.820536 

0.822939 

1600 

.837083 

•839396 

.841697 

.843986 

.846263 

1700 

•859679 

.861875 

.864060 

.866234 

.868398 

1800 

.881156 

.883247 

.885327 

.887398 

.889459 

1900 

.901622 

.903616 

.905602 

.907578 

•909545 

* 

50 

60 

70 

80 

90 

400 

0.423492 

0.429462 

0-435351 

0.441161 

0.446894 

500 

600 

0.479791 
.529623 

0.485040 
•534305 

0.490225 
•538938 

0-495350 

•543522 

0.500415 
•548058 

700 

.574321 

•57854§ 

.582734 

.586880 

•590987 

800 

.614845 

.618696 

.622515 

.626299 

.630051 

900 

.651908 

.655446 

•658955 

•662437 

.665890 

1000 

0.686055 

0.689327 

0.692574 

0.695797 

0.698996 

IIOO 

.717712 

•720755 

•723776 

.726776 

.729756 

1  200 
1300 

.747218 
.774845 

.750061 
•7775J4 

.752886 
.780166 

•755692 
.782802 

.785422 

1400 

.800820 

•803334 

.805834 

.808319 

.810790 

1500 

1600 
1700 
1800 

0.825329 
.848528 
.870550 
.891510 

0.827705 
.850781 
.872692 
•893551 

0.830069 

•853023 
.874824 

•895583 

0.832420 

•855253 
.876945 
•897605 

0.834758 

.857471 
.879056 
.899618 

1900 

.911504 

•9*3454 

•915395 

.917327 

.919251 

SMITHSONIAN  TABLES. 


TABLE  157. 


169 


DETERMINATION  OF   HEIGHTS  BY  THE   BAROMETER, 


Formula  of  Babinet:  Z  —  C  ^°       B. 
B0  +  B 

C  (in  feet)  =  52494  [i  +  /0  +  *~ 
C  (in  meters)  =  16000  [i  +  il^J 


I  English  measures. 


metric  measures. 


In  which  Z  =  difference  of  height  of  two  stations  in  feet  or  meters. 
BQ,  B  =  barometric  readings  at  the  lower  and  upper  stations  respectively,  corrected  for  all 

sources  of  instrumental  error. 
^0,  t  —  air  temperatures  at  the  lower  and  upper  stations  respectively. 

Values  of  C. 


ENGLISH  MEASURES. 

METRIC  MEASURES. 

*  Co  +  4 

C 

LogC 

H'o  +  0. 

C 

LogC 

Fahr. 

Feet. 

Cent. 

Meters. 

10° 

49928 

4.69834 

—10° 

'536°, 

4.18639 

15 

505H 

•70339 

—8 

15488 

.19000 

—6 

15616 

•'9357 

20 

5!094 

4.70837 

—4 

15744 

.19712 

25 

5l677 

•71330 

—  2 

15872 

.20063 

30 

52261 

4.71818 

0 

16000 

4.20412 

35 

52844 

•72300 

+  2 

16128 

.20758 

4 

16256 

.2IIOI 

40 

45 

53428 
54011 

4.72777 
.73248 

6 
8 

16384 
16512 

.21442 
.21780 

50 

54595 

4-737I5 

10 

16640 

4.22II5 

55 

55178 

•74177 

12 
14 

16768 
16896 

.22448 
.22778 

60 

5576i 

474633 

16 

17024 

.23106 

65 

56344 

•75085 

18 

17152 

•23431 

70 

56927 

4-75532 

20 

17280 

4-23754 

75 

575" 

•75975 

22 

17408 

.24075 

24 

J7536 

•24393 

80 

58094 

4.76413 

26 

17664 

.24709 

85 

58677 

.76847 

28 

17792 

.25022 

90 

59260 

477276 

30 

17920 

4-25334 

95 

59844 

.77702 

32 

18048 

•25643 

18176 

•2595° 

100 

60427 

4.78123 

36 

18304 

•26255 

Values  only  approximate.     Not  good  for  great  altitudes.    A  more  accurate  formula  with 
corresponding  tables  may  be  found  in  Smithsonian  Meteorological  Tables,  3  revised  ed.  1906- 

SMITHSONIAN  TABLES. 


TABLE  158. 


BAROMETRIC 


Barometric  pressures  corresponding  to  different 
This  table  is  useful  when  a  boiling-point  apparatus  is  used 


(a)  Common  Measure.* 


Temp.  °  F. 

.0 

.1 

.2 

.3 

A 

.5 

.6 

.7 

.8 

.9 

185 

186 

17.06 
17.42 

17.09 
17-47 

I7.I3 
17.51 

17.17 
17.54 

17.20 
17.58 

17.24 
17.62 

17.28 
17.66 

I7.32 
17.70 

17-35 
17-74 

17-39 
17.77 

187 

1  88 

17.81 
18.20 

17-85 
18.24 

17.89 
18.28 

17.93 
18.32 

17.97 
18.36 

18.01 
18.40 

18.05 
18.44 

1  8.08 
18.48 

1  8.  1  2 

18.52 

18.16 

18.56 

189 

190 

18.60 
19.00 

18.64 
19.04 

1  8.68 
19.08 

18.72 
19.12 

18.76 
19.16 

18.80 
19.21 

18.84 
19.25 

18.88 
19.29 

18.92 
19.33 

18.96 
19-37 

191 

192 

19.41 
19-83 

r9-45 
19.87 

19.49 
19.91 

19-54 
19.96 

19.58 

20.00 

19.62 
20.04 

19.66 
20.08 

19.70 
20.13 

J9-75 
20.17 

19.79 

2O.2I 

193 

194 

20.26 
20.68 

20.30 
20.73 

20.34 
20.78 

20.38 
20.82 

20.43 
20.86 

20.47 
20.91 

20.51 
20.95 

20.56 
20.99 

20.60 
21.04 

20.64 
2  1.  08 

195 

196 

21.  n 

21.58 

21.17 
21.62 

21.22 
21.67 

21.26 

21.71 

21.31 
21.76 

21-35 
21.80 

21.40 
21.85 

21.44 
21.90 

21.48 
21.94 

21-53 
21.99 

197 

198 

22.03 
22.50 

22.08 
22.55 

22.13 
22-59 

22.17 
22.64 

22.22 
22.69 

22.27 
22.73 

22.31 

22.78 

22.36 
22.83 

22.41 

22.88 

22.45 
22.92 

199 

200 

22.97 
23-45 

23.02 
23-50 

23.07 
23-55 

23.12 
23.60 

23.16 
23.65 

23.21 
23.70 

23.26 
23-75 

23-31 
23-79 

23.36 
23.84 

23.40 
23.89 

201 

202 

23-94 
24.44 

23-99 
24.49 

24.04 
24-54 

24.09 
24.59 

24.14 
24.64 

24.19 
24.69 

24.24 
24.74 

24.29 
24.79 

24.34 
24.85 

24.39 
24.90 

203 

204 

24-95 
25.46 

25.00 
25-52 

25.05 
25.57 

25.10 
25.62 

25.15 
25.67 

25.20 
25.72 

25.26 
2578 

25-31 
25-83 

%& 

25.41 
25.94 

205 

206 

25-99 
26.52 

26.04 
26.58 

26.09 
26.63 

26.15 
26.68 

26.2O 
26.74 

26.25 
26.79 

26.31 
26.85 

26.36 
26.90 

26.41 

26.96 

26.47 

27.01 

207 

208 

27.06 
27.62 

27.12 
27.67 

27.17 
27-73 

27.23 
27.78 

27.28 
27.84 

27.34 
27.90 

27.39 
2795 

2745 
28.01 

27.51 

28.07 

27.56 
28.12 

209 

2IO 

28.18 
28.75 

28.24 
28.81 

28.29 
28.87 

28.35 
28.92 

28.41 
28.98 

28.46 
29.04 

28.52 
29.10 

28.58 
29.16 

28.63 

29.21 

28.69 
29.27 

211 

212 

29-33 
29.92 

29-39 
29.98 

2945 
30.04 

29.51 
30.10 

29-57 
30.16 

29.63 
30.22 

29.68 
30.28 

29.74 
30-34 

29.80 
30.40 

29.86 
30.46 

*  Pressures  in  inches  of  mercury 

The  values  at  the  lower  temperatures  are  perhaps  J%  too  low.    Table  (b)  is  based  on  more  recent  data  (1913). 
SMITHSONIAN  TABLES. 


TABLE  1  58  (continued). 


171 


PRESSURES. 


temperatures  of  the  boiling-point  of  water. 

in  place  of  the  barometer  for  the  determination  of  heights. 


(b)  Metric  Measure.* 


Temp.°C. 

.0 

.1 

.2 

.3 

.4 

.5 

.8 

.7 

.8 

.9 

80° 

355-5 

356-9 

3584 

359-8 

361.3 

362.7 

364.2 

365-7 

367.1 

368.6 

81 

370.1 

371.6 

373-1 

374-6 

376.1 

377-6 

379-1 

380.6 

382.2 

383.7 

82 

385-2 

386.8 

388.3 

389-9 

391-4 

393-0 

394-6 

396.2 

397-7 

399-3 

83 

400.9 

402.5 

404.1 

4057 

407.3 

408.9 

410.5 

412.2 

413.8 

415.4 

84 

417.1 

418.7 

420.4 

422.0 

423.7 

4254 

427.0 

428.7 

430-4 

432-1 

85 

433-8 

435-5 

437-2 

438.9 

440.6 

442.4 

444.1 

4458 

447-6 

449-3 

86 

451.1 

452.8 

454-6 

456.4 

458.1 

459-9 

461.7 

463.5 

465-3 

467.1 

8? 

468.9 

470.7 

472.5 

474-4 

476.2 

478.0 

479-9 

481.7 

483-6 

485.5 

88 

487-3 

489.2 

491.1 

493-0 

494-9 

496.8 

498.7 

500.6 

502.5 

504.4 

89 

506.4 

508.3 

510.2 

512.2 

5'4-i 

516.1 

518.1 

520.0 

522.0 

524-0 

90 

526.0 

528.0 

530-0 

532.0 

534-0 

536.0 

538.1 

540.1 

542-2 

544-2 

9i 

546.3 

548.3 

550-4 

552-5 

554-6 

556.6 

558.7 

560.8 

563-0 

565-1 

92 

567.2 

569-3 

5714 

573-6 

575-7 

577-91 

580.1 

582.2 

584-4 

586.6 

93 

588.8 

591.0 

593-2 

595-4 

597-6 

599.8 

602.0 

604.3 

606.5 

608.8 

94 

611.0 

6i3-3 

615.6 

617.8 

620.1 

622.4 

624.7 

627.0 

629.4 

631-7 

95 

634.0 

636-3 

638.7 

641.0 

643-4 

645.8 

648.1 

650.5 

652.9 

655-3 

96 

657.7 

660.1 

662.5 

664.9 

667.4 

669.8 

672.2 

674.7 

677.2 

679.6 

97 

682.1 

684.6 

687.1 

689.6 

692.1 

694.6 

697.1 

699-6 

702.2 

704-7 

98 

707-3 

709.8 

712.4 

7i5-o 

717.6 

720.2 

722.8 

7254 

728.0 

730.6 

99 

733-2 

735-9 

738-5 

741.2 

743-8 

746.5 

749-2 

751-9 

754-6 

757-3 

100 

760.0 

762.7 

7654 

768.2 

770.9 

773-7 

776.4 

779-2 

782.0 

784.8 

*  Pressure  in  millimeters  of  mercury. 


SMITHSONIAN  TABLES. 


172 


TABLES   159-162. 
STANDARD  WAVE-LENGTHS, 


TABLE  159.  —  Absolute  Wave-length  of  Red  Cadmium  Line  In  Air,  760  mm.    Pressure,  15°  C. 

6438.4722     Michelson,  Travaux  et  Mem.  du  Bur.  intern,  des  Poids  et  Mesures,  n,  1895. 
6438.4700    Michelson,  corrected  by  Benoit,  Fabry,  Perot,  C.  R.  144,  1082,  1907. 
6438.4696     (accepted  primary  standard)  Benoit,  Fabry,  Perot,  C.  R.  144,  1082,  1907. 


TABLE  160.— International  Secondary  Standards.    Iron  Arc  Lines. 

Adopted  as  secondary  standards  at  the  International  Union  for  Cooperation  in  Solar  Research 
(transactions,  1910).  Means  of  measures  of  Fabry-Buisson  (i),  Pfund  (2),  and  Eversheim  (3).  Re- 
ferred to  primary  standard  =  Cd.  line,  A  =  6438.4696  Angstroms  (serving  to  define  an  Angstrom). 
76o  mm.,  15°  C.  Iron  rods,  7  mm.  diam.  length  of  arc,  6  mm.;  6  amp.  for  A.  greater  than  4000 
Angstroms,  4  amp.  for  lesser  wave-lengths;  continuous  current,  +  P°le  above  the  — ,  220  volts; 
source  of  light,  2  mm.  at  arc's  center.  Lines  adopted  in  1910. 


Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

4282.408 

4547.853 

4789.657 

5083.344 

5405.780 

56iq.66l 

6230.734 

4315.089 

4592.658 

4878.225 

5110.415 

5434.527 

5658.836 

6265.145 

4375-934 

4602.947 

4903-325 

5167.492 

5455-6I4 

5763.013 

6318.028 

4427.314 
4466.556 

4647439 
4691.417 

4919.007 
500I.88I 

5192.363 
5232.957 

5497-522 
5506.784 

6027.059 
6065.492 

6335-34I 
6393.612 

4494.572 

4707.288 

5012.073 

5266.569 

5569-633 

6137.701 

6430.859 

4531.155 

4736.786 

5049.827 

5371-495 

5586.772 

6191.568 

6494.993 

TABLE  161. —International  Secondary  Standards.    Iron  Arc  Lines. 

Adopted  in  1913.     (4)  Means  of  measures  of  Fabry-Buisson,  Pfund,  Burns  and  Eversheim. 


Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

Wave-length. 

3370.789 
3399-337 
3485.345 
35I3.82I 
3556.88i 

3606.682 
3640.392 

3676.313 
3677.629 
3724.380 

3753.615 
3805.346 
3843.261 
3850.820 
3865.527 

3906.482 
3907.937 
3935.818 
3977746 
4021.872 

4076.642 
4118.552 
4134.685 
4147.676 
4191.443 

4233-615 
5709.396 
6546.250 
6592.928 
6678.004 

6750.250 
5857  .7  59  Ni 
5892.882  Ni 

(i)  Astrophysical  Journal,  28,  p.  169,  1908;  (2)  Ditto,  28,  p.  197,  1908;  (3)  Annalen  der  Physik,  30, 
p.  815, 1909.  See  also  Eversheim,  ibid.  36,  p.  1071,  1911  ;  Buisson  et  Fabry,  ibid.  38,  p.  245,  1912  ; 
(4)  Astrophysical  Journal,  39,  p.  93,  1914. 


TABLE  162. —Some  of  the  Stronger  Lines  of  Some  of  the  Elements. 


Barium 

5535-7 

Helium 

5875.8 

Magnesium 

5167.5 

Sodium   . 

5890.2 

Caesium 

4555-4 

"    . 

5876.2 

5r72-9 

5896.2 

4593-3 

Hydrogen 

4101.8 

« 

5l83-8 

Strontium 

4607-5 

Calcium 
Cadmium 

5589.0 
4799-9 

it 

4340-7 
4861.5 

Mercury 
Potassium 

5461.0 
7668.5 

ti 

ft 

5481.2 
6408.6 

« 

6438.5 

« 
Lithium 

6563.0 
6708.2 

« 
Rubidium 

7701.9 
6298.7 

Thallium. 

5350.6 

SMITHSONIAN  TABLES. 


TABLE  163. 
STANDARD   SOLAR   WAVE-LENGTHS.     ROWLAND'S   VALUES. 


173 


Wave-lengths  are  in  Angstrom  units  (10  7  mm.),  in  air  at  20°  C  and  76  cm.  of  mercury  pressure. 
The  intensities  run  from  I,  just  clearly  visible  on  the  map,  to  1000  for  the  H  and  K  lines;  below 
i  in  order  of  faintness  to  oooo  as  the  lines  are  more  and  more  difficult  to  see.  This  table  contains 
only  the  lines  above  5. 

N  indicates  a  line  not  clearly  defined,  probably  an  undissolved  multiple  line ;  s,  a  faded  appear- 
ing line;  d,  a  double.  In  the  "substance"  column,  where  two  or  more  elements  are  given,  the 
line  is  compound ;  the  order  in  which  they  are  given  indicates  the  portion  of  the  line  due  to  each 
element ;  when  the  solar  line  is  too  strong  to  be  due  wholly  to  the  element  given,  it  is  represented, 
-Fe,  for  example;  when  commas  separate  the  elements  instead  of  a  dash,  the  metallic  lines  coin- 
cide with  the  same  part  of  the  solar  line,  Fe,  Cr,  for  example. 

Capital  letters  next  the  wave-length  numbers  are  the  ordinary  designations  of  the  lines.  A  indi- 
cates atmospheric  lines,  (wv),  due  to  water  vapor,  (O),  due  to  Oxygen. 


Wave- 
length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave- 
length. 

Sub- 
stance. 

Inten- 
sity. 

3037.5103 

Fe 

10  N 

3372.947 

Ti-Pd 

10  d? 

3533-345 

Fe 

6 

3047.7253 

Fe 

20  N 

3380.722 

Ni 

6N 

3536-709 

Fe 

7 

3053-530S 

— 

7d? 

3414.911 

Ni 

15 

3541-237 

Fe 

7 

Mn,  Ni 

IO 

3423.848 

Ni 

7 

3542.232 

Fe 

6 

3057-5525 

Ti,  Fe 

20 

3433-7  !  5 

Ni,  Cr 

8d? 

3555.079 

Fe 

9 

3059.2123 
3067.3693 

Fe 
Fe 

20 
8 

3440.7623  )  0 
3441-1555  ) 

Fe 
Fe 

20 
IS 

3558.6723 
3565-5355 

Fe 
Fe 

8 

20 

3073.091 

Ti,- 

6Nd? 

3442.118 

Mn 

6 

3566.522 

Ni 

10 

3078.7693 

Ti,  - 

8d? 

3444.0203 

Fe 

8N 

3570.2733 

Fe 

2O 

3088.1453 

Ti 

7d? 

3446.406 

Ni 

15 

3572.014 

Ni 

6 

3134.2303 

Ni,  Fe 

8 

3449.583 

Co 

6d? 

3572.712 

Se,  - 

6 

3188.656 

-  Fe 

6d? 

3453-039 

Ni 

6d? 

3578.832 

Cr 

10 

3236.7033 

Ti 

7N 

3458.601 

Ni 

8 

3581.3493 

Fe 

3° 

3239.170 

Ti 

7 

3461.801 

Ni 

8 

3584-800 

Fe 

6 

3242.125 

Ti,  - 

8 

3462.950 

Co 

6 

3585-I05 

Fe 

6 

3243.189 
3247.6883 

-,  Ni 
Cu 

6 

10 

3466.0153 
3475.5943 

Fe 
Fe 

6 

IO 

3585-479 
3585.859 

Fe 
Fe 

I 

3256.021 

Fe? 

6 

3476.8493 

Fe 

8 

3587.130 

Fe 

8 

3267.8343 

V 

6 

3483.923 

Ni 

6d? 

3587.370 

Co 

7; 

3271.129 

Fe 

6 

3485.493 

FeCo 

6 

3588.084 

Ni 

3271.791 

Ti,  Fe 

6d? 

3490.7335 

Fe 

10  N 

3593.636 

Cr 

9 

3274.0963 

3277.482 

Cu 

Co-Fe 

IO 

3493-"4 
3497-9823 

Ni 
Fe 

10  N 
8 

3594.784 
3597.854 

Fe 

Ni 

6 
8 

3286.898 

3295-95IS 

Fe 
Fe,  Mn 

?N 

3500.9963 
3510.466 

Ni 
Ni 

6d? 

8 

3605.4795 
3606.8383 

Cr 

Fe 

\ 

3302.5103 

Na 

6 

3512.785 

Co 

6 

3609.0083 

Fe 

20 

3315-807 

Ni 

7d? 

35I3-965S 

Fe 

7 

3612.882 

Ni 

6d? 

3318.1603 

Ti 

6 

3515.206 

Ni 

12 

3617.9345 

Fe 

6 

3320.391 

Ni 

7 

35I9-904 

N 

7 

3618.9193 

Fe 

20 

3336-820 

Mg 

8N 

3521.4103 

Fe 

8 

3619.539 

Ni 

8 

3349-597 

Ti 

7 

3524-677 

Ni 

20 

3621.6125 

Fe 

6 

3361.327 

Ti 

8 

3526.183 

Fe 

6 

3622.1473 

Fe 

6 

3365-908 

Ni 

6 

3526.988 

Co 

6 

3631.6053 

Fe 

'5 

3366.311 
3369-7I3 

Ti,  Ni 

Fe,  Ni 

6d? 
6 

3533-I56 

Fe-Co 
Fe 

6 
6 

3640.5353 
3642.820 

Cr-Fe 
Ti 

6 
7 

Corrections  to  reduce  Rowland's  wave-lengths  to  standards  of  Table  160  (the  accepted  standards,  1913).  Temperature 

15°  C,  pressure  760  mm. 

'  The  differences  "  (Fabry-Buisson-arc-Iron) —  (Rowland-solar-iron)  'r  lines  were  plotted,  a  smooth  curve  drawn,  and 

the  following  values  obtained  : 

Wave-length        3000.        3100.        3200.        3300.        3400.         3500.        3600.        3700, 
Correction         — .106     — .115      — .124      — .137     — .148     — .154     — .155     — .140 

H.  A.  Rowland,  "  A  preliminary  table  of  solar-spectrum  wave-lengths,"  Astrophysical  Journal,  1-6,  1893-1897. 
SMITHSONIAN  TABLES. 


TABLE   1  63  (continued). 
STANDARD  SOLAR  WAVE-LENGTHS.     ROWLAND'S    VALUES. 


Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

3647.9883 

Fe 

12 

3826.0275 

Fe 

20 

4045-975S 

Fe 

30 

365  I-  247 

Fe,- 

6 

3827.980 

Fe 

8 

4055.7013 

Mn 

6 

3651.614 

Fe 

7 

3829.5015 

Mg     . 

IO 

4057.668 

— 

7 

Fe,  Cr 

6 

3831.837 

Ni 

6 

4063.7593 

Fe 

20 

3680.0693 
3684.2583 

Fe 
Fe 

,1 

3832.4505 
3834.364 

Mg 
Fe 

15 

10 

4068.137 
4071.9085 

Fe-Mn 
Fe 

6 

15 

3685-339 

Ti 

lod? 

3838.4355 

Mg-C 

25 

4077.8855 

Sr 

8 

3686.141 

Ti-Fe 

6 

3840.5805 

Fe-C 

8 

4i02.oooH5 

H,  In 

4oN 

3687.6103 

Fe 

6 

384LI95 

Fe-Mn 

10 

4121.4775 

Cr-Co 

6d? 

3689.614 

Fe 

6 

3845.606 

C-Co 

8d? 

4128.251 

Ce-V,- 

6d 

370L234 

Fe 

8 

3850.118 

Fe-Cr 

IO 

4132-235 

Fe-Co 

10 

3705.7085 
3706.175 

Fe 

Ca,  Mn 

A 

3856.5245 
3857.805 

Fe 
Cr-C 

8 
6d? 

4137.156 
4140.089 

Fe 
Fe 

6 
6 

3709.3893 

Fe 

8 

3858.442 

Ni 

7 

4144.038 

Fe 

15 

3716.5913 

Fe 

7 

3860.0553 

Fe-C 

20 

4167.438 

— 

8 

3720.0845 

Fe 

40 

3865.674 

Fe-C 

7 

4187.204 

Fe 

6 

3722.6923 

Ni 

10 

3872.639 

Fe 

6 

4191.595 

Fe 

6 

3724.526 

Fe 

6 

3878.152 

Fe-C 

8 

4202.1983 

Fe 

8 

3732.5455 

Co-Fe 

6 

3878.720 

Fe 

7Nd? 

4226-9O4sg 

Ca 

20  d? 

3733-469S 

Fe- 

7d? 

3886.4343 

Fe 

15 

4233-772 

Fe 

6 

3735-OI4s 

Fe 

40 

3887.196 

Fe 

7 

4236.112 

Fe 

8 

3737.2815 
3738.466 

Fe 

36 

3894.211 
3895-803 

Fe 

8d 
7 

4250.2873 
4250.9455 

Fe 
Fe 

8 
8 

3743-508 

Fe-Ti 

6 

3899.850 

Fe 

8 

4254.5053 

Cr 

8 

3745-7I7S 

Fe 

8 

3903.090 

Cr,  Fe,  Mo 

10 

4260.6405 

Fe 

10 

3746.0585 

Fe 

6 

3904.023 

— 

8d 

4271.9343 

Fe 

15 

3748.4085 
3749.6315 

Fe 
Fe 

IO 

20 

3905.6605 
3906.628 

Si 
Fe 

12 

10 

4274.9583 
4308.08  1  sG 

Cr 
Fe 

7d? 

3753732 

Fe-Ti 

6d? 

3920.410 

Fe 

10 

4325-939S 

Fe 

8 

3758-375S 
3759-447 

Fe 

Ti 

i2d? 

3923-054 
3928.0755 

Fe 

Fe 

i2d? 
8 

4340.6341*7 
4376.1073 

H 
Fe 

20N 

6 

3760.196 

Fe 

5 

3930.450 

Fe 

8 

4383.7203 

Fe 

15 

3761.464 

Ti 

7 

3933-523 

— 

8N 

4404.9273 

Fe 

10 

3763-945s 

Fe 

10 

Ca 

1000 

4415.2935 

Fe 

8 

3765.689 

Fe 

6 

3934.108 

Co,  V-Cr 

8N 

4442.510 

Fe 

6 

3767.3418 

Fe 

8 

3944.1605 

Al 

15 

4447.8925 

Fe 

6 

3775-7I7 
378p74s 

Ni 
Ni 

6 

3956.819 
3957-I77S 

Fe 
Fe-Ca 

7d? 

4494.7385 
4528.798     . 

Fe 
Fe 

6 

8 

3788.0463 

Fe 

9 

3961.6743 

Al 

20 

4534.I39 

Ti-Co 

6 

3795.1475 

Fe 

8 

3968.350 

-,  Zr 

6N 

4549.808 

Ti-Co 

6d? 

3798.6553 

Fe 

6 

3968.62  53  H 

Ca 

700 

4554.2115 

Ba 

8 

3799.6933 

Fe 

7 

3968.886 

— 

6N 

4572.1563 

Ti- 

6 

3805.4863 

Fe 

6 

3969.413 

Fe 

10 

4603.126 

Fe 

6 

3806,865 

Mn-Fe 

8d? 

3974.904 

Co-Fe 

6d? 

4629.5215 

Ti-Co 

6 

3807.293 

Ni 

6 

3977.8915 

Fe 

6 

4679.0275 

Fe 

6 

3807.681 

V-Fe 

6 

3986.9035 

— 

6 

4703.1775 

Mg 

10 

3814.698 

- 

8 

4005.408 

Fe 

7 

4714.5993 

Ni 

6 

3815.9875 

Fe 

15 

4030.9185 

Mn 

tod? 

4736.963 

Fe 

6 

3820.5863!, 
3824.591 

Fe-C 
Fe 

25 

4033.2245 
4034.6443 

Mn 
Mn 

8d? 
6d 

4754-2253 
4783.6133 

Mn 
Mn 

6 

Corrections  to  reduce  Rowland's  wave-lengths  to  standards  of  Table  160  (the  accepted  standards,  1913).    Temperature 
15°  C,  pressure  760  mm. : 

Wave-length     3600.      3700.      3800.      3900.      4000.     4100.     4200.      4300.      4400.      4500.      4600.      4700.      4800. 
Correction      — .155  — .140  — .141  — .144  —  148  — .152  — .156  — .161  —  167  — .172  — .176  — .179  — .179. 


SMITHSONIAN  TABLES. 


TABLE  1  63  (continued).  175 

STANDARD   SOLAR   WAVE-LENGTHS.    ROWLAND'S   VALUES. 


Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Substance. 

Inten- 
sity. 

Wave-length. 

Sub- 
stance. 

Inten- 
sity. 

486r.527sF 

H 

3° 

5948.7653 

Si 

6 

6563.o45sC 

H 

40 

4890.9483 

Fe 

6 

5985.0403 

Fe 

6 

6593.1613 

Fe 

6 

4891.683 

Fe 

8 

6003.2393 

Fe 

6 

6867.45736 

A(0) 

6d? 

4919.1743 

Fe 

6 

6008.7853 

Fe 

6 

6868.336  L 

A(0) 

6 

4920.685 

Fe 

10 

6013.7153 

Mn 

6 

6868.478  Js 

A(0) 

6 

4957-7855 

Fe 

8 

6oi6.86lS 

Mn 

6 

6869.1423 

A(0) 

7 

5050.0083 

Fe 

6 

6o22.0l6s 

Mn 

6 

6869.3535 

A(0) 

6 

ci67%497sb4 

Mg 

15 

6024.2813 

Fe 

7 

6870.116! 

A(0) 

7  (.  j 

5171.7783 

Fe 

6 

6065.7093 

Fe 

7 

6870.249  f 

A(0) 

71  d 

Mg 

20 

6102.3923 

Fe 

6 

6871.1803 

A(0) 

8 

5183.7913^ 

Mg 

3° 

6102.9373 

Ca 

9 

6871.5323 

A(0) 

10 

5233.1223 

Fe 

7 

6108.3343 

Ni 

6 

6872.4863 

A(0) 

ii 

5266.7383 

Fe 

6 

6122.4343 

Ca 

10 

6873.0803 

A(0) 

12 

5269-723sE 

Fe 

8d? 

6136.8293 

Fe 

8 

6874.0373 

A(0) 

12 

5283.8023 

Fe 

6 

6137.915 

Fe 

7 

6874.8993 

A(0) 

'3 

5324.3733 

Fe 

7 

6141.9383 

Fe,Ba 

7 

6875.8303 

A(0) 

J3 

5328.236 

Fe 

8d? 

6I55-350 

- 

7 

6876.9583 

A(0) 

5340.121 

Fe 

6 

6162.3903 

Ca 

15 

6877.8823 

A(0) 

12 

534I-2I3 

Fe 

7 

6169.2493 

Ca 

6 

6879.2883 

A(0) 

12 

5367.6693 

Fe 

6 

6169.7783 

Ca 

7 

6880.1723 

A(0) 

6 

5370.1663 

Fe 

6 

6170.730 

Fe-Ni 

6 

6884.0763 

A(0) 

IO 

5383.5783 

Fe 

6 

6191.3933 

Ni 

6 

6886.0003 

A(0) 

II 

5397-3445 

Fe 

7d? 

6191.7793 

Fe 

9 

6886.9903 

A(0) 

12 

5405.9893 

Fe 

6 

6200.5273 

Fe 

6 

6889.1923 

A(0) 

13 

5424.2903 

Fe 

6 

6213.6443 

Fe 

6 

6890.1513 

A(0) 

5429.911 

Fe 

6d? 

6219.4943 

Fe 

6 

6892.6183 

A(0) 

14 

5447.1303 

Fe 

6d? 

6230.9433 

V-Fe 

8 

6893.5603 

A(0) 

15 

5528.6413 

Mg 

8 

6246.5353 

Fe 

8 

6896.2893 

A(0) 

14 

5569.848 

Fe 

6 

6252.7733 

-Fe 

7 

6897.2083 

A(0) 

15 

5573-075 

Fe 

6 

6256.5723 

Ni-Fe 

6 

6900.1993 

A(0) 

14 

5586.991 

Fe 

7 

6301.718 

Fe 

7 

6901.1173 

A(0) 

15 

5588.9853 

Ca 

6 

6318.239 

Fe 

6 

6904.3623 

A(0) 

14 

5615-8773 

Fe 

6 

6335-554 

Fe 

6 

6905.2713 

A(0) 

14 

5688.4363 

Na 

6 

6337048 

Fe 

7 

6908.7833 

A(0) 

571  1.3133 

Mg 

6 

6358.898 

Fe 

6 

6909.6763 

A(0) 

J3 

5763.2183 

Fe 

6 

6393.8203 

Fe 

7 

6913.4483 

A(0) 

ii 

5857.6743 

Ca 

8 

6400.2173 

Fe 

8 

6914.3373 

A(0) 

ii 

5862.5823 

Fe 

6 

6411.8653 

Fe 

7 

6918.3703 

A(0) 

9 

5890.18630-2 

Na 

3° 

6421.5703 

Fe 

6919.2503 

A(0) 

9 

5896.155  Dj 

Na 

20 

6439.2933 

Ca 

8 

6923-553S 

A(0) 

9 

5901.6823 

A(wv) 

6 

6450.0333 

Ca 

6 

6924.4273 

A(0) 

9 

5914.4303 

-  A(wv) 

6 

6494.0043 

Ca 

6 

A,  - 

6N 

5919.8603 

A(vvv) 

7 

6495-2I3 

'  Fe 

8 

7206.692 

-A 

6 

5930.4063 

Fe 

6 

6546.4795 

Ti-Fe 

6 

Corrections  to  reduce  Rowland's  wave-lengths  to  standards  of  Table  160  (the  accepted  standards,  1913).    Temperature 
15°  C,  pressure  760  mm. : 

Wave-length        4800.        4900.        5000.        5100.        5200.        5300.        5400.        5500.        5600.        5700.        5800. 
Correction       — ,179     — .176     — .173     — .170     — .166     — .171     — .212     — .217     —.218     — .213     — .209 


Wave-length        5800.        5900.        6000.        6100.        6200.        6300.        6400.        6500.        6600. 
Correction        —.209      —.209     —.213     —.214     —.213      —.210     —.209    —.210. 


6700.        6800. 


SMITHSONIAN  TABLES. 


Ij6  TABLE    164. 

TERTIARY   STANDARD   WAVE-LENGTHS.     IRON    ARC   LINES. 

For  arc  conditions  see  Table  160,  p.  172.  For  Hnes  of  group  c  class  5  for  best  results  the 
slit  should  be  at  right  angles  to  the  arc  at  its  middle  point  and  the  current  should  be  reversed 
several  times  during  the  exposure. 


Wave-lengths. 

Class. 

Inten- 
sity. 

Wave-lengths. 

Class. 

Inten- 
sity. 

Wave-lengths. 

Class. 

Inten- 
sity. 

#2781.840 

4 

4337-052 

b3 

5 

5332-909 

34 

2 

*28o6.985 

7 

4369777 

£3 

534L032 

34 

5 

#2831.559 

3 

4415.128 

bi 

8r 

5365404 

ai 

2 

*2858.34i 

3 

4443.198 

b3 

3 

5405.780 

a 

6 

*29oi.382 

4 

4461.658 

*3 

4 

5434-528 

a 

6 

*2926.584 

5 

4489.746 

*3 

3 

5473-9I3 

a 

4 

*2986.46o 

3 

4528.620 

C4 

7 

5497-521 

a 

4 

*3°°o.453 

4 

4619.297 

C4 

4 

5501.471 

a 

4 

*3°53-o7o 

4 

4786.811 

C4 

3 

5506.784 

a 

3 

*3ioo.838 
#3154.202 

2 

4 

487I-331 
4890.769 

C5 
C5 

8 
7 

J5535-4I9 
5563.612 

a 
b 

2 

3 

#3217.389 

4 

4924.773 

a 

3 

5975-352 

b 

2 

#3257.603 

4 

4939-685 

a 

3 

6027.059 

b 

3 

*33°7-238 
*3347-932 

4 
4 

4973-  "3 
4994-133 

a 
a 

2 

3 

6065.495 
6136.624 

b 
b 

4 
5 

#3389.748 

3 

5041.076 

a 

3 

6I57-734 

b 

4 

#3476.705 

5 

5041.760 

a 

4 

6165.370 

b 

3 

#3506.502 

5 

5051.641 

a 

4 

6I73.345 

b 

4 

*3553-74i 
#3617.789 

I 

5079.227 
5079-743 

a 
a 

3 
3 

6200.323 
6213.441 

b 
b 

4 

5 

#3659.521 

5 

5098.702 

a 

4 

6219.290 

b 

*3705-567 

6R 

5123.729 

a 

4 

6252.567 

b 

6 

*3749487 

8R 

5127.366 

a 

3 

6254.269 

b 

4 

#3820.430 

8R 

5150.846 

a 

4 

6265.145 

b 

5 

*3859-9*3 

7R 

5ISI-9I7 

a 

3 

6297.802 

b 

4 

#3922.917 
#3956.682 
#4009.718 

6R 
6 

5 

5  i  94-950 
5202.341 
5216.279 

a 
a 
a 

5 
5 
5 

6430.859 
6494.992 

b 
b 
b 

6 

#4062.451 
14132.063 

bi 

4 
7 

5227.191 
5242.495 

a4 
a 

8 
3 

t4'75-639 

b 

4 

5270-356 

34 

8 

14202.031 

bi 

7* 

5328.043 

ai 

7 

14250.791 

b2 

7 

5328.537 

34 

4 

*  Measures  of  Burns.  t  Means  of  St.  John  and  Burns. 

J  Means  of  St.  John  and  Goos.  Others  are  means  of  measures  by  all  three.  References  :  St.  John  and  Ware, 
Astrophysical  Journal,  36,  1912;  38,  1913;  Burns,  Z.  f.  wissen.  Photog.  12,  p.  207,  1913,  J.  de  Phys.  1913,  and  unpub- 
lished data;  Goos,  Astrophysical  Journal,  35,  1912;  37,  1913.  The  lines  in  the  table  have  been  selected  from  the 
many  given  in  these  references  with  a  view  to  equal  distribution  and  where  possible  of  classes  a  and  b. 

For  class  and  pressure  shifts  see  Gale  and  Adams,  Astrophysical  Journal,  35,  p.  10,  1912. 
Class  a:  "This  involves  the  well-known  flame  lines  (de  Watteville,  Phil.  Trans.  A  204,  p.  139. 
1904),  i.e.  the  lines  relatively  strengthened  in  low-temperature  sources,  such  as  the  flame  of  the  arc, 
the  low-current  arc,  and  the  electric  furnace.  (Astrophysical  Journal,  24,  p.  185,  1906,  30,  p.  86, 


pressure  are  assigned  to  it  for  the  present.  These  are  bright  and  symmetrically  widened  under 
pressure,  and  show  mean  pressure  displacements  of  0.009  Angstrom  per  atmosphere  for  the  lines 
in  the  region  \  5975-6678  according  to  Gale  and  Adams.  Group  c  contains  lines  showing  much 
larger  displacements.  The  numbers  in  the  class  column  have  the  following  meaning :  i,  sym- 
metrically reversed  ;  2,  unsymmetrically  reversed  ;  3,  remain  bright  and  fairly  narrow  under  pres- 
sure ;  4,  remain  bright  and  symmetrical  under  pressure  but  become  wide  and  diffuse  ;  5,  remain 
bright  and  are  widened  very  unsymmetrically  toward  the  red  under  pressure." 

For  further  measures  in  International  units  see  Kayser,  Bericht  iiber  den  gegenwartigen 
Stand  der  Wellenlangenmessungen,  International  Union  for  Cooperation  in  Solar  Research,  1913. 
For  further  spectroscopic  data  see  Kayser's  Handbuch  der  Spectroscopie. 

SMITHSONIAN  TABLES. 


TABLE  165. 
WAVE-LENGTHS   OF    FRAUNHOFER    LINES. 


177 


For  convenience  of  reference  the  values  of  the  wave-lengths  corresponding  to  the  Fraunhofer 
lines  usually  designated  by  the  letters  in  the  column  headed  "  index  letters,"  are  here  tabulated 
separately.  The  values  are  in  ten  millionths  of  a  millimeter,  on  the  supposition  that  the  D  line 
value  is  5896.155.  The  table  is  for  the  most  part  taken  from  Rowland's  table  of  standard  wave- 
lengths. 


Index  Letter. 

Line  due  to  — 

Wave-length  in 
centimeters  X  io>. 

Index  Letter. 

Line  due  to  — 

Wave-length  in 
centimeters  X  jo8. 

A 

(O 

(o 

7621.28* 
7594.06* 

G 

r 

(Ca 

4308.081 
4307.907 

a 

- 

7164.725 

g 

Ca 

4226.904 

B 

0 

6870.l82t 

horH5 

H 

4102.000 

CorHa 

H 

6563-045 

H 

Ca 

3968.625 

a 

O 

6278.303  t 

K 

Ca 

3933.825 

D! 

Na 

5896.155 

L 

Fe 

3820.586 

r>2 

Na 

5890.186 

M 

Fe 

3727.778 

D3 

He 

5875.985 

N 

Fe 

3581.349 

f  Fe 

5270.558 

O 

Fe 

344LI55 

(Ca 

5270.438 

P 

Fe 

3361.327 

E2 

Fe 

5269.723 

Q 

Fe 

3286.898 

bi 

Mg 
Mg 

5I8379I 
5172.856 

R 

r 

(Ca 

3181.387 
3I79-453 

b3 

r 

(Fe 
C  Fe 

5169.220 
5169.069 
5167.678 

Si) 
S2) 

Fe 
«  Fe 
Fe 

3100.787 
3100.430 
3100.046 

(Mg 

5l67497 

s 

Fe 

3047.725 

For  Hp 

H 

4861.527 

T 

Fe 

3020.76 

d 

Fe 

4383-721 

t 

Fe 

2994-53 

G'  or  Hy 

H 

4340-634 

U 

Fe 

2947.99 

f 

Fe 

4325-939 

*  The  two  lines  here  given  for  A  are  stated  by  Rowland  to  be :  the  first,  a  line  "beginning  at  the  head  of  A,  out- 
side edge  ;  "  the  second,  a  "  single  line  beginning  at  the  tail  of  A." 

t  The  principal  line  in  the  head  of  B. 

t  Chief  line  in  the  a  group. 

See  Table  163,  Rowland's  Solar  Wave-lengths  (foot  of  page)  for  correction  to  reduce  these  values  to  standard  system 
of  wave-lengths,  Table  160. 

SMITHSONIAN  TABLES. 


178  TABLES  166-168. 

TABLE  168. -Photometric  Standards. 

No  primary  photometric  standard  has  been  generally  adopted  by  the  various  governments.  In 
Germany  the  Herner  lamp  is  most  used ;  in  England  the  Pentane  lamp  and  sperm  candles  are 
used ;  in  France  the  Carcel  lamp  is  preferred;  in  America  the  Pentane  and  Hefner  lamps  are  used 
to  some  extent,  but  candles  are  more  largely  employed  in  gas  photometry.  For  the  photometry 
of  electric  lamps,  and  generally  in  accurate  photometric  work,  electric  lamps,  standardized  at  a 
national  standardizing  institution,  are  commonly  employed. 

The  "  International  candle  "  is  the  name  recently  employed  to  designate  the  value  of  the  candle 
as  maintained  by  cooperative  effort  between  the  national  laboratories  of  England,  France,  and 
America;  and  the  value  of  various  photometric  units  in  terms  of  this  international  candle  is  given 
in  the  following  table  (taken  from  Circular  No.  15  of  the  Bureau  of  Standards). 

i  International  Candle  =  i  Pentane  Candle. 
i  International  Candle  =  i  Bougie  Decimale. 
i  International  Candle  =  i  American  Candle. 
i  International  Candle  =  1.11  Hefner  Unit. 
I  International  Candle  =  0.104  Carcel  Unit. 

Therefore  i  Hefner  Unit  =  0.90  International  Candle. 

The  values  of  the  flame  standards  most  commonly  used  are  as  follows : 

1.  Standard  Pentane  Lamp,  burning  pentane 10.0  candles. 

2.  Standard  Hefner  Lamp,  burning  amyl  acetate 0.9  candles. 

3.  Standard  Carcel  Lamp,  burning  colza  oil 9.6  candles. 

4.  Standard  English  Sperm  Candle,  approximately    ....  i.o  candles. 

Slight  differences  in  candle  power  are  found  in  different  lamps,  even  when  made  as  accurately 
as  possible  to  the  same  specifications.  Hence  these  so-called  primary  standards  should  be  them- 
selves standardized. 

TABLE  167.— Intrinsic  Brightness  of  Varions  Light  Sources. 


Barrows. 

Ives  &  Luckiest 

. 

National  Electric 
Lamp 
Association. 

C.  P.  per  Sq.  In. 
of  surface 
of  light. 

C.  P.  per  Sq.  In. 
of  surface 
of  light. 

C.  P.  per  Sq. 
Mm.  of  sur- 
face of  light. 

C.  P.  per  Sq.  In. 

of  surface 
of  light. 

Sun  at  Zenith   ... 

600,000 

_ 

_ 

600,000 

Crater,  carbon  arc     . 

200,000 

84,000 

130. 

200,000 

Open  carbon  arc 

10,000-50,000 

10,000-50,000 

Flaming  arc       ... 

5,000 

_ 

_ 

5,000 

Magnetite  arc   .        .        *                 • 

_ 

4,000 

6.2 

_ 

Nernst  Glower 

800-1,000 

(nsv.6  amp.  d.c.)  3,010 

4-7 

(l-5  W.p.C.)  2,200 

Tungsten  incandescent,  1.15  w.  p.  c- 

- 

- 

I,OOO 

Tungsten  incandescent,  1.25  w.  p.  c- 

1,000 

1,000 

1.64 

875 

Tantalum  incandescent,  2.0  w.  p.  c. 

750 

580 

0.9 

75° 

Graphitized    carbon    filament,     2.5 

625 

7  qo 

625 

Carbon  incandescent,  3.1  w.  p.  c.     . 

480 

485 

0.75 

480 

Carbon  incandescent,  3.5  w.  p.  c.     . 
Carbon  incandescent,  4.0  w.  p.  c.     . 

375 
300 

400 
325 

0.63 
0.50 

375 

Inclosed  carbon  arc  (d.  c.) 

100-500 

100-500 

Inclosed  carbon  arc  (a.  c.) 
Acetylene  flame  (i  ft.  burner)  . 

75-100 

53-o 

0.082 

75-200 
75-100 

Acetylene  flame  (%  ft.  burner) 

33-o 

0.057 

- 

Welsbach  mantle      .... 

20-25 

31.9 

0.048 

20-50 

Welsbach  (mesh)       .... 

56.0 

0.067 

_ 

Cooper  Hewitt  mercury  vapor  lamp 
Kerosene  flame          .... 

16.7 
4-8 

14.9 
9.0 

0.023 
0.014 

3-87 

Candle  flame     .                          . 

_ 

Gas  flame  (fish  tail)  .... 
Frosted  incandescent  lamp 
Moore  carbon-dioxide  tube  lamp 

3 

4-8 
0.6 

2.7 

0.004 

3-8 
2-5 
o-3-I-75 

Taken  from  Data,  1911. 
TABLE  168.  — Visibility  ol  White  Lights. 


Range. 

Candle  Power. 

1 

2 

i  sea-rcile=  1855  meters      .... 

0.47 

0.41 

2      "      "           . 

1.9 

1.6 

5    "    "        •        

u.  8 

10. 

1  Paterson  and  Dudding.  *  Deutsche  Seewarte.  o 

The  energy  falling  on  i  sq.  cm.  at  im.  from  a  candle  is  about  4  ergs  per  sec.   (Rayleigh,  about  8  according  to  Ang- 
strom.) 


TABLE  169. 
EFFICIENCY  OF  VARIOUS  ELECTRIC  LIGHTS. 


179 


Amperes. 

Terminal 
Watts. 

Lumens. 

Kw-hours 
for  100,000 
Lumen- 
hours. 

Total  cost 
per  100,000 
Lumen-hours 
at  10  cts. 
per  Kw-hour. 

Regenerative  d.-c.,  series  arc 

5-5 

385 

11,670 

3-3 

0-339 

Regenerative  d.-c.,  multiple  arc 
Magnetite  d.-c.,  series  arc 

It 

528 

11,670 
7,370 

5.18 
7.16 

0.527 
0.729 

Flame  arc,  d.-c.,  inclined  electrodes 

IO.O 

550 

8,640 

6-37 

0.837 

Mercury  arc,  d.-c.,  multiple 
Flame  arc,  d.-c.,  inclined  electrodes 

8.0 

385 
440 

4,400 
6,140 

15.92 
7.16 

0.89 
0.966 

Flame  arc,  d.-c.,  vertical  electrodes 

8.0 

440 

6,140 

7.16 

0.966 

Luminous  arc,  d.-c.,  multiple 

6.6 

726 

7,370 

0.988 

Open  arc,  d.-c.,  series 

9.6 

480 

5,025 

9-55 

.079 

Magnetite  arc,  d.-c.,  series 

4.0 

320 

2,870 

11.15 

•'3 

Flame  arc,  a.-c.,  vertical  electrodes 

IO.O 

467 

5»340 

8.75 

.275 

Flame  arc,  a.-c.,  inclined  electrodes 

IO.O 

467 

5>340 

8.75 

.275 

Open  arc,  d.-c.,  series 

6.6 

325 

2,920 

IMS 

.305 

Tungsten  series 

6.6 

75 

626 

12.0 

.384 

Flame  arc,  a.-c.,  inclined  electrodes 

8.0 

374 

3,9*0 

9-55 

•405 

Inclosed  arc,  d.-c.,  series 

6.6 

475 

3,3T5 

14.32 

•459 

Luminous  arc,  d.-c.,  multiple 

4.0 

440 

2,870 

15-32 

•547 

Tungsten,  multiple 
Nernst,  a.-c.,  3-glower 

0-545 
1.87 

60 
414 

475 
2,160 

12.6 

19.2 

$ 

Nernst,  d.-c.,  3-glower 

1.87 

414 

2,160 

19.2 

.90 

Inclosed  arc,  a.-c.,  series 

7-5 

480 

2,410 

19.9 

2.05 

Inclosed  arc,  a.-c.,  series 

6.6 

425 

2,020 

21.3 

2.193 

Tantalum,  d.-c.,  multiple 

— 

40 

199 

21.  1 

2.31 

Tantalum,  a.-c.,  multiple 

— 

40 

199 

21.  1 

2.504 

Carbon,  3.1  w.  p.  c.,  multiple 

— 

49.6 

166 

29.9 

3-24 

Carbon,  3.5  w.  p.  c.,  series 

6.6 

2IO 

626 

33-6 

347 

Carbon,  3.5  w.  p.  c.,  multiple 

— 

56 

166 

33-7 

3-50 

Inclosed  arc,  d.-c.,  multiple 

5-° 

550 

i,535 

35-8 

3.66 

Inclosed  arc,  d.-c.,  multiple 

3-5 

385 

1,030 

37-4 

3-84 

Inclosed  arc,  a.-c.,  multiple 
Inclosed  arc,  a.-c.,  multiple 

6.0 
4.0 

as 

1,124 
688 

38.3 
41.4 

3-94 
4-265 

Paper  by  Prof.  J.  M.  Bryant  and  Mr.  H.  G.  Hake,  Engineering  Experiment  Station,  University  of  Illinois. 
SMITHSONIAN  TABLES. 


l8o  TABLES  170-172. 

SENSITIVENESS  OF  THE   EYE  TO  RADIATION. 

(Compiled  from  Nutting,  Bulletin  of  the  Bureau  of  Standards.) 

Radiation  is  easily  visible  to  most  eyes  from  0.330/4  in  the  violet  to  0.770/4  in  the  red.  At  low 
intensities  approaching  threshold  values  (red  vision)  the  maximum  of  spectral  sensibility  lies 
in  the  green  at  about  0.510/4  for  90%  of  all  persons.  At  higher  intensities  with  the  establish- 
ment of  cone  vision  the  maximum  shifts  towards  the  yellow  at  least  as  far  as  0.560^. 

TABLE  170.  -Variation  of  the  Sensitiveness  of  the  Eye  with  the  Wave-length  at  Low  Intensities  (near 

Threshold  Values).    Konig. 


A 

.410 

•430 

.450 

.470 

.490 

.510 

.530 

•55° 

•570 

•590 

.610 

Mean  sensitiveness 

0.02 

0.06 

0.23 

0.49 

0.8  1 

1.  00 

0.8  1 

0.49 

0.22 

0.077 

0.026 

TABLE  171.  —  Variation  of  Sensitiveness  to  Radiation  of  Greater  Intensities. 

The  sensibility  is  approximately  proportional  to  the  intensity  over  a  wide  range.  The  ratio  of 
optical-  to  radiation-intensity  increases  more  rapidly  for  the  red  than  for  the  blue  or  green 
(Purkinje  phenomenon). 

The  intensity  is  given  for  the  spectrum  at  0.535/1  (green). 


Intensity  (metre-candles)  =: 
Ratio  to  preceding  step  — 

.00024 

.00225 

9-38 

.0360 
16 

•575 
16 

2.30 

4 

9.22 

4 

36.9 

147.6 

4 

590-4 

Wave-length,  A. 

Sensitiveness. 

0.430/4 

.081 

.093 

.I27 

.128 

.114 

.114 

_ 

_ 

_ 

45° 

•33 

.30 

.29 

•31 

•23 

•175 

.16 

— 

— 

.470 

•03 

•59 

•54 

.# 

•51 

.29 

.26 

•23 

- 

.490 

.96 

(.89) 

(-76) 

(-89) 

(.83) 

•5° 

•45 

•38 

•35 

•5°5 

1.  00 

I.OO 

I.OO 

I.OO 

•99 

(.76) 

.66 

.61 

•54 

.520 

.88 

.86 

.86 

•94 

•99 

(-85) 

.8S 

•8S 

.82 

•535 

.61 

.62 

•63 

.72 

.91 

(.98) 

.98 

•99 

.98 

•555 

.26 

•3° 

•34 

.41 

.62 

•«4 

•93 

•97 

.98 

•575 

.074 

.102 

.122 

.168 

(-39) 

(•63) 

(-76) 

(-82) 

(.84) 

•590 

.025 

.034 

•054 

.091 

.27 

•49 

.61 

.68 

.69 

.605 

.008 

.OI2 

.024 

.056 

•173 

•35 

US) 

•54 

•55 

.625 

.004 

.OO4 

.Oil 

.027 

.098 

.20 

.27 

•35 

•35 

.650 

.000 

.000 

.003 

.007 

.025 

.060 

.085 

.122 

•133 

.670 

.000 

.000 

.OOI 

.002 

.007 

.017 

.025 

.030 

.030 

\,  maximum  sensitiveness 

•503 

•504 

•5°4 

.508 

•5'3 

•530 

•541 

•543 

•544 

TABLE  172.  —  Sensibility  to  Small  Differences  in  Intensity  measured  as  a  Fraction  of  the  Whole. 


A  = 

.670 

.605 

•575 

•5°5 

.470 

•430 

White 

I0in  m.  c.  = 

0.060 

0.0056 

0.0029 

0.00017 

O.OOOI2 

0.00012 

0.00072 

I 

81: 

Konig's  dat 

a,  measures  from  one  normal 
Jerson  only. 

1,000,000 

- 

_ 

- 

_ 

_ 

_ 

.036 

200,000 

- 

.042 

- 

- 

- 

- 

.027 

100,000 

— 

.024 

.032 

— 

— 

•— 

.019 

50,000 

.021 

.025 

.026 

- 

- 

— 

.017 

20,000 

.016 

.018 

.020 

.019 

_ 

_ 

.017 

IO,OOO 

.016 

.016 

.018 

.018 

- 

- 

.018 

5,000 

.018 

.016 

.017 

.016 

_ 

_ 

.018 

2,000 

.016 

.018 

.018 

.017 

.Ol8 

_ 

.018 

1,000 

.017 

•  020 

.018 

.018 

.017 

.018 

.018 

500 

.020 

.O2I 

.018 

.019 

.Ol8 

.021 

.019 

200 

.022 

•022 

.022 

.022 

.021 

.024 

.022 

IOO 

.029 

.028 

.027 

.024 

.022 

•025 

.030 

50 

.038 

.038 

•032 

.025 

•025 

.027 

.032 

IO 

-06S 

.061 

.058 

.036 

•037 

.040 

.048 

5 

.092 

.103 

.089 

.049 

.046 

.049 

.059 

I 

.258 

.212 

.170 

.080 

.088 

.074 

.123 

o-5 

.376 

.276 

.21 

.091 

.096 

.097 

.188 

O.  IO 

- 

- 

.40 

.133 

.138 

•137 

•377 

0.05 

- 

- 

- 

.183 

.185 

.154 

.484 

O.OI 

— 

- 

- 

.271 

.289 

.249 

0.005 

•325 

.300 

.312 

" 

The  sensibility  to  small  differences  in  inten- 
sity is  independent  of  the  intensity  (Fech- 
ner's  law).  About  0.016  for  moderate 
intensities.  Greater  for  extreme  values. 

It  is  independent  of  wave-length,  extremes 
excepted  (Konig's  law). 

Sensibility  to  slight  differences  in  wave- 
length has  two  pronounced  maxima  (one 
in  the  yellow,  one  in  the  green)  and  two 
slight  maxima  (extreme  blue,  extreme 
red). 

The  visual  sensation  as  a  function  of  the 
time  approaches  a  constant  value  with  the 
lapse  of  time.  With  blue  light  there 
seems  to  be  a  pronounced  maximum  at 
0.07  sec.,  with  red  a  slight  one  at  0.12  sec- 
onds, with  green  the  sensation  rises  stead- 
ily to  its  final  value.  For  lower  intensi- 
ties these  max.  occur  later. 

An  intensity  of  500  metre-candles  is  about 
that  on  a  horizontal  plane  on  a  cloudy 
day. 


SMITHSONIAN  TABLES. 


TABLES  1  73-1  76. -SOLAR  ENERGY.  l8l 

TABLE  173.— The  Solar  Constant 

Solar  constant  (amount  of  energy  falling  at  normal  incidence  on  one  square  centimeter  per 
minute  on  body  at  earth's  mean  distance)  =  1.932  calories  =  mean  696  determinations  1902 — 12. 
Apparently  subject  to  variations,  usually  within  the  range  of  7  per  cent,  and  occurring  irregularly 
in  periods  of  a  week  or  ten  days. 

Computed  effective  temperature  of  the  sun :  from  form  of  black-body  curves,  6000°  to  7000° 
Absolute  ;  from  Amax.  =  2930  and  max.  =  0.470^,  6230° ;  from  total  radiation,  J  =  76.8x10-1*  X  T4, 
5830°. 

TABLE  174.  —  Solar  spectrum  energy  (arbitrary  units)  and  its  transmission  by  the  earth's  atmosphere. 
Values  computed  from  em=  e0am,  where  em  is  the  intensity  of  solar  energy  after  transmission 
through  a  mass  of  air  m;  m  is  unity  when  the  sun  is  in  the  zenith,  and  approximately  =  sec. 
zenith  distance  for  other  positions  (see  table  180) ;  e0=the  energy  which  would  have  been  ob- 
served had  there  been  no  absorbing  atmosphere ;  a  is  the  fractional  amount  observed  when  the 
sun  is  in  the  zenith. 


Transmission  coef- 

Intensity Solar  Energy,    *$£** 

A 

ficients,  a. 

M 

£ 

{* 

,    | 
1  £ 

%  -3 
%   > 

c 

••Sg-f 

iia 

l| 

Mount  Wilson. 

Washington. 

S" 

&'* 

H   G 

O 

m=:o 

m=i 

m=i 

2 

4 

6 

m=i 

2 

3 

4 

6 

0.30 

_ 

(.460) 

(-550) 



54 

30 

25 

II 

2 

z 

_ 



— 





•32 

— 

•  520 

.615 

— 

in 

68 

58 

30 

8 

2 

— 



— 

— 

— 

•34 

— 

.692 

— 

232 

160 

7» 

26 

9 

— 



— 

— 

— 

•36 

_ 

•635 

.741 

— 

302 

224 

192 

122 

49 

20 

•M 

— 

— 

— 

—— 

•38 

(.380) 

.676 

.784 

.56* 

354 

278 

239 

162 

74 

34 

134 

51 

19 

7 

3 

.40 

.00 

•729 

.809 

.768 

414 

335 

302 

220 

117 

62 

232 

130 

73 

41 

13 

.46 

.690 

•  832 

.887 

.829 

618 

548 

428 

296 

205 

426 

294 

203 

140 

67 

•5° 

•733 

.862 

.919 

•850 

606 

557 

522 

450 

334 

248 

441 

323 

237 

174 

94 

.60 

•779 

.900 

.940 

.866 

504 

474 

454 

409 

268 

393 

300 

238 

185 

112 

.70 

.858 

•95° 

.964 

•9°3 

364 

351 

346 

329 

297 

268 

3" 

268 

230 

197 

H5 

.80 

.886 

.970 

.976 

.915 

266 

260 

258 

250 

235 

221 

236 

209 

185 

164 

MS 

I.OO 

.922 

.980 

•975 

.941 

166 

162 

163 

160 

154 

147 

153 

141 

130 

120 

102 

1.50 

2.00 

.938 
•9V 

.976* 
.970* 

.965 
•932 

.961 
.940 

63 
25 

61 
23 

61* 
24* 

60* 

23* 

& 

$ 

59 
23 

55 

21 

52 
19 

49 
17 

43 

Transmission  coefficients  are  for  period  when  there  was  apparently  no  volcanic  dust  in  the  air. 
*  Possibly  too  high  because  of  increased  humidity  towards  noon. 

TABLE  175.  -  The  intensity  of  Solar  Radiation  in  different  sections  of  the  spectrum,  ultra-violet,  visual 

infra-red.    Calories. 


Wave-length. 

Mount  Whitney. 

Mount  Wilson. 

Washington. 

V-           /* 

m=:o 

m:=i 

2 

3 

4 

m—  i 

2 

3 

4 

m=i 

2 

3 

4 

o.oo  to  0.4; 

•3i 

•25 

.19 

.16 

•i3 

•23 

.16 

.12 

.09 

•  13 

.06 

.04 

.02 

0.45   to  0.70 
0.70    to       oo 

•71 

.91 

.67 

.87 

.62 

•85 

.58 
.82 

£ 

•65 
.69 

% 

& 

•45 
•63 

s 

.40 

.62 

•3° 

•57 

.24 

•53 

o.oo   to       w 

1-93 

1.78 

1.66 

1.56 

1.47 

'-57 

1.42 

1.28 

1.17 

1-35 

1.  08 

.90 

•79 

TABLE  176.  — Distribution  of  brightness  (Radiation)  over  the  Solar  Disk. 

(These  observations  extend  over  only  a  small  portion  of  a  sun-spot  cycle.) 


Wave- 
length. 

V- 
0.323 

0.386 

f* 
0.433 

/«• 
0.456 

/* 
0.481 

M 
0.501 

M 
0-534 

J* 
0.604 

M 
0.670 

/"• 
0.699 

A* 

0.866 

P 
1.031 

M 
1.225 

M 

1.655 

M 

2.097 

0.00 

144 

338 

4S6 

5i5 

5" 

489 

46} 

399 

333 

307 

174 

III 

77.6 

39-5 

14.0 

D 

0.40 

128 

3" 

423 

486 

483 

463 

44° 

382 

320 

295 

169 

108 

75-7 

38-9 

13-8 

1 

0.55 

120 

289 

395 

455 

4S6 

437 

417 

36S 

308 

284 

163 

105-5 

71-8 

38-2 

13.6 

K 

0.65 

112 

267 

368 

428 

430 

414 

396 

348 

295 

273 

*59 

J°3  . 

72.2 

37-6 

13-4 

J^ 

0.75 

99 

240 

333 

390 

394 

380 

366 

326 

281 

258 

152 

99 

69.8 

36.7 

13-1 

0.825 

86 

214 

296 

35i 

SS8 

347 

337 

304 

262 

243 

»45 

94-5 

67.1 

35-7 

12.8 

§ 

o.87S 

76 

1  88 

266 

3*7 

324 

323 

3»2 

284 

247 

229 

138 

90.5 

64.7 

34-7 

12.5 

1 

0.92 

64 

163 

233 

277 

290 

286 

281 

259 

227 

212 

130 

86 

61.6 

33-6 

12.2 

fe  1  0.95 

49 

141 

205 

242 

255 

254 

254 

237 

210 

*95 

122 

81 

58.7 

32-3 

II-7 

Taken  from  vols.  II  and  III  and  unpublished  data  of  the  Astrophysical  Observatory  of  the 
Smithsonian  Institution.  Schwartzchild  and  Villiger :  Astrophysical  Journal,  23,  1906. 
SMITHSONIAN  TABLES. 


TABLES   177-180. 
ATMOSPHERIC   TRANSPARENCY   AND   SOLAR    RADIATION. 

TABLE  177.—  Transmission  of  Radiation  Through  Moist  and  Dry  Air. 

This  table  gives  the  wave-length,  A  ;  a  the  transmission  of  radiation  by  dry  air  above  Mount 
Wilson  (altitude  =  1730  m.  barometer,  620  mm.)  for  a  body  in  the  zenith  ;  finally  a  correction  fac- 
tor, aw,  due  to  such  a  quantity  of  aqueous  vapor  in  the  air  that  if  condensed  it  would  form  a  layer 
i  cm.  thick.  Except  in  the  bands  of  selective  absorption  due  to  the  air,  a  agrees  very  closely  with 
what  would  be  expected  from  purely  molecular  scattering.  aw  is  very  much  smaller  than  would  be 
correspondingly  expected,  due  possibly  to  the  formation  of  ions  by  the  ultra-violet  light  from  the 
sun.  The  transmission  varies  from  day  to  day.  However,  values  for  clear  days  computed  as  fol- 
lows agree  within  a  per  cent  or  two  of  those  observed  when  the  altitude  of  the  place  is  such  that 
the  effect  due  to  dust  may  be  neglected,  e.  g.  for  altitudes  greater  than  1000  meters.  If  B  = 

B^ 

the  barometric  pressure  in  mm.,  w,  the  amount  of  precipitable  water  in  cm.,  then  aB  =  a620  a^-  w  is 
best  determined  spectroscopically  (Astrophysical  Journal,  35,  p.  149,  1912,37,  p.  359,  1913)  other- 

h 


wise  by  formula  derived  from  Hann,  w=  2.3e 
station,  h,  the  altitude  in  meters. 


io 


ew  being  the  vapor  pressure  in  cm.  at  the 


A(M) 

a 

aw 

•360 
(.660) 
•950 

•384 

•713 
.960 

413 
.783 
•965 

.840 
.967 

88? 
.885 

•977 

f 

•574 
•905 
•974 

.624 
.929 
.978 

•653 
•938 
.985 

.720 
.970 
.988 

.986 
.986 
.990 

1.74 
.990 
.990 

Fowle,  Astrophysical  Journal,  38,  1913. 
TABLE  178.— Brightness  ol  (radiation  from)  Sky  at  Mt.  Wilson  (1730  m.)  and  Flint  Island  (sea  level). 


0-15° 
1500* 

"5 

51.0 

3-9 

15-35° 
400 

122 
58.8 
17.9 

35-50° 
520 
128 

9J-5 
22.5 

50-6o0 

610 
150 
87.2 
21.4 

60-70° 
660 
185 
104.3 
29.2 

70-80° 
700 

210 
II7.6 

35-3 

80-90° 
720 
460 
125.3 
80.0 

- 

Sun. 
636 

210 

io8  X  mean  ratio  sky/sun   Mt.  Wilson     . 
Flint  Island    . 
Ditto  X  area  of  zone          Mt.  Wilson     . 
Flint  Island    . 

- 

- 

5° 
•533 
.046 
423 

.056 

.102 

15° 
.900 
•233 
403 

.110 

•343 

25° 

1-233 

•524 
.385 

.162 
.686 

35° 
1.358 
.780 
365 

.189 
.969 

47i° 
i.4i3 
1.041 
346 

.205 
1.246 

65° 
1.496 
1-355 
326 

.226 
1.581 

82  J° 
I.52I 
1.507 
310 

.240 

1-747 

Sun's  brightness,  cal.  per  cm.2  per  min.    . 
Ditto  on  horizontal  surface 
Mean  brightness  on  normal  surface  sky  X  io8/sun 
Total  sky  radiation  on  horizontal  cal.  per  cm.8 
per  m.         

*  Includes  allowance  for  bright  region  near  sun.  For  the  dates  upon  which  the  observation  of  the  upper  portion  of 
table  were  taken,  the  mean  ratios  of  total  radiation  sky/sun,  for  equal  angular  areas,  at  normal  incidence,  at  the  island 
and  on  the  mountain,  respectively,  were  636  X  io— 8  and  210  X  io—  °,  on  a  horizontal  surface,  305  X  io— 8  and  77  X  10—8; 
for  the  whole  sky,  at  normal  incidence,  0.57  and  0.20;  on  a  horizontal  surface  0.27  and  0.07.  Annals  of  the  Astro- 
physical  Observatory  of  the  Smithsonian  Institution,  vols.  II  and  III,  and  unpublished  researches  (Abbot). 

TABLE  179.  — Relative  Distribution  in  Normal  Spectrum  of  Sunlight  and  Sky-light  at  Mount  Wilson. 

Zenith  distance  about  50°. 


M 

M 

A« 

H 

M 

/* 

C 

D 

b 

F 

Place  in  Spectrum 

0.422 

0-457 

0.491 

o.S66 

0.614 

0.660 

Intensity  Sunlight 
Intensity  Sky-light 
Ratio  at  Mt.  Wilson 

186 
1194 
642 

232 
986 
425 

227 
701 
3°9 

211 

395 
187 

191 
231 
121 

1  66 
174 

!05 

102 

143 

246 

3i6 

Ratio  computed  by  Rayleigh 
Ratio  observed  by  Rayleigh 

- 

- 

I  O2 
IO2 

164 
168 

258 
291 

328 
369 

TABLE  180.— Air  Masses. 

See  Table  174  for  definition.  Besides  values  derived  from  the  pure  secant  formula,  the  table 
contains  those  derived  from  various  other  more  complex  formula,  taking  into  account  the  curva- 
ture of  the  earth,  refraction,  etc.  The  most  recent  is  that  of  Bemporad. 


Zenith  Dist. 

0° 

20° 

40° 

60° 

70° 

75° 

80° 

8S° 

88° 

Secant 
Forbes 
Bouguer 
Laplace 
Bemporad 

1.  00 
I.OO 
I.OO 
I.OO 
I.OO 

1.064 
1.065 
1.064 

1.305 
1.306 

!-305 

2.OOO 

T-995 
1.990 

1-993 
1-995 

2.924 
2.902 
2.900 
2.899 
2.904 

3.864 
3.809 
3-805 

5.76 

5-57 
5.56 

5-56 
5.60 

11.47 

10.22 
IO.2O 
IO.2O 
10.39 

28.7 
18.9 
19.0 

18.8 
19.8 

The  Laplace  and  Bemporad  values,  Lindholm,  Nova  Acta  R.  Soc.  Upsal.  3,  1913  ;  the  others,  Radau's  Actino- 
metric,  1877. 


TABLES  181-182. 
RELATIVE  INTENSITY  OF  SOLAR  RADIATION. 

TABLE  181.  —  Mean  Intensity ./  for  24  hours  of  solar  radiation  on  a  horizontal  surface  at  the  top  of  the 

atmosphere  and  the  solar  radiation  - 1 .  In  terms  of  the  solar  radiation,  AO, 

at  earth's  mean  distance  from  the  sun. 


RELATIVE  MEAN  VERTICAL  INTENSITY  (  ^—  J  • 

Motion  of 

\-«o/ 

the  sun 

j. 

Date. 

in 

LATITUDE  NORTH. 

longi- 
tude. 

A° 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

Jan. 

0 

o-99 

0.303 

0.265 

O.22O 

0.169 

0.117 

0.066 

0.018 

1-0335 

Feb. 

3x-54 

.312 

.282 

.244 

.200 

.150 

.100 

.048 

0.006 

1.0288 

Mar. 

59-  i  4 

•320 

•303 

.279 

•245 

.204 

.158 

.108 

.056 

0.013 

1.0173 

May 

89.70 
119.29 

•317 

•303 

.319 
,318 

.312 
•330 

•295 
.329 

.209 
.320 

•235 
.302 

•195 
.27S 

.148 
•253 

.101 

•255 

0.082 
•259 

1.0009 
0.9841 

June 

149.82 

.287 

•334 

•345 

•349 

•34  S 

•337 

•344 

.360 

.366 

0.9714 

July 

179-39 

.283 

.312 

•333 

•347 

•352 

•3SJ 

•345 

•356 

•373 

•379 

0.9666 

Aug. 

209.94 

.294 

.316 

•330 

-334 

•330 

.318 

.300 

.282 

•295 

.300 

0.9709 

Sept. 
Oct. 

240.50 
270.07 

.310 

•3*7 

.318 
,308 

.289 

•305 
.261 

.285 
.225 

•256 

.220 

.180 
.084 

.139 
.065 

.140 

0.9828 
0.9995 

Nffv. 

300.63 

.312 

.286 

.251 

.211 

.164 

.114 

.063 

.018 

1.0164 

Dec. 

330.19 

•304 

.267 

.224 

•175 

.124 

.072 

.024 

1.0288 

Year.... 

0-305 

0.301 

0.289 

0.268 

0.241 

0.209 

0.173 

0.144 

0-133 

0.126 

TABLE  182.  —  Mean  Monthly  and  Yearly  Temperatures. 

Mean  temperatures  of  a  few  selected  American  stations,  also  of  a  station  of  very  high,  one  of  very  low  and  one  of 
very  small,  range  of  temperature. 


Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Year. 

i  Hebron-Rama  (Labr.) 

—  20.7 

—20.9 

-15-6 

—  6.9 

+   0.2 

+  4S 

+  7.6 

+  8.0 

+  4-5 

—  0.8 

—  6.2 

—  16.2 

—  5-2 

2  Winnipeg  (Canada)     . 
3  Montreal 

—21.6 

—  10.9 

—  18.8 

II.  O 

—  4-3 

+  1.9 

+  4-8 

+10.9 

+  i2.6| 

+17.1 
+  18.3 

+18.9 
+20.5 

+17.6 

+  11.6 
+r4-7 

+  4-1 

+  7-8 

-7.6 

—   O.2 

—15.7 
—  7.1 

+  0.6 
+  5-5 

4  Boston                            . 

—  2.8 

2.2 

+    1-2 

+  7-3 

+13-6 

+  19.1 

--2I.8 

--20.6 

+  16.9 

~T~    4*8 

—  0.5!+  9.2 

5  Chicago 

-4-8 

—   2.9 

+    1-2 

+  7-9 

+  I9-7 

--22.2 

--21.  6 

-J-I7.Q+II.1 

+  3-6 

+  9-1 

6  Denver 
7  Washington 

2.1 
+   0.7 

+    0.1 
+    2.1 

+  3-8 
+  5-2 

+  8.3 
+11.7 

+13-6 
+17-7 

--19.1 

+22.9 

+22.1 
+  24.9 

--2I.2 

--23-7 

+16.6 
+19.9 

+10.3 

+'3-4 

+  3-3 
+  6.9 

o.o 
+  2.3 

+  9-7 

+  12.6 

8  Pikes  Peak 

—l6.4 

-IS.6 

—13-4 

—10.4 

—  5-3 

--  0.4 

+  4-S 

—  0.3 

—  u.8 

—14.4 

—  7.1  ' 

9  St.  Louis                       . 

—  0.8 

+  1-7 

+    6.2 

+13-4 

+  18.8 

--24.0 

+26.0 

--24.9 

+20.8 

--14.2 

+  6.4 

+    2.O 

+13.1 

10  San  Francisco 

+  10.1 

+10.9 

+  12.0 

+  12.6 

+I.V7 

--14.7 

+  14.6 

--I4-8 

.4-15.8 

--15-2 

+  10.8+13.2 

ii  Yuma   . 

+12.3 

+  14.9 

+  18.1 

+2I.O 

+2S-I 

--29.4 

+33-1 

--32.6 

+29.1 

--22.8 

+16.6 

+  13.3+22.3 

12  New  Orleans 

+I4-S 

+  16.7 

+20.6 

--26.8 

+27.9 

--27  5 

+2v7 

--2I.O 

+  '5-9 

+13.1+20.4 

13  Massaua 

+2S.6 

+26.0 

+27-1 

+29.0 

+3I-I 

--33-5 

+34-8 

--34-7 

+33-3 

--3I-7 

+29.0 

+27.0+30.3 

14  Ft.  Conger  (Greenl'd) 
15  Werchojansk 
16  Batavia 

—39-° 
—51.0 
+25-3 

—40.1 
—45-3 
+25-4 

—33.5 

+11:1 

—25.3 

IO.O 
+    2.0 
+26.4 

--  0.4 
+12.3 
+26.0 

+    2.8 

j-'S-S 
+25-7 

+    I.O 
+  10.  1 

+25.9 

—  9.0 
+  2.5 
+26.3 

—22.7 
—15.0 
+26.4 

—30.9 
-37-8 
+26.2 

-33-4 

—47-0 
+25.6 

—  20.  o 

-16.7 

+25.9 

.5,630.0  W,— ;  (2)  +49-9,  97-1  W,  233m.;  (3)  +4S-S,  73-6  W,  S7m.; 
105.0  W,  i6i3m.;    (7)  +38.9,  77-°  W,  34m.;    (8) 


39-7> 


Lat.,  Long.,  Alt.  respectively :    (i) 
(4)  +  42.3,  71.  i  W,  38m. ;    (5)  +  41-9, 

+  38.8,  105.0  W,  43o8m.  ;  (9)+38.6,  90.2  W,  17301.;  (10)  +37-8,"i22.5  W,  47m.;  (n)+32.7,  114.6  W,  4301.; 
(12)  +30.0,  90.1  W,  i6m.;  (13) +  15.6,  37.5  E,9m.;  (14) +81.7,  64.7  W.,  —  ;  (15) +67.6,  133.8  E,  i4om.;  (16)  — 6.2, 
106.8  E,  7m. 


;    (6)  + 
m.;    (10) 


Taken  from  Hann's  Lehrbuch  der  Meteorologie,  2'nd  edition,  which  see  for  further  data. 


SMITHSONIAN  TABLES. 


184  TABLES  183-185.   INDEX  OF  REFRACTION  FOR  GLASS. 

TABLE  183.  —  Glasses  Made  by  Schott  and  Gen,  Jena. 

The  following  constants  are  for  glasses  made  by  Schott  and  Gen,  Jena :  «A,  «c»  «D>  «F,  «G»  are 
the  indices  of  refraction  in  air  for  ^=0.7682^,  C  =0.6563^1,  0=0.5893,  F=o.486i,  G' =0.4341. 
v=(nv — I)/(«F — «c).  Ultra-violet  indices:  Simon,  Wied.  Ann.  53,  1894.  Infra-red:  Rubens, 
Wied.  Ann.  45,  1892.  Table  is  revised  from  Landolt,  Bornstein  and  Meyerhoffer,  Kayser,  Hand- 
buch  der  Spectroscopie,  and  Schott  and  Gen's  list  No.  751,  1909.  See  also  Hovestadt's  "Jena 
Glass." 


Catalogue  Type  = 

0546 

O38r 

Oi84 

O  102 

Oi6s 

S57 

Designation     = 

Zinc-Crown. 

Higher  Dis- 
persion Crown. 

Light  Silicate 
Flint. 

Heavy  Silicate 
Flint. 

Heavy  Silicate 
Flint. 

Heaviest  Sili- 
cate Flint. 

Melting  Numbers 

1092 

1151 

45i 

469 

500 

163 

v             — 

60.7 

51.8 

41.1 

33-7 

27.6 

22.2 

.   f    Cd  0.2763;* 

I.56759 

_ 

_ 

_ 

_ 

_ 

jc 

Cd    .2837 

1-56372 

- 

- 

— 

— 

— 

% 

Cd    .2980 

I.55723 

•57093 

1-65397 

- 

- 

- 

£ 

Cd    .3403 

I.54369 

.55262 

1.63320 

1.71968 

.85487 

- 

I 

Cd    .3610 

I-53897 

.54664 

1.61388 

1.70536 

.83263 

- 

£ 

H      .4340/1 

1.52788 

•53312 

1-59355 

1.67561 

.78800 

1-94493 

T3 

H      .4861 

1.52299 

•52715 

•58515 

1.66367 

.77091 

1.91890 

1- 

Na    .5893 

1.51698 

.52002 

•57524 

1.64985 

•75130 

1.88995 

H      .6563 

1.51446 

•S1?™ 

•57II9 

1.64440 

.74368 

1.87893 

I 

K      .7682 

i-5"43 

.51368 

.56669 

1.63820 

•73530 

1.86702 

>J 

.8ooM 

1.5103 

•5i3i 

•5659 

I-6373 

•7339 

1.8650 

'o 

1.200 

1.5048 

.5069 

•5585 

1.6277 

•7215 

1.8481 

*o 
B 

1.  600 

1.5008 

.5024 

•5535 

1.6217 

•7i5i 

1.8396 

M 

2.000 

1.4967 

•4973 

•5487    • 

1.6171 

.7104 

1.8316 

2.400 

- 

•544° 

1.6131 

- 

1.8286 

Percentage  composition  of  the  above  glasses  : 

O  546,  SiO2,  65.4;  K2O,  15.0;  Na2O,  5.0;  BaO,  9.6;  ZnO,  2.0;  Mn2O3,  o.i  ;  As2O3,  0.4; 

B203,  2.5. 

0381,  SiO2,  68.7;  PbO,  13.3;  Na2O,  15.7;  ZnO,  2.0;  MnO2,  o.i  ;  As2O5,  0.2. 

O  184,  SiO2,  53.7  ;  PbO,  36.0;  K2O,  8.3;  Na2O,  i.o;  Mn2O3,  0.06;  As2O3,  0.3. 

O  102,  SiO2,  40.0;  PbO,  52.6;  K2O,  6.5;  Na2O,  0.5;  Mn2O3,  0.09;  As2O5,  0.3. 

O  165,  SiO2,  29.26;  PbO,  67.5;  K2O,  3.0;  Mn2O3,  0.04;  As2O3,  0.2. 

S  57,     SiO2,  21.9;  PbO,  78.0;  As2O6,  o.i. 

TABLE  184.  —  Jena  Glasses. 


«D-I 

Specific 

«K      nc 

*»—  *C 

nV        «A 

«F        «D 

nor      nf 

Weight. 

O  225  Light  phosphate  crown     .     . 
O  802  Boro-silicate  crown  .... 
UV  3199  Ultra-violet  crown   .    .     . 
0227  Barium-silicate  crown   .     .     . 
O  1  14  Soft-silicate  crown   .... 
O  608  High-dispersion  crown      .     . 
UV  3248  Ultra-violet  flint  .     .     .     . 
O  381  High-dispersion  crown      .     . 
O  602  Baryt  light  flint     

•S'59 
•4967 
•5035 
•5399 
•SIS' 
•5M9 
•5332 
.5262 
•5676 

•00737 
0765 
0781 
0909 
0910 
0943 
0964 
1026 

70.0 
64.9 
64-4 

59-4 
56.6 
54-6 
55-4 
5i-3 

.00485 

0504 
0514 
0582 
0577 
°595 

0611 
0644 
0675 

.00515 
0534 
0546 
0639 
0642 
0666 
0680 
0727 

.00407 
0423 
0432 
05U 
0521 
0543 
0553 
0596 
0618 

2.58 
2.38 
2.41 
2-73 
2-55 
2.60 

2-75 
2.70 

S  389  Borate  flint                      .          . 

5686 

r(  5 

2  83 

O  726  Extra  light  flint    
O  154  Ordinary  light  flint   .... 
O  184        "           '•".... 
O  748  Baryt  flint   

•5398 
•5710 
.5900 

1142 

1327 
1438 

47-3 
43-o 
41.1 

0711 

0819 

0882 

08lO 
0943 

1022 

0669 
0791 
0861 

2.87 
3.16 
3.28 

3  67 

64.80 

77  8 

1180 

7    87 

041         "        "... 

0  165       "        "   . 

4  78 

4280 

2808 

S  57  Heaviest  flint     

.9626 

4882 

19.7 

2767 

3547 

3252 

6-33 

TABLE  185.  —  Change  of  Indices  of  Refraction  for  1°  0  in  Units  of  the  Fifth  Decimal  Place. 


No.  and  Designation. 

Mean 
Temp. 

C 

D 

F 

G' 

—  A« 

IOO 

n 

S  57  Heavy  silicate  flint      .     .     . 
O  154  Light  silicate  flint     .     .     . 
O  327  Baryt  flint  light    .... 
O  225  Light  phosphate  crown 

58.8° 
58.4 
58.3 
58.1 

1.204 
0.225 

—0.008 

—  O.2O2 

1.447 
0.261 
0.014 
—  0.190 

2.090 
0.334 
0.080 
—o.i  68 

2.810 
0.407 
0.137 
—  0.142 

0.0166 
0.0078 
0.0079 
0.0049 

SMITHSONIAN  TABLES. 


Pulfrich,  Wied.  Ann.  45,  p.  609,  1892. 


TABLES  186-188.    INDEX  OF  REFRACTION, 
TABLE  186.  -Index  oi  Refraction  of  Rock  Salt  In  Air. 


*! 

n. 

Obser- 
ver. 

MM). 

«. 

Obser- 
ver. 

MM). 

«. 

Obser- 
ver. 

0.185409 

1.89348 

M 

0.88396 

.534011 

L 

5.8932 

.516014 

P 

.204470 

1.76964 

" 

.972298 

•532532 

" 

•515553 

L 

.291368 
.358702 
.441587 

1.61325 

L57932 
1.55962 

N 

.98220 
1.036758 
1.1786 

•532435 
.531762 

.530372 

P 
L 
P 

6.4825 
7.0718 

.513628 
•5I3467 
.511062 

P 
L 
P 

.486149 

" 

" 

.530374 

L 

7.6611 

.508318 

1.553406 

L 

1.55.5137 

.528211 

" 

7-9558 

.506804 

" 

1-553399 

P 

1.7680 

•527440 

P 

8.8398 

-502035 

.58902 

1.544340 

L 

.527441 

L 

10.0184 

.494722 

-58932 

i-5443I3 

P 

2.073516 

.526554 

" 

11.7864 

.481816 

,656304 

1.540672 

P 

2.35728 

•525863 

P 

1  2.9650 

.471720 

1.540702 

L 

(4 

.525849 

L 

14.1436 

.460547 

.706548 

1-538633 

P 

2.9466 

.524534 

P 

I4-7330 

.454404 

" 

.766529 

1.536712 

P 

3-5359 

•523173 

15-3223 

.447494 

" 

.76824 

1.53666 

M 

4.1252 

.521648 

P 

15.9116 

.441032 

.78576 

1-536138 

P 

.521625 

L 

20.57 

-3735 

RN 

.88396 

I-5340II 

P 

5.0092 

.518978 

P 

22.3 

.340 

where  ^=2.33016$ 
MI  =0.01  278685 
Ax2  =0.0  1  48  500 
^2=0.005343924 


\22=o.o25474i4 
/£  =0.0009285837 
^=0.000000286086 


32=5.680137 
^73=12059.95 
A3'2=36oo.  (P) 


TABLE  187.-  Change  of  Index  of  Refraction  for  1°  0  in  Units  of  the  5th  Decimal  Place. 


O.2O2/4 

4-3-134 

Mi 

0.441/4 

—3-425 

Mi 

Cline 

—3-749 

PI 

0.760/4 

—3-73 

L 

.2IO 

+  1-570 

« 

.508 

—  3-5J7 

M 

D    " 

—3-739 

" 

1.368 

—3.88 

L 

.224 

—O.l87 

" 

.643 

—3-636 

M 

F    " 

-3.648 

" 

1.88 

-3-85 

L 

.298 

—2.727 

G'  " 

-3-585 

M 

4.3 

-3.82 

L 

L    Annals  of  the  Astrophysical   Observatory 
of  the  Smithsonian  Institution,  Vol.  I,  1900. 
M   Martens,  Ann.  d.  Phys.  6,  1901,  8,  1902. 
Mi  Micheli,  Ann.  d.  Phys.  7,  1902. 


P  Paschen,  Wied.  Ann.  26,  1908. 
PI  Pulfrich,  Wied.  Ann.  45,  1892. 
RN  Rubens  and  Nichols,  Wied.  Ann.  60, 1897. 


TABLE  188.  —Index  of  Refraction  of  Silvine  (Potassium  Chloride)  in  Air. 


MM). 

n 

Obser- 
ver. 

MM). 

n. 

Obser- 
ver. 

MM). 

n. 

Obser- 
ver. 

0.185409 

1.82710 

M 

1.1786 

1.478311 

P 

8.2505 

1.462726 

P 

.200090 

1.71870 

" 

1.47824 

W 

1.46276 

W 

.21946 

1.64745 

1.7680 

1.475890 

P 

8.8398 

1.460858 

P 

.257317 

I.58I25 

« 

1.47589 

W 

M 

1.46092 

W 

.281640 

L55836 

2.35728 

I-474751 

P 

10.0184 

1.45672 

P 

.308227 

I.54I36 

2.9466 

1.473834 

« 

" 

1-45673 

W 

.358702 

I.52II5 

M 

1-47394 

W 

11.786 

1.44919 

P 

.394415 
.467832 

1.51219 

1.50044 

3-5359 

1.473049 
1.47304 

P 

W 

12.965 

1.44941 
1.44346 

W 

P 

.508606 

1.49620 

4.7146 

1.471122 

P 

1.44385 

W 

.58933 

1.49044 

P 

a 

1.47129 

W 

14.144 

1.43722 

P 

.67082 

1.48669 

M 

5-3039 

1.470013 

P 

15.912 

1.42617 

" 

.78576 

1.483282 

P 

« 

1.47001 

W 

17.680 

1.41403 

« 

.88398 

1.481422 

P 

5-8932 

1.468804 

P 

20.60 

1.3882 

RN 

.98220 

1.480084 

1.46880 

W 

22.5 

1-369 

<t 

^2=2.174967  A22=o.o25555o  f>2= 3.866619 

MI= 0.008344206  £=0.000513495  ^3=5569.715 

Ai2=o.oi  19082  h =0.000000 1 67  587          Aa2=3292.47         (P) 

M2= 0.00698  382 
W  Weller,  see  Paschen's  article.    Other  references  as  under  Table  187,  above. 

SMITHSONIAN  TABLES. 


i86 


TABLES   189-192. 

INDEX  OF  REFRACTION. 

TABLE  189.  -  Index  of  Refraction  of  Fluorite  in  Air. 


MM) 

n 

Obser- 
ver 

MM) 

n 

Obser- 
ver 

MM) 

n 

Obser- 
ver. 

0.1856 

1.50940 

S 

-4733 

1.42641 

P 

4.1252 

1.40855 

P 

.19881 

1.49629 

it 

•5715 

1.42596 

u 

4.4199 

1.40^9 

.21441 

1.48462 

« 

.6206 

1.42582 

" 

4.7146 

1.40238 

.22645 

1.47762 

(4 

.7680 

1.42507 

M 

5.0092 

1.39898 

•25713 

1.46476 

" 

•9153 

I-42437 

« 

5-3036 

'•39529 

•32525 

1.44987 

«< 

.9644 

1.42413 

" 

5-5935 

1.39142 

•34555 

1.44697 

M 

2.0626 

1.42359 

« 

5-8932 

1.38/19 

.39681 

I.442I4 

" 

2.1608 

1.42308 

« 

6.482? 

1.37819 

.48607 

I437I3 

P 

2.2IOO 

1.42288 

" 

7.0718 

1.36805 

•58930 

J-43393 

P 

2-3573 

1.42199 

M 

7.6612 

1.35680 

.65618 
.68671 

1-43257 
1.43200 

S 

2-5537 
2.6519 

1.42088 
1.42016 

« 
« 

8-2505 
8.8398 

1-34444 

I-33079 

.71836 

i  -43  T  57 

« 

2.7502 

1.41971 

M 

9.4291 

1.31612 

.76040 

1.43101 

M 

2.9466 

1.41826 

u 

51-2 

3-47 

RA 

.8840 

1.42982 

P 

3-  '43° 

1.41707 

" 

61.1 

2.66 

H 

1.1786 

1.42787 

(1 

3-2413 

1.41612 

M 

CO 

2-63 

S 

I-3756 

1.42690 

(. 

35359 

I.4I379 

" 

M733 

1.42641 

3-8306 

I.4II2O 

References  under  Table  173. 

where  a2  =  2.032 
^  =  0.0062183 
Ai'2  =  0.007706 
<?  =  0.003  1  999 


/"=  0.00000291  6 

£2  =  6.09651 
M-2  =0.0061386 
AV2  =  0.00884 


Ar2=i26o.5 


(P) 


TABLE  190.  —  Change  of  Index  of  Refraction  for  1°  0  in  Units  of  the  6th  Decimal  Place. 
C  line,  — 1.220 ;  D,  —1.206;  F,  —1.170;  G,  —1.142.      (PI) 


TABLE  191. —Index  of  Refraction  of  Iceland  Spar  (CaCOj  in  Air. 


A  (,x) 

»0 

«« 

Obser- 
ver. 

A  (,*) 

«0 

ne 

Obser- 
ver. 

A  Ox) 

«0 

ne 

Obser- 
ver. 

0.198 

_ 

1.5780 

M 

0.508 

1.6653 

1.4896 

M 

0.991 

1.6438 

1.4802 

C 

.2OO 

1.9028 

'•5765 

«i 

•533 

1.6628 

1.4884 

« 

1.229 

!-6393 

1.4787 

.208 
.226 

1.8673 
1.8130 

1.5664 
1.5492 

" 

'643 

1.6584 
1.6550 

1.4864 
1.4849 

« 

1.307 

1-497 

x-6379 
1.6346 

I-4783 
1-4774 

.298 

1.7230 

I-SISl 

C 

.656 

1.6544 

1.4846 

" 

1.682 

1-6313 

•340 
.361 

1.7008 
1.6932 

1.5056 
1.5022 

M 
C 

.670 
.760 

1-6537 

1.6500 

1.4843 
1.4826 

it 

1-749 
1.849 

1.6280 

1.4764 

.410 

1.6802 

1.4964 

_ 

.768 

1.6497 

1.4826 

M 

1.908 

_ 

1-4757 

•434 

T-6755 

1-4943 

M 

.801 

1.6487 

1.4822 

C 

2.172 

1.6210 

(( 

.486 

1.6678 

1.4907 

•905 

1.6458 

1.4810 

« 

2.324 

1-4739 

M 

C    Carvallo,  J.  de  Phys.  (3),  9,  1900. 

M   Martens,  Ann.  der  Phys.  (4)  6,  1901,  8,  1902. 

P    Paschen,  Wied.  Ann.  56,  1895. 


PI 

RA    Rubens-Aschkinass, 

S       Starke,  Wied.  Ann.  60,  1897. 


Pulfrich,  Wied.  Ann  45,  1892. 

Wied.  Ann.  67,  1899. 


TABLE  192.  —Index  of  Refraction  of  Nitroso- dim  ethyl- aniline.    (Wood.) 


A 

n 

A 

n 

A 

n 

A 

n 

A 

n 

0.497 
.500 

2.140 
2.114 

0-525 
•536 

T-945 
1.909 

0.584 
.602 

1.815 
1.796 

0.636 
•647 

1.647 
1.758 

0.713 
-730 

I.7I8 
I-7I3 

.506 

2.074 

•546 

1.879 

.611 

1-783 

•659 

1-75° 

•749 

1.709 

.508 
.516 

2.025 
1.985 

:$ 

I-857 
1.834 

.620 
.627 

1.778 
1.769 

.669 
.696 

1-743 
1-723 

-763 

1.697 

Nitroso-dimethyl-aniline  has  enormous  dispersion  in  yellow  and  green,  metallic  absorption  in  violet.    See  Wood, 

Phil.  Mag  1903. 
SMITHSONIAN    TABLES. 


TABLES   193-194. 
INDEX  OF  REFRACTION. 

TABLE  193.  —  Index  of  Refraction  of  Quartz  (8102). 


i87 


Wave- 
length. 

Index 
Ordinary 
Ray. 

Index 
Extraordinary 
Ray. 

Tempera- 
ture °  C. 

Wave- 
length. 

Index 
Ordinary 
Ray. 

Index 
Extraordinary 
Ray. 

Tempera- 
ture °  C. 

0.185 
•T93 

1.67582 
•65997 

1.68999 
•67343 

18 

« 

0.656 
.686 

1.54189 
.54099 

1.55091 
.54998 

18 

.198 

.65090 

.66397 

.760 

•539J7 

.54811 

« 

.206 

.64038 

.65300 

1.160 

•5329 

- 

.214 

.63041 

.64264 

•969 

.5216 

— 

.219 

.62494 

.63698 

2.327 

•S^6 

- 

.231 

.61399 

.62560 

.84 

•5°39 

- 

•257 

.59622 

.60712 

3.18 

.4944 

— 

.274 
•340 

•58752 
.56748 

.59811 
•57738 

3 

•4799 
.4679 

Rubens. 

_ 

.396 

.55815 

.56771 

4.20 

•4569 

- 

.410 
.486 

•55650 
.54968 

.56600 
.55896 

6.45 

.417 
.274 

_ 

0.598 

1.54424 

1-55334 

7.0 

1.167 

" 

Except  Rubens'  values,  —  means  from  various  authorities. 


TABLE  194.  —Indices  of  Refraction  for  various  Alums.* 


& 

u 

Index  of  refraction  for  the  Fraunhofer  lines. 

Q 

I 

0) 

H 

a 

B 

c 

D 

E 

b 

P 

a 

Aluminium  Alums,    .ft  Al(SO4)2+i2H2O.t 

Na 
NH3(CH8) 
K 

1.667 
1.568 
1-735 

17-28 
7-17 
14-15 

1.43492 

•45OI3 
.45226 

I-43563 
.45062 

•453°3 

143653 
•45:77 
•45398 

1.43884 
.45410 
•45645 

1.44185 
.45691 
•45934 

1.44231 

•45749 
45996 

1.44412 

•45941 
.46181 

1.44804 

•46363 
.46609 

Rb 
Cs 
NH4 

1.852 
1.961 
1.631 

7-21 

15-25 

15-20 

•45232 
•45437 
•45509 

.45328 
•45599 

•45417 
.45618 

•45693 

.45660 
•45856 
•45939 

•45955 
.46141 
•46234 

•45999 
.46203 
.46288 

.46192 
.46386 
.46481 

.46618 
.46821 
.46923 

Tl 

2.329 

10-23 

.49226 

•493  i  7 

•49443 

.49748 

.50128 

.50209 

•50463 

.51076 

Chrome  Alums.     /?Cr(SO4)2+i2H2O.t 

Cs 

2.043 

6-12 

1.47627 

I-47732 

1.47836 

1.48100 

1.48434 

1.48491 

1.48723 

1.49280 

K 
Rb 
NH4 

1.817 
1.946 
1.719 

6-17 

12-17 

7-18 

.47642 
.47660 
.47911 

47738 
•47756 
.48014 

.47865 
.47868 
.48125 

•48137 
.48151 
.48418 

.48459 
.48486 
•48744 

•48513 
.48522 

•48794 

•48753 
•48775 
.49040 

•493°9 
•49323 

•49594 

Tl 

2.386 

9-25 

.51692 

.51798 

•51923 

.52280 

.52704 

•52787 

.53082 

•53808 

Iron  Alums.    tfFe(SO4)2-f-i2H2O.t 

K 
Rb 

1.806 
1.916 

7-1  1 
7-20 

1.47639 
.47700 

1.47706 
.47770 

147837 
•47894 

1.48169 
.48234 

1.48580 
.48654 

1.48670 
.48712 

1.48939 
.49003 

1.49605 

Cs 

2.061 

20-24 

.47825 

.47921 

.48042 

48378 

•48797 

.48867 

.49136 

.49838 

NH4 

1-713 

7-20 

.47927 

.48029 

.48150 

.48482 

.48921 

.48993 

.49286 

.49980 

Tl 

2-385 

15-17 

•5I674 

•51943 

•52365 

•52859 

.52946 

•53284 

.54112 

*  According  to  the  experiments  of  Soret  (Arch.  d.  Sc.  Phys.  Nat.  Genfeve,  1884,  1888,  and  Comptes  Rendus,  1885). 

t  R  stands  for  the  different  bases  given  in  the  first  column. 

For  other  alums  see  reference  on  Laudolt-Bornstem-Roth  Tabellen. 

SMITHSONIAN  TABLFS. 


1 88 


TABLE  195. 
INDEX   OF   REFRACTION. 

Various  Monorefringent  or  Optically  Isotroplc  Solids. 


Substance. 

Line  of 
Spectrum. 

Index  of 
Refraction. 

Authority. 

Agate  (light  color)      

red 

I.C174 

De  Senarmont. 

Albite  glass         ...                 .        . 

D 

o 

1.4890 

Larsen,  1909 

Ammonium  chloride  
Anorthite  glass  

D 
D 

1.6422 

I.C7CC 

Grailich. 
Larsen,  1909. 

D 

I.7CC 

DesCloiseaux 

D 

*•/  jj 
1.5716 

Fock. 

Bell  metal           
Blende         

D 
Li 

Na 

1.0052 
2.34165 
2.76Q21 

Beer. 
Ramsay. 

Tl 
C 
D 

2.40069 
1.46245 
1.46107 

F 
C 
D 

1.47024 
I.5I222 
1.51484 

Bedson  and 
Carleton  Williams. 

Camphor    

F 
D 

1.52068 

\  '-532 

Kohlrausch. 

Diamond  (colorless)  

(red 

I  1-5462 
2.414     } 

Mulheims. 
DesCloiseaux. 

|  green 
(B 
<  D 

2.428     f 

2.46062  ) 

2  46986  I 

Schrauf 

<I 

2.47902  ) 

1.6 

Ayrton  &  Perry 

ft 

1  C 

2.03 
2.19 

2.31           > 

Means 

Garnet  (different  varieties) 
Gum  arabic         

G 

IH 

D 
red 

1.97 
1-32 

$  1-74  to 

1  1-90          f 
I.48O 

Various. 
Tamin 

tt 

I   114 

Wollaston 

Lime  CaO  

D 

1.832 

Wright,  1909. 

Magnesium  oxide        

D 

1.734 

Wright,  1909. 

Obsidian     

D 

(  i.  482  to 

Various. 

Opal   . 

D 

}   1.496 
j  1.406 

Pitch  ........ 

red 
D 

1  1-450 

I.53I 
I.ccq-'    ) 

Wollaston. 

"          chlorstannate    .... 
iodide        
Phosphorus         

« 

(4 

red 

"-OS74    I 

1.6666    ) 
2.1442 
1.619 

Topsoe  and 
Christiansen. 

Gladstone  &  Dale. 
Jamin. 

Canada  balsam     .... 

u 

« 

1.528 
i  -^48 

Wollaston. 
Jamin. 

« 

I.H28 

u 

Mastic  
Peru  balsam          .... 

Selenium,  vitreous      .        .        .        . 

« 

D 
fA 

JB 

i-535 
1-593 
2.612     ) 
2.680 

Wollaston. 
Baden  Powell. 

Wood. 

C  bromide          

I  C 

1S 

2.729 
2-93       J 

2  2C1        ) 

Silver  <  chloride  

*3      ( 

2  06  1        / 

Wernicke 

u 

2  182       ) 

« 

I   rj  CQ 

Dussaud. 

Spinel          .        .        .        . 
Strontium  nitrate        .        .        . 

« 

u 

\-&t 

DesCloiseaux. 
Fock. 

SMITHSONIAN  TABLES. 


TABLE  196. 
INDEX  OF  REFRACTION. 

Unlazial  Crystals. 


189- 


Substance. 

Line  of 
spectrum. 

Index  of  refraction. 

Authority. 

Ordinary 
ray. 

Extraordin- 
ary ray. 

Alunite  (alum  stone) 

D 

I-573 

1.592 

Levy  &  Lacroix. 

Ammonium  arseniate 

red 

1-577 

1.524 

De  Senarmont. 

Anatase      

D 

2-5354 

2-4959 

Schrauf. 

Apatite        

D 

1.6390 

1-6345 

« 

Benzil          

D 

1.6588 

1.6784 

DesCloiseaux. 

Beryl  .        . 

D  I 

1.589  to 
1.570 

1.582  to 

1.566 

f  Various. 

Brucite       

D 

1.560 

1.581 

Kohlrausch. 

Calomel      

D 

I-9732 

2.6559 

Dufet 

Cinnabar    

red 

2.854 

3-199 

DesCloiseaux 

Corundum  (ruby,  sapphire,  etc.) 

red    | 

1.767  to 
1.769 

'•759 

1.762 

*    ;: 

Dioptase     

green 

1.667 

1-723 

Dolomite    

D  1 

1.667  to 
1.696 

i.  506  to 

1.512 

>  Various. 

Emerald  (pure)  
Gehlenite    

green 
D 

1.584 

1.578 

1.661 

DesCloiseaux. 
Wright,  1908. 

Greenockite        

D 

2.'5o6 

2.529 

Merwin,  1912. 

Iceat-8°C  

D 

1.309 

'•313 

Meyer. 

Idocrase      

D     | 

1.719  to 

1.717  to 

>  DesCloiseaux. 

1.722 

1.720 

J 

D 

I    C?Q 

I.C4I 

Kohlrausch. 

Magnesite  

D 

•  JJ7 

1.717 

•"OH-* 
*>$*$ 

Mallard. 

Nephelite   

D 

1.541 

'•537 

Bowen,  1912. 

Potassium  arseniate  .... 

red 

1.564 

'•SIS 

DesCloiseaux. 

"                "          .... 

red 

1*493 

1.501 

De  Senarmont. 

Rutil  

D 

2.6158 

2.9029 

Barwald. 

red 

7.084 

2.881 

Fizeau. 

Sodium  arseniate        .... 

D 

j  •wt-'H- 
1-459 

1.467 

Baker. 

"       nitrate   

D 

1.587 

J-336 

Schrauf. 

"       phosphate      .... 

D 

1.446 

2.452 

Dufet. 

Strychnine  sulphate   .... 

D 

1.614 

'W 

Martin. 

Tin  stone   

D 

1.997 

2.093 

Grubenman. 

Tourmaline  (colorless) 

D 

1.637 

1.619 

Heusser. 

"            (different  colors)    . 

D  I 

1.633  to 
1.650 

1.616  to 
1.625 

>  Jerofejew. 

Wurtzite     

D 

2.356 

2.378 

Merwin,  1912. 

Zircon  (hyacinth)        .... 

red 

1.92 

1.97 

De  Senarmont. 

. 

D 

1.924 

1.968 

Sanger. 

SMITHSONIAN  TABLES. 


TABLE   197. 
BIAXIAL  CRYSTALS. 


Substance. 

Line  of 
spec- 
trum. 

Index  of  Refraction. 

Authority. 

Minimum. 

Interme- 
diate. 

Maximum. 

Amphibole 

D 

T-633 

1.642 

I.657 

Levy-Lacroix. 

Andalusite 

red 

1.632 

1.638 

1.643 

Levy-Lacroix. 

Anemousite 

D 

1-5549 

I.SS87 

L5634 

Wright  1910. 

Anglesite 

D 

1.8771 

1.8823 

1.8936 

Arzruni. 

Anhydrite 

D 

1-5693 

1.5752 

1.6130 

MUlheims. 

Anorthite 

D 

1.576 

1.589 

Bowen  1912 

Antipyrin 

D 

1-5697 

1.6935 

I-7324 

Liweh. 

Aragonite 
Axinite 

D 
red 

I-530I 
1.6720 

1.6779 

1.6859 
I.68IO 

Rudberg. 
DesCloiseaux. 

Barite   . 

D 

1.636 

1.637 

1.648 

Various. 

Borax    . 

D 

1.4467 

1.4694 

1.4724 

Dufet. 

Carnegeite 

D 

1.509 

I.5H 

Bowen  1912. 

Copper  sulphate   . 

D 

1.5140 

1.^68 

1-5433 

Kohlrausch. 

Gypsum 

D 

1.5208 

1.5228 

1.5298 

Mtilheims. 

Hillebrandite 

D 

1.605 



I.6T2 

Wright  1908. 

Magnesium  Carbonate 

D 

1.495 

1.501 

1.526 

Genth,  Penfield. 

Magnesium  Sulphate    . 

D 

1.432 

1-455 

1.460 

Means. 

Mica  (muscovite)  . 

D 

1.5601 

r-5936 

1-5977 

Pulfrich. 

Olivine  .... 

D 

1.661 

1.678 

1.697 

DesCloiseaux. 

Orthoclase    . 

D 

1.5190 

!-5237 

1.5260 

« 

Potassium  bichromate  . 

D 

1.7202 

1.7380 

1.8197 

Dufet. 

"          nitrate 

D 

1.3346 

1-5056 

1.5064 

Schrauf. 

"          sulphate 

D 

1.4932 

1.4946 

1.4980 

Topsoe  &  Christiansen. 

Spurrite 

D 

1.640 

1.674 

1.679 

Wright  1908. 

Sugar  (Cane) 

D 

1-5397 

1.5667 

1.5716 

Calderon 

Sulphur  (rhombic) 

D 

I.9505 

2-0383 

2-2405 

Schrauf. 

Topaz  (Brazilian) 

D 

1.6294 

1.6308 

I.6375 

Mulheims. 

Topaz  (different  kinds) 

D! 

1.638  to 
1.613 

1.631  to 
1.616 

1.637  to 
1.623 

-  Various. 

Wallastonite 

D 

1.620 

1.632 

1.634 

Means. 

Zinc  sulphate 

D 

1.4568 

1.4801 

1.4836 

Topsoe  &  Christiansen. 

SMITHSONIAN  TABLES. 


TABLE  198. 
INDEX  OF  REFRACTION. 

Indices  of  Refraction  relative  to  Air  for  Solutions  of  Salts  and  Acids. 


191 


Substance. 

Indices  of  refraction  for  spectrum  lines. 

Density. 

Temp.  C 

D 

Authority. 

C 

P 

Hy 

H 

(a)  SOLUTIONS  IN  WATER. 

Ammonium  chloride 

1.067 

27°-05 

I-37703 

I-37936 

I-38473 

1.39336 

Willigen. 

' 

1 

" 

.025 

29-75 

•34850 

•35050 

•355*5 

•36243 

M 

Calcium  chloride 

•398 

44000 

44279 

•44938 

.46001 

« 

M 

a 

.215 

22.9 

-394II 

•39652 

40206 

41078 

« 

" 

it 

•143 

25.8 

•37152 

•37369 

.37876 

.38666 

M 

Hydrochloric  acid    . 
Nitric  acid  .... 
Potash  (caustic)   .     . 

I.I66 

•359 
416 

20.75 

18.75 
II.O 

1.40817 

•39893 
.40052 

1.41109 

40181 
40281 

141774 

40857 
40808 

142816 
.41961 
41637 

U 

Fraunhofer. 

Potassium  chloride  . 

normal  solution 

.34087 

.34278 

•34719 

i-35°49 

Bender. 

" 

M 

double  normal 

.34982 

•35*79 

•35645 

•35 

994 

" 

" 

" 

triple  normal 

•35831 

.36029 

•3651  2 

390 

" 

Soda  (caustic)      .     . 
Sodium  chloride  .     . 

1.376 

21.6 

18.07 

141071 

.37562 

I4I334 
•37/89 

I4I936 

.38322 

1.38746 

1.42872 

Willigen. 
Schutt. 

a 

" 

.109 

18.07 

•35751 

•35959 

.36442 

•36823 

M 

(i 

" 

•035 

18.07 

.34000 

•34I91 

.34628 

•34969 

* 

Sodium  nitrate     .     . 

1.358 

22.8 

1.38283 

I-38535 

I-39I34 

140121 

Willigen. 

Sulphuric  acid 

.811 

I8.3 

•43444 

43669 

.44168 

44883 

1 

1 

" 

M 

•632 

18.3 

42227 

42466 

42967 

43694 

< 

< 

" 

" 

.221 

I8.3 

•36793 

•37009 

.37468 

.38158 

< 

< 

" 

M 

.028 

I8.3 

•33663 

.33862 

•34285 

•34938 

t 

' 

Zinc  chloride    .     .     . 

1-359 

26.6 

1-39977 

1.40222 

140797 

141738 

i 

(      • 

. 

.209 

264 

•37292 

•37515 

.38026 

.38845 

« 

()))  SOLUTIONS  IN  ETHYL 

ALCOHOL. 

Ethyl  alcohol  .     .     . 

0.789 

25-5 

I-3579I 

I-3597I 

I-36395 

1.37094 

Willigen. 

" 

" 

•932 

27.6 

•35372 

.35556 

•35 

986 

.36662 

u 

Fuchsin   (nearly  sat- 

urated)    . 

. 

_ 

16.0 

.3918 

•398 

.361 

•3759 

Kundt. 

Cyanin  (saturated)    . 

- 

16.0 

.3831 

— 

•3705 

.3821 

M 

NOTE.  — 

Cyanin  in  chloroform  also  acts  anomalously 

;  for  example,  Sieben  gives  for 

a  4.5  per  cent,  solution  U.A=  14593,  /*a=  1-4695,  juF(green)  =  14514,  yu<?  (blue)  =  14554. 
For  a  9.9  per  cent,  solution  he  gives  /*.<=  1.4902,  pp  (green)  =  14497,  /io(blue)  =  14597. 

(C)  SOLUTIONS  OF  POTASSIUM  PERMANGANATE  IN  WATER.* 

Wave- 
length 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

Wave- 
length 

Spec- 
trum 

Index 
for 

Index 
for 

Index 
for 

Index 
for 

in  cms. 
X  io6. 

Hue. 

I  %  SOl. 

2  %  SOl. 

3  %  sol. 

4%  sol. 

in  cms. 
Xio«. 

line. 

I  %  SOl. 

2  %  sol. 

3  %  sol. 

4  %  sol. 

68.7 

B 

1.3328 

1-3342 

_ 

1.3382 

5r.6 

_ 

1.3368 

I-3385 

_ 

_ 

65.6 

C 

•3335 

•3348 

I-3365 

•3391 

50.0 

— 

•3374 

•3383 

1.3386 

1.3404 

6l.7 

— 

•3343 

•3365 

•3381 

.3410 

48.6 

F 

•3377 

.3408 

59-4 

- 

•3354 

•3373 

•3393 

•3426 

48.0 

- 

.3381 

•3395 

•3398 

•3413 

58-9 

D 

•3353 

•3372 

— 

.3426 

464 

— 

•3397 

.3402 

•3414 

•3423 

56.8 

— 

•3362 

•3387 

.3412 

•3445 

44-7 

— 

•3407 

.3421 

.3426 

•3439 

55-3 

— 

•3366 

•3395 

•34i7 

•3438 

43-4 

— 

•3417 

— 

— 

.-34.C2 

*•/"  .2 

52-7 

E 

•3363 

— 

42-3 

— 

•3431 

•3442 

•3457 

•3468 

52.2 

•3362 

•3377 

•3388 

SMITHSONIAN  TABLES. 


*  According  to  Christiansen. 


TABLE  199. 

INDEX   OF   REFRACTION. 

Indices  of  Refraction  of  Liquids  relative  to  Air. 


Substance. 

Temp. 

Index  of  refraction  for  spectrum  lines. 

Authority. 

0 

D 

F 

H7 

H 

Acetone     .... 

10° 

1.3626 

1.3646 

1.3694 

I-3732 

_ 

Korten. 

Almond  oil     ... 

o 

4755 

.4782 

4847 

_ 

Olds. 

Analin*     .... 
Aniseed  oil    ... 

20 
21.4 

•5993 
.5410 

.5863 
•5475 

.6041 
•5647 

.6204 

— 

Weegmann. 
Willigen. 

«              a 

!5-! 

.5508 

•5572 

•5743 

- 

1.6084 

Baden  Powell. 

Benzene  t  .... 

10 

1.4983 

1.5029 

1.5148 

_ 

1-5355 

Gladstone. 

« 
Bitter  almond  oil    . 
Bromnaphtalin  .     . 

21.5 
2O 
20 

4934 
•5391 
.6495 

4979 
.6582 

•5095 
•5623 
.6819 

•5775 
.7041 

•53°4 
.7289 

Landolt. 
Walter. 

Carbon  disulphide  J 

O 

1.6336 

I-6433 

1.6688 

1.6920 

i-7i75 

Ketteler. 

u                       u 

2O 

.6182 

.6276 

•6523 

.6748 

.6994 

a 

"                 " 

10 

.6250 

•6344 

•6592 

.7078 

Gladstone. 

«                 « 

19 

.6189 

.6284 

•6352 

_ 

.7010 

Dufet. 

Cassia  oil  .     .     .     . 

10 

.6007 

.6104 

.6389 

_ 

•7039 

Baden  Powell. 

"       "   . 

22.5 

•5930 

.6026 

.6314 

- 

•6985 

«          «« 

Chinolin    .... 
Chloroform    .    .     . 

20 

10 

1.6094 
.4466 

1.6171 
.4490 

1.6361 

4555 

1.6497 

.4661 

Gladstone. 
Gladstone  &  Dale. 

. 

3° 

— 

4397 

— 

.4561 

«<               « 

"            ... 

20 

4437 

~TT^/ 

.4462 

4525 

_ 

Lorenz. 

Cinnamon  oil     .     . 

23-5 

.6077 

.6188 

.6508 

- 

- 

Willigen. 

Ether     . 

15 

1-3554 

1.3566 

1.3606 

_ 

1-3683 

Gladstone  &  Dale. 

u 

15 

0 

•3573 
•3677 

•3594 
•3695 

.3641 
•3739 

•3773 

•37i3 

Kundt. 
Korten. 

Ethyl  alcohol      .     . 

, 

IO 

•3636 

•3654 

.3698 

•3732 

— 

« 

<«           « 
«           « 

20 

15 

•3596 
.3621 

.3614 
•3638 

•3657 
•3683 

.3690 

•3751 

u 

Gladstone  &  Dale. 

Glycerine  .... 

20 

1.4706 

_ 

1.4784 

1.4828 

_ 

Landolt. 

Methyl  alcohol  .     . 

15 

•3308 

1.3326 

•3362 

— 

.3421 

Baden  Powell. 

Olive  oil    .... 

0 

4738 

4763 

4825 

_ 

Olds. 

Rock  oil    .... 

O 

4345 

4573 

4644 

- 

- 

« 

Turpentine  oil    .     . 

10.6 

'•47IS 

1.4744 

1.4817 

_ 

M939 

Fraunhofer. 

«           « 

20.7 

.4692 

.4721 

4793 

- 

49i3 

Willigen. 

Toluene     .... 

20 

.4911 

4955 

.5070 

•5!7° 

Bruhl. 

Water§      .... 

20 

•3312 

•3330 

•3372 

•3404 

•3435 

Means. 

*  Weegmann  gives  HD=  1.59668  —  .000518 1.  Knops  gives  ftF=  1.61500—  .00056 1. 
t  Weegmann  gives  /x^zz  1.5 1474  —  .000665*.  Knops  gives  M/>—  !'5i399  —  .000644*. 
%  Wiillner  gives /IAC=  1.63407 —  .00078^;  ft^=  1.66908  —  .00082*;  /iA  =  1.69215  —  .00085^. 

§  Dufet  gives  ftp— 1.33397 — io~ 7(i2S  ^  +  20.6^  —  .000435  ^  —  .oons^4)  between  o°  and  50°;  and  nearly  the 
same  variation  with  temperature  was  found  by  Ruhlmann,  namely,  M.D—  1-33373  —  io~7  (20. 14 ^  +  .000494 /*). 

SMITHSONIAN  TABLES. 


TABLE  200. 
INDEX  OF  REFRACTION. 

Indices  of  Refraction  of  Gases  and  Vapors. 


193 


A  formula  was  given  by  Biot  and  Arago  expressing  the  dependence  of  the  index  of  refraction  of  a  gas  on  pressure  and 
temperature.  More  recent  experiments  confirm  their  conclusions.  The  formula  is  nt—  i  =  ^  ^ ~->  where 
nt  is  the  index  of  refraction  for  temperature  t,  no  for  temperature  zero,  a  the  coefficient  of  expansion  of  the  gas 
with  temperature,  and  /  the  pressure  of  the  gas  in  millimeters  of  mercury. 


(a)     Indices  of  refraction. 

Spectrum 

io3  (n-i) 

Spectrum 

10'  (n-i) 

Wave- 

(n-i )  io». 

line. 

Air. 

line. 

Air. 

length. 

Air. 

O.                N. 

H. 

A 

.2905 

M 

•2993 

V- 

.4861 

.2951 

.2734         .3012 

.1406 

B 

.2911 

N 

•3°°3 

.5461 

.2936 

.2717         .2998 

•J397 

C 

.2914 

0 

•3OI5 

•5790 

.2930 

.2710           — 

•!393 

D 

.2922 

P 

3°23 

•6563 

.2919 

.2698         .2982 

.1387 

E 

•2933 

Q 

•3031 

.4360 

.2971 

.2743          co2 

.1418 

F 

.2943 

R 

•3°43 

.5462 

•2937 

.2704        .4506 

•!397 

G 

.2962 

S 

•3°53 

.6709 

.2918 

.2683        .4471 

•1385 

H 

.2978 

T 

.3064 

6.709 

.2881 

.2643        48°4 

.1361 

K 

.2980 

U 

•3075 

8.678 

.2888 

.2650        .4579 

.1361 

L 

.2987 

First  4, 

Cuthbertsons  ;  the  rest,  Koch,  1909. 

(b)  The 

following  are   compiled   mostly  from   a  table  published  by  Briihl  (Zeits.  fur  Phys.  Chem.  vol.  7, 

pp.  25-27). 

The  numbers  are  from  the  results  of  experiments  by 

Biot  and  Arago,  Dulong,  Jamin, 

Ketteler, 

Lorenz,  Mascart,  Chappius,  Rayleigh,  and  Riviere  and  Prytz.     When  the  number  given  rests  on  the  authority 

of  one  observer  the  name  of  that  observer  is  given.     The  values  are  for  o°  Centigrade  and  760  mm.  pressure. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Substance. 

Kind  of 
light. 

Indices  of  refraction 
and  authority. 

Acetone 

D 

I.OOIO79-I.OOIIOO 

Hydrogen     .     . 

white 

1.000138-1.000143 

Ammonia 

white 

1.000381-1.000385 

" 

D 

1.000132  Burton. 

u 
Argon  . 

D 
D 

1.000373-1.000379 
1.000281  Rayleigh. 

Hydrogen  sul-  ( 
phide    .     .     ( 

D 
D 

1.000644  Dulong. 
1.000623  Mascart. 

Benzol 

.     .      . 

D 

1.001700-1.001823 

Methane  .     .     . 

white 

1.000443  Dulong. 

Bromine 

D 

1.001132  Mascart. 

u 

D 

1.000444  Mascart. 

Carbon  dioxide 

white 

i  .000449-1  .000450 

Methyl 

alcohol  . 

D 

.000549-1  .000623 

" 

" 

D 

1.000448-1  .000454 

Methyl  ether     . 

D 

.000891  Mascart. 

Carbon  disul-    { 

white 

1.001500  Dulong. 

Nitric  oxide  .     . 

white 

.000303  Dulong. 

phide 

.  } 

D 

1.001478-1.001485 

" 

" 

D 

.000297  Mascart. 

Carbon  mon-     j 

white 

1.000340  Dulong. 

Nitrogen  .     .     . 

white 

.000295-1  .000300 

oxide 

white 

1.000335  Mascart. 

" 

. 

D 

.000296-1.000298 

Chlorine 

. 

white 

1.000772  Dulong. 

Nitrous 

oxide    . 

white 

1.000503-1.000507 

n 

. 

D 

1.000773  Mascart. 

« 

u 

D 

1.000516  Mascart. 

Chloroform  .     . 

D 

1.001436-1.001464 

Oxygen 

white 

1.000272- 

1.000280 

Cyanogen 

.      . 

white 

1.00083 

4  Dulong. 

u 

. 

D 

1.000271-1.000272 

" 

. 

D 

1.00078 

4-1.00082:; 

Pentane 

. 

D 

1.001711  Mascart. 

Ethyl  alcohol    . 

D 

1.000871-1.000885 

Sulphur  dioxide 

whit? 

1.000665  Dulong. 

Ethyl  ether  .     . 

D 

1.001521-1.001544 

« 

" 

D 

1.000686  Ketteler. 

Helium 

D 

1.000036  Ramsay. 

Water  . 

.     .     . 

white 

1.000261  Jamin. 

Hydrochloric    j 

white 

1.000449  Mascart. 

« 

. 

D 

1.000249-1.000259 

acid  . 

( 

D 

1.000447 

SMITHSONIAN  TABLES. 


194  TABLES  2O1-203. 

MEDIA  FOR  DETERMINATIONS  OF  REFRACTIVE   INDICES  WITH 
THE   MICROSCOPE. 

TABLE  201.  -Liquids,  nD  (0.589,*)  =  1.74  to  1.87. 

In  100  parts  of  methylene  iodide  at  20°  C.  the  number  of  parts  of  the  various  substances  in- 
dicated in  the  following  table  can  be  dissolved,  forming  saturated  solutions  having  the  permanent 
refractive  indices  specified.  When  ready  for  use  the  liquids  can  be  mixed  by  means  of  a  dropper 
to  give  intermediate  refractions.  Commercial  iodoform  (CHI3)  powder  is  not  suitable,  but  crys- 
tals from  a  solution  of  the  powder  in  ether  may  be  used,  or  the  crystalized  product  may  be 
bought.  A  fragment  of  tin  in  the  liquids  containing  the  SnI4  will  prevent  discoloration. 


CHI3. 

SnI4. 

Aslg. 

SbI3. 

S. 

«na  at  20°. 

12 

.764 

25 

.783 

25 

12 

.806 

3° 

6 

.820 

27 

13 

7 

.826 

40 

27 

16 

.842 

14 

8 

10 

.853 

35 

3i 

16 

8 

10 

.868 

TABLE  202.  —Resin-like  Substances,  nD  (0.589M  =1.68  to  2.10. 

Piperine,  one  of  the  least  expensive  of  the  alkaloids,  can  be  obtained  very  pure  in  straw-colored 
crystals.  When  melted  it  dissolves  the  tri-iodides  of  arsenic  and  antimony  very  freely.  The 
solutions  are  fluid  at  slightly  above  100°  and  when  cold,  resin-like.  A  solution  containing  3  parts 
antimony  iodide  to  one  part  of  arsenic  iodide  with  varying  proportions  of  piperine  is  easier  to 
manipulate  than  one  containing  either  iodide  alone.  The  following  table  gives  the  necessary  data 
concerning  the  composition  and  refractive  indices  for  sodium  light.  In  preparing,  the  constituents, 
in  powder  of  about  i  mm.  grain,  should  be  weighed  out  and  then  fused  over,  not  in,  a  low  flame. 
Three-inch  test  tubes  are  suitable. 


Per  cent  Iodides. 

oo. 

10. 

20. 

30. 

40. 

SO. 

60. 

70. 

80. 

Index  of  refraction 

1.683 

1.700 

1.725 

I  756 

1.794 

1.840 

1.897 

1.968 

2.O5O 

TABLE  203.  —Permanent  Standard  Resinous  Media,  nD  (0.6*9*0=1.546  to  1.682. 

Any  proportions  of  piperine  and  rosin  form  a  homogeneous  fusion  which  cools  to  a  transparent 
resinous  mass.  The  following  table  shows  the  refractive  indices  of  various  mixtures.  On 
account  of  the  strong  dispersion  of  piperine  the  refractive  indices  of  minerals  apparently  matched 
with  those  of  mixtures  rich  in  this  constituent  are  0.005  to  o.oi  too  low.  To  correct  this  error  a 
screen  made  of  a  thin  film  of  7  per  cent  antimony  iodide  and  93  per  cent  piperine  should  be 
used  over  the  eye-piece.  Any  amber-colored  rosin  in  lumps  is  suitable. 


Per  cent  Rosin. 

oo. 

IO. 

20. 

3°- 

40. 

5°- 

60. 

7o. 

80. 

9o. 

100. 

Index  of  refraction 

1.683 

1.670 

1.657 

1.643 

1.631 

1.618 

1.604 

1.590 

1-575 

1.560 

1-544 

All  taken  from  Merwin,  Jour.  Wash.  Acad.  of  Sc.  3,  p.  35,  1913. 
SMITHSONIAN  TABLES. 


TABLES  204-205. 

OPTICAL   CONSTANTS   OF   METALS. 
TABLE  204. 


'95 


Two  constants  are  required  to  characterize  a  metal  optically,  the  refractive  index,  #,  and  the 
absorption  index,  k,  the  latter  of  which  has  the  following  significance  :  the  amplitude  of  a  wave 
after  travelling  one  wave-length,  A.1  measured  in  the  metal,  is  reduced  in  the  ratio1  I  :e  —  2Jrk  or  for 

any  distance  d,  i  :  e  —  ^-.  for  the  same  wave-length  measured  in  air  this  ratio  becomes  i  :  e  -  ^—  _ 
nk  is  sometimes  called  the  extinction  coefficient.  Plane  polarized  light  reflected  from  a  polished 
metal  surface  is  in  general  elliptically  polarized  because  of  the  relative  change  in  phase  between 
the  two  rectangular  components  vibrating  in  and  perpendicular  to  the  plane  of  incidence.  For  a 
certain  angle,  £  (principal  incidence)  the  change  is  90°  and  if  the  plane  polarized  incident  beam 
has  a  certain  azimuth  ^  (Principal  azimuth)  circularly  polarized  light  results.  Approximately, 
(Drude,  Annalen  der  Physik,  36,  p.  546,  1889), 

k  =  tan  2    (i  —  cot  2£)  and  n  = 


For  rougher  approximations  the  factor  in  parentheses  may  be  omitted.     R  =  computed  per- 
centage reflection. 

TABLE  205. 

(The  points  have  been  so  selected  that  a  smooth  curve  drawn  through  them  very  closely  indicates  the  characteristics 

of  the  metal.) 


I 

Computed. 

Metal. 

A 

* 

* 

n 

k 

nk 

R 

Authority. 

| 

M 

% 

Cobalt 

0.231 

64°3i' 

29°39 

1.  10 

1.30 

J-43 

32- 

Minor. 

•275 

70   22 

29  59 

1.41 

1-52 

2.14 

46. 

11 

.500 

77     5 

3i  53 

*»Q3 

1-93 

3-72 

66. 

M 

.650 

79    o 

3r  25 

2.35 

1.87 

4.40 

69. 

Ingersoll. 

I.OO 

81  45 

29    6 

3.63 

1.58 

5-73 

73- 

" 

1.50 

83    21 

26  18 

5.22 

1.29 

6-73 

75- 

n 

2.25 

83    48 

26    5 

5-65 

1.27 

7.18 

76. 

'• 

Copper 

.231 

65  57 

26  14 

1.05 

i-45 

29. 

Minor. 

•347 

65     6 

28  16 

1.19 

1-23 

1.47 

32. 

n 

.50° 

70  44 

33  46 

1.  10 

2.13 

2-34 

56. 

" 

.650 

74  16 

41  30 

0.44 

7-4 

3-26 

86. 

Ingersoll. 

.870 

78  40 

42  30 

o-35 

II.  0 

3-85 

91. 

** 

i-75 

84    4 

42  30 

0.83 

11.4 

9.46 

96. 

" 

2.25 

85  13 

42  30 

1.03 

11.4 

11.7 

97- 

" 

4.00 

87    20 

42  30 

1.87 

11.4 

21.3 

Forst.-Fre"ed. 

5-50 

88  oo 

41  50 

9.0 

28.4 

H 

Gold 

I.OO 

8i45 

44  oo 

0.24 

28.0 

6.7 

" 

2.00 

85  30 

43  56 

0.47 

26.7 

12.5 

" 

3-oo 

87  05 

43  50 

0.80 

24-5 

19.6 

*   " 

88  15 

43  25 

1.81 

18.1 

33- 

t( 

Indium 

I.OO 

82  10 

29  IS 

3-85 

i.  60 

6.2 

1C 

2.00 

83  10 

29  40 

4-3° 

1.66 

7.1 

M 

3-00 

81  40 

30  40 

3-33 

1.79 

6.0 

" 

5-00 

79  0° 

32    20 

227 

2.03 

4.6 

" 

Nickel 

0.420 

72  20 

3*  42 

1.41 

1.79 

2-53 

54- 

Tool. 

0.589 

76     i 

1.79 

1.86 

3-33 

62. 

Drude. 

0.750 

78  45 

32     6 

2.19 

1.99 

4.36 

70. 

Ingersoll. 

I.OO 

80  33 

32      2 

2.63 

2.00 

5.26 

74- 

M 

Platinum 

2.25 

I.OO 

84  21 
75  30 

33  30 
37  oo 

3-95 
1.14 

2-33 

3.25 

9.20 
3-7 

85- 

Forst.-Fre*ed. 

2.00 

74  30 

39  5° 

0.70 

5.06 

3-5 

«          « 

3-00 

73  50 

41  oo 

0.52 

6.52 

3-4 

"          " 

Silver 

5.00 
0.226 

72  oo 
62  41 

42  10 

22    l6 

o-34 
1.41 

9.01 

0.75 

i.  ii 

18. 

Minor. 

•293 

63   «4 

18  56 

0.62 

0.97 

17. 

11 

.316 

52  28 

15  38 

1.13 

0.38 

0-43 

4- 

M 

•332 

52     i 

37     2 

0.41 

1  .61 

0.65 

32. 

" 

•395 

66  36 

43     6 

0.16 

12.32 

1.91 

87. 

" 

.500 

72  31 

43  29 

0.17 

17.1 

2-94 

93. 

H 

.589 

75  35 

43  47 

0.18 

20.6 

3-64 

95- 

" 

•750 

79  26 

44     6 

0.17 

30.7 

5..6 

97- 

Ingersoll. 

I.OO 

82     o 

44    2 

0.24 

29.0 

6.96 

98. 

" 

1.50 

84  42 

43  48 

0.45 

23-7 

10.7 

98. 

1 

2.25 
3-00 

86  18 
87  10 

43  34 
42  40 

0.77 
1.65 

19.9 

12.2 

20.1 

99. 

Forst.-Fre*ed. 

Steel 

4.50 

0.226 

88  20 
66  51 

41   10 
28  .7 

4-49 
1.30 

7.42 
1.26 

3f|4 

35- 

Minor. 

•257 

68  35 

28  45 

1.38 

1.35 

iM 

40. 

" 

.325 

69  57 

30    9 

'•53 

2.09 

45- 

u 

.500 

75  47 

29      2 

2.09 

1.50 

3-14 

57- 

ii 

.650 

77  48 

27    9 

2.70 

J-33 

3-59 

59- 

Ingersoll. 

1.50 

81  48 

28  51 

3-7* 

5-75 

73- 

" 

2.25 

83    22 

30  36 

4.14 

1.79 

7.41 

80. 

" 

Drude,  Annalen  der  Physik  und  Chemie,  39,  p.  481,  1890;  42,  p.  186,  1891;  64,  p.  159,  1898.  Minor,  Annalen 
der  Physik,  10,  p.  581,  1903.  Too  ,  Physical  Review,  31,  p.  i,  1910.  Ingersoll,  Astrophysical  Journal,  32,  p.  265, 
1910;  Fbrsterling  and  Fre"edericksz,  Annalen  der  Physik,  40,  p.  201,  1913. 

SMITHSONIAN  TABLES. 

196 


TABLES  206-207. 
OPTICAL  CONSTANTS  OF  METALS. 

TABLE  206. 


Metal. 

A. 

n. 

k. 

R. 

Ref. 

Metal. 

A. 

n. 

k. 

R. 

Ref. 

Al* 

0.589 

1.44 

5-32 

83 

I 

Rh* 

P- 
0-579 

i-54 

4.67 

78 

3 

Sb.* 

•589 

3-°4 

4-94 

70 

I 

Se.J 

.400 

2.94 

2.3I 

44 

5 

Bi.tJ 

white 

2.26 

2 

.490 

3.12 

1.49 

35 

5 

Cd* 

.589 

I-I3 

5.01 

85 

I 

.589 

2-93 

0-45 

25 

5 

Cr* 

•579 

2.97 

70 

3 

.760 

2.60 

O.o6 

20 

5 

Cb* 

•579 

1.80 

2.  II 

41 

3 

Si.* 

.589 

4.18 

0.09 

38 

6 

Au.t 

•^57 

0.92 

I.I4 

28 

4 

1.25 

3-67 

0.08 

33 

6 

.441 

1.18 

1.85 

42 

4 

3-53 

0.08 

6 

•589 

0.47 

82 

4 

Na.  (liq.) 

.589 

.004 

2.61 

99 

i 

I.  crys. 

•589 

3-34 

o-57 

30 

4 

Ta.* 

•579 

2.05 

2.31 

44 

3 

Ir* 

•579 

2.13 

4.87 

75 

3 

Sn.« 

•589 

1.48 

5-25 

82 

i 

Fe.§ 

•257 

I.OI 

0.88 

16 

4 

W.* 

•579 

2.76 

2.71 

49 

3 

.441 

1.28 

1-37 

28 

4 

V.* 

•579 

3-03 

3-51 

58 

3 

•589 

I-5I 

1.63 

33 

4 

Zn* 

•257 

0-55 

0.61 

20 

4 

Pb* 

.589 

2.OI 

3-48 

62 

i 

.441 

o-93 

3-!9 

73 

4 

Mg* 

•589 

0-37 

4.42 

93 

i 

•589 

1.93 

4.66 

74 

4 

Mn* 

•579 

2-49 

3^9 

64 

3 

.668 

2.62 

5.08 

73 

4 

Hg.  (liq.) 

•326 

0.68 

2.26 

66 

4 

Pd* 
Pt.t 

•44  r 

•579 
•257 
.441 

I.OI 

1.62 
1.72 
1.62 
1.17 
1.94 
2.63 
2.91 

3-42 
441 
4.70 

3-4i 
1.65 
3.16 

74 

75 

59 

CO 

4 
4 
4 
3 

4 
4 
4 
4 

A.  =  wave-length,  n  =  refraction  index. 
k  =  absorption  index,  'R  =  reflection, 
(i)  Drude,  see  Table  205;  (2)  Kundt,  prism 
used,  Ann.  der  Physik  und  Chemie,  34,  p.  477, 
36,  p.  824,  1889;  (3)  v.   Wartenberg,  Verh. 
deutsch.   Physik.   Ges.  12,  p.  105,  1910;  (4) 
Meier,  Annales  der  Physik,  10,  p.  581,  1903; 

Ni* 

.275 

1.09 

i  16 

3-7 

4 

(5)  Wood,  Phil.  Mag.  (6),  3,  607,  1902  ;  (6) 

.441 
•589 

,.!6 

1.30 

1.23 
1.97 

25 

43 

4 
4 

Ingersoll,  see  Table  205. 
*  solid,   t  electrolytic,  \  prism,  §  deposited 

as  film  in  vacuo. 

TABLE  207.— Reflecting  Power  of  Metals. 


Wave- 

J= 
Q-aJ 

length 

<J 

.n 
03 

s 

d 

o' 

!-,' 

M 

s 

0 

X 

s 

js 
K 

33 

s 

H 

c 

CO 

& 

> 

£ 

M 

Per  cents. 

, 

_ 

_ 

_ 

_ 

22 

_ 

72 

46 

_ 

76 

34 

38 

_ 

_ 

49 

57 

_ 

.6 

— 

S3 

— 

— 

24 

— 

73 

48 

— 

77 

32 

4S 

49 

— 

Si 

58 

— 

.8 

- 

S4 

— 

— 

2S 

— 

74 

S2 

— 

81 

29 

64 

48 

— 

S6 

60 

— 

I.O 
2.O 

71 
82 

II 

72 
87 

67 

72 

27 

35 

78 
87 

74 
77 

58 
§2 

n 

84 
9i 

28 
28 

78 
90 

50 
S2 

K 

62 

8S 

61 
69 

80 
92 

4.0 

92 

68 

96 

81 

48 

94 

84 

90 

88 

92 

28 

93 

72 

93 

7.0 

96 

7i 

98 

93 

54 

95 

9i 

93 

94 

94 

28 

94 

68 

81 

95 

88 

98 

10.0 

98 

72 

98 

97 

S9 

96 

94 

97 

9S 

28 

— 

84 

96 

- 

98 

12.0 

98 

99 

97 

96 

95 

97 

" 

95 

85 

96 

99 

Coblentz,  Bulletin  Bureau  of  Standards,  2,  p.  457,  1906,  7,  p.  197,  1911.  The  surfaces  of  some 
of  the  samples  were  not  perfect  so  that  the  corresponding  values  have  less  weight.  The  methods 
for  polishing  the  various  metals  are  described  in  the  original  articles. 

SMITHSONIAN  TABLES. 


TABLES  208-21 0.-THE  REFLECTION  OF  LIGHT. 


197 


According  to  Fresnel  the  amount  of  light  reflected  by  the  surface  of  a  transparent  medium 

=  1  (A  +  B\  = l  \  S!n!!l'Tr!  +  tan!!/~r!  [  ;  A  is  the  amount  polarized  in  the  plane  of  inci- 

2  I  sm2  (*  +  r)       tan   (*  +  r}  f 
deuce ;  B  is  that  polarized  perpendicular  to  this  ;  *  and  r  are  the  angles  of  incidence  and  refraction. 

TABLE  208.  —Light  reflected  when  i  =  0°  or  Incident  Light  Is  Normal  to  Surface. 


ft. 

iCnhS 

H. 

f£+S 

«. 

1  («*  +  ^)- 

«. 

\(A+B). 

1.00 

0.00 

•4 

2.78 

2.O 

ii.  ii 

5- 

44-44 

1.02 
1.05 
I.I 

0.0  1 

0.06 
0.23 

i 

•7 

4.00 

5-33 
6.72 

2.25 
2-5 

2.75 

14.06 

18.37 
22.89 

5-83 

10. 
IOO. 

50.00 
66.67 
96.08 

1.2 

0.83 

.8 

8.16 

3- 

25.00 

00 

100.00 

i-3 

1.70 

•9 

9-63 

4- 

36.00 

TABLE  209.  —Light  reflected  when  n  Is  near  Unity  or  equals  l  +  <ln. 


i. 

A. 

B. 

IM+-S), 

A-Bm 
A+B 

0° 

I.OOO 

I.OOO 

.000 

0.0 

5 

1.015 

.985 

.000 

5'5 

10 

1.063 

•939 

.001 

6.2 

15 

1.149 

.862 

.005 

14-3 

20 

1.282 

-752 

.017 

26.0 

25 

1.482 

.612 

.047 

41-5 

3° 

1.778 

444 

.III 

6O.O 

35 

2.221 

.260 

.240 

79.1 

40 

2.904 

.088 

.496 

94-5 

45 

4-000 

.000 

2.OOO 

IOO.O 

50 

5-857 

.176 

3.016 

94.5 

£ 

9-239 
l6.000 

1.081 

4.000 

5.l6o 
IO.OOO 

79.1 

60.0 

65 

3«.34j5 

12.952 

22.149 

41.5 

70 

73-°79 

42.884 

57-981 

26.0 

i! 

222.85 
1099.85 

167.16 

195.00 
1035-53 

14.3 

6.2 

85 

1  7330-64 

16808.08 

17069.36 

i-5 

90 

00 

00 

00 

o.o 

TABLE  210.  — Light  reflected  when  n  =  1.55. 


I. 

r. 

A. 

B. 

dA.\ 

dB^ 

UA+B). 

A-Bm 

A+B 

0   / 

o 

O   0.0 

4-65 

4.65 

0.130 

0.130 

4-65 

0.0 

5 

10 

3  13-4 
6  25.9 

4.70 
4.84 

4.61 
4-47 

•131 
•135 

:3 

4-65 
4.66 

I.O 

4.0 

15 

9  36.7 

5-09 

4.24 

.141 

.121 

4.66 

9.1 

20 

12  44.8 

5-45 

3-92 

.150 

.114 

4.68 

16.4 

25 

IS  49-3 

5-95 

3.50 

.161 

.105 

4-73 

25-9 

30 

18  49-i 

6.64 

3.00 

.175 

.094 

4.82 

37-8 

35 

21  43.1 

7-55 

2.40 

.191 

.O8l 

4.98 

Si-7 

40 

24  30.0 

8-77 

i-75 

.210 

.066 

5.26 

66.7 

45 
So 

27  8.5 
29  37-1 

10.38 
12.54 

i.  08 
0.46 

•233 
.263 

*049 
.027 

5-73 
6.50 

81.2 
92.9 

55 

3i  54-2 

15-43 

0.05 

•303 

007 

7-74 

99-3 

60 

33  58-1 

19-35 

0.12 

•342 

-.013 

9-73 

98.8 

65 

35  47-o 

24.69 

I-I3 

•375 

-.032 

12.91 

91.2 

70 

37  19-* 

3!-99 

4.00 

.400 

—.050 

18.00 

77-7 

75 

38  32-9 

42.00 

10.38 

.410 

-.060 

26.19 

61.8 

80 

39  26.8 

55-74 

23-34 

•370 

-.069 

3954 

41.0 

82  30 

39  45-9 

64.41 

34-°4 

.320 

—.067 

49.22 

30.8 

85  o 

39  59'6 

74-52 

49-03 

.250 

-.061 

61.77 

20.6 

86  o 

40  3'  6 

79.02 

56.62 

.209 

—•055 

67.82 

16.5 

87  o 

40  6.7 

83.80 

65-32 

•  163 

—  .046 

74-56 

12.4 

88  o 

40  8.9 

88.88 

75-31 

.118 

—.036 

82.10 

8.3 

89  o 

40  IO.2 

94.28 

86.79 

.063 

—  .022 

90.54 

4.1 

90  o 

40  10.7 

IOO.OO 

100.00 

.000 

—  .000 

100.00 

0.0 

Angle  of  total  polarization  =  5 7°  xo'.s,  A  =  16.99. 

*  This  column  pives  the  degree  of  polarization.  t  Columns  5  and  6  furnish  a  means  of 

determining  A  and  B  for  other  values  of  «.   They  represent  the  change  in  these  quantities  for  a  change  of  «  ot  o.oi. 

Taken  from  E.  C.  Pickering's  "  Applications  of  Fresnel's  Formula  for  the  Reflection  of  Light." 
SMITHSONIAN  TABLES. 


198  TABLES  211-212. 

REFLECTION  OF  METALS. 

TABLE  211.  —  Perpendicular  Incidence  and  Reflection. 

The  numbers  give  the  per  cents  of  the  incident  radiation  reflected. 


2^r^* 

M 

*^S 

*^f 

"^ 

i 

3 

t 

<  JL 

irf 

i 

'i 

\ 

1 

'i 

| 

a. 
•S 

M 
a 

i 

1 

/-backed  G 

s  Magnaliu 
1+vMg. 

chiinemann 
Sn-\-2qNi- 

1+ 

Nickel. 
'ically  Dep 

,t 

If 

55  1 

1 

it 
If 

It 

s, 

"o^ 
0.5 

Brass. 
owbridge). 

Silver. 
ally  Depos 

> 

w 

i 

•5  J 

^  « 

w^ 

£ 

1 

s 

•| 

I 

g 

i 

a 

i 

Z 

fi 

& 

1 

1 

^ 

I 

1 

a 

.251 

. 

_ 

67.0 

3S.8 

29.9 

37-8 

_ 

32.9 

2S-9 

33.8 

38.8 

_ 

34.1 

.288 

- 

- 

70.6 

37-1 

37.7 

42.7 

- 

24.3 

38.8 

34-0 

- 

21.2 

.305 

- 

- 

72.2 

37.2 

41.7 

44.2 

~ 

37.2 

25-3 

39-8 

31.8 

— 

.316 
.326 

_ 

_ 

75-5 

39-3 

- 

45-2 

- 

40.3 

24.9 

41.4 

28.6 

- 

I4.6 

•338 

— 

— 

— 

46.5 

— 

— 

— 

— 

— 

— 

55.5 

•357 
•385 

- 

- 

81.2 
83.9 

43-3 
44-3 

51.0 

48.8 
49.6 

- 

45-o 
47.8 

27-3 
28.6 

434 

454 

27.9 

27.1 

- 

74-5 
81.4 

.420 

83.3 

47-2 

S64 

56.6 

_ 

51.9 

32.7 

Si.8 

29-3 

_ 

86.6 

45° 
.500 

85.7 

86.6 

72.8 
70.9 

834 
83-3 

49-2 
49-3 

60.0 
63.2 

38 

48.8 
53-3 

544 
54-8 

37-0 
43-7 

547 
584 

33-  i 
47.0 

~ 

90-5 
91-3 

•55° 

88.2 

71.2 

82.7 

48.3 

64.0 

62.6 

59-5 

54-9 

47-7 

61.1 

74.0 

- 

92.7 

.660 
.650 
.700 

88.1 
89.1 
89.6 

69.9 
71-5 

72.§ 

83.0 
82.7 

47-5 
5J-5 
54-9 

64.3 
654 
66.8 

64.9 
66.6 
68.8 

83-5 
89.0 
90.7 

554 
56.4 
57-6 

71.8 
80.0 
83-1 

64.2 

66-5 
69.0 

844 
88.9 

92-3 

- 

92.6 
94-7 
954 

.800 

_ 

_ 

84.3 

63.1 

_ 

69.6 

_ 

58.0 

88.6 

70.3 

94-9 

_ 

96.8 

I.O 

— 

— 

84.1 

69.8 

70.5 

72.0 

- 

63.1 

90.1 

72.9 

— 

97.0 

j.'5 

— 

- 

85.1 

79.1 

75-° 

78.6 

— 

70.8 

93-8 

77-7 

97-3 

— 

98.2 

2.O 

_ 

— 

86.7 

82.3 

80.4 

83-S 

_ 

76.7 

95-5 

80.6 

96.8 

91.0 

97-8 

3-° 

_ 

— 

874 

8S4 

86.2 

88.7 

_ 

83.0 

97.1 

88.8 

_ 

93-7 

98  i 

4.0 

- 

- 

88.7 

87.1 

88.5 

91.1 

- 

87.8 

97.3 

91-5 

96.9 

95-7 

98.5 

5.0 

— 

— 

89.0 

87.3 

89.1 

944 

— 

89.0 

97-9 

93-5 

97.0 

95-9 

98.1 

7.0 

— 

- 

90.0 

88.6 

90.1 

94.3 

— 

92.9 

98.3 

95-5 

98.3 

97.0 

98.5 

9.0 

— 

— 

90.6 

90-3 

92.2 

95-6 

— 

92-9 

984 

954 

98.0 

97-8 

98.7 

I  I.O 

- 

- 

90.7 

90.2 

92.9 

95-9 

- 

94.0 

98.4 

98.3 

96.6 

98.8 

14.0 

92.2 

90-3 

93-6 

97-2 

" 

96.0 

97-9 

904 

97-9 

98.3 

Based  upon  the  work  of  Hagen  and  Rubens,  Ann.  der  Phys.  (i)  352,  1900;  (8)  r,  1902;  (n)  873,  1903. 
Taken  partly  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 

TABLE  212.  —  Percentage  Diffuse  Reflection  from  Miscellaneous  Substances. 


Lamp-blacks. 

; 

« 

S. 

8 

Wave- 
length 
M 

1 

£S 

si 

|8 

Acetylene 

£ 

-a 

6 

•31 

3| 

£u 

i 

^j 

i 

o 

Lead  oxid 

< 

Zinc  oxide 

£ 

£ 

IS 

Lead 
carbonate 

"13 

"f 
< 

Black  Veli 

Black  felt. 

Red  brick 

*.6o 

3-2 

2S. 

S2. 

84. 

82. 

89. 

is- 

1.8 

14. 

30. 

*95 

34 

J-3 

I.I 

0.6 

i-3 

i.i 

88. 

86. 

75- 

93- 

21. 

44 

3-2 

"•3 

•9 

.8 

1.2 

14 

jl. 

21. 

8. 

18. 

29. 

37 

8.8 

3-8 

1-3 

1.2 

1.6 

2.1 

26. 

2. 

3- 

S- 

ii. 

2.7 

12. 

24.0 

44 

3-o 

4.0 

2.1 

5-7 

4.2 

10. 

6. 

5- 

7- 

*Not  monochromatic  (max.)  means  from  Coblentz,  J.  Franklin  Inst.  1912.  Bulletin  Bureau  of  Standards,  9,  p.  283, 
1912,  contains  many  other  materials. 

SMITHSONIAN  TABLES. 


TABLES  21 3-21 5 . 
TRANSMISSIBILITY  FOR  RADIATION  OF  JENA  GLASSES. 

TABLE  213. 

Coefficients,  a,  in  the  formula  It  —  7<xz*,  where  70  is  the  Intensity  before,  and  /«  after,  transmission 
through  the  thickness  /,  expressed  in  centimeters.  Deduced  from  observations  by  Miiller, 
Vogel,  and  Rubens  as  quoted  in  Hovestadt's  Jena  Glass  (English  translation). 


Coefficient  of  transmission,  a. 

Type  of  Glass. 

•375  M 

390** 

.400  p. 

•434  M 

.436/* 

•4551* 

•477  M 

.503  M 

.580/01 

•677  M 

O  340,  Ord.  light  flint 
O  102,  H'vy  silicate  flint 

.388 

456 
.02  s 

.614 
463 

.569 
.502 

.680 

.566 

.834 
•663 

.880 
.700 

.880 

.782 

.878 
.828 

•939 
•794 

O   93,  Ord. 
O  203,     "            "    crown 
O  598,  (Crown) 

.583 

•583 

•695 

.667 

.714 
.806 

•797 

.807 
.822 
.770 

•899 
.860 
.771 

.871 
.872 
.776 

•903 
.872 
.818 

•943 
•903 
.860 

x= 

0.7, 

0.95** 

i.iM 

1.4  n 

1.7  M 

2.0  ft. 

2-3  M 

2-5/1* 

2.7  M 

2-9  f* 

3'*M 

S  204,  Borate  crown 
S  179,  Med.  phosp.  cr. 

I.OO 

% 

•94 
•95 

.90 
.90 

.85 

.84 

.81 

.67 

.69 

49 

43 
•87 

3 

.18 

- 

O  1  143,  Dense,  bor.  sil.  cr. 

.98 

_ 

•97 

— 

•95 

•93 

.90 

.84 

•7i 

47 

.27 

O  1092,  Crown 

•99 

.96 

•95 

•99 

.91 

.82 

•71 

.60 

48 

.29 

O  1151,       " 

.98 

— 

.99 

•99 

.98 

•94 

.90 

•79 

•75 

45 

•32 

O  451,  Light  flint 

I.OO 

- 

- 

.98 

•Q  ^ 

.92 

.84 

.78 

•34 

O  469,  Heavy  " 

I.OO 

- 

.98 

- 

•99 

.98 

.98 

•97 

.90 

.66 

•50 

0  500,       «       «« 

I.OO 

— 

I.OO 

— 

I.OO 

— 

I.OO 

•99 

.92 

•74 

•53 

S  163,       "       " 

I.OO 

I 

.98 

•99 

•99 

•94 

.78 

.60 

TABLE  214. 

Note  :  With  the  following  data,  t  must  be  expressed  in  millimeters ;  i.  e.  the  figures  as  given 
give  the  transmissions  for  thickness  of  i  mm. 


Wave-length  in  ft. 

No.  and  Type  of  Glass. 

Visible  Spectrum. 

Ultra-violet  Spectrum. 

.644  M- 

•578  f- 

•546  /* 

•5091* 

.480  M 

•436  M 

.405  f* 

•384  M 

.361  n 

•340  M 

•332  f- 

•309  M 

.80, 

F38i5  Dark  neutral 

•35 

•35 

•37 

•31) 

•34 

•30 

•15 

.06 

F45I2  Red  filter 

.94 

•OS 

F  2745  Copper  ruby 

•39 

47 

47 

45 

43 

43 

F43I3  Dark  yellow 
F435I  Yellow 

.98 

•97 
•97 

% 

•93 

.09 

44 

•IS 

F4937  Bright  yellow 

I.O 

I.O 

I.O 

•99 

•74 

.40 

•31 

.28 

.22 

,18 

.14 

.06 

F  4930  Green  filter 

•'7 

•5° 

.64 

.62 

44 

^3873  Blue  filter 

- 

.18 

•50 

•73 

.69 

•59 

•36 

.10 

F3654    Cobalt    glass, 

transparent  for  outer 

red 

— 

— 

— 

•IS 

44 

.8s 

I.O 

I.O 

I.O 

I.O 

I.O 

.c8 

F  3653  Blue,  ultraviolet 
F  37  28  Didymium,  str'g 
bands 

•99 

.72 

•99 

.96 

.11 

•95 

.65 
.96 

I.O 

•99 

I.O 

•99 

I.O 

.89 

I.O 

.89 

I.O 

•77 

•54 

.18 

This  and  the  following  table  are  taken  from  Jenaer  Glas  fur  die  Optik,  Liste  751,  1909 
TABLE  215.  -  TransmisslMllty  of  Jena  Ultra-violet  Glasses. 


No.  and  Type  of  Glass. 

Thickness. 

0-397  M 

0.383  M 

0.361  ft. 

0.346  /x 

0-325  M 

0.309  /A 

0.280  ft 

UV  3199  Ultra-violet 

i  mm. 

I.OO 

I.OO 

I.OO 

I.OO 

I.OO 

0.95 

0.56 

2  mm. 

0.99 

0.99 

0.99 

0.97 

0.90 

0.57 

«<               «« 

i  dm. 

0-95 

0.95 

0.89 

0.70 

0.36 

UV3248         « 

i  mm. 
2  mm. 

I.OO 

0.98 

I.OO 

0.98 

I.OO 

0.98 

I.OO 

0.92 

0.98 

0.78 

0.91 
0.38 

0-35 

«<               <t 

i  dm. 

0.96 

0.87 

0.79 

045 

0.08 

SMITHSONIAN  TABLES. 


200 


TABLE    216. 
TRANSMISSIBILITY    FOR    RADIATION. 

Transmissibility  of  the  Various  Substances  of  Tables  166  to  175. 


Alum  :  Ordinary  alum  (crystal)  absorbs  the  infra-red. 

Metallic  reflection  at  9.05/1  and  30  to  40^. 

Rock-salt :  Rubens  and  Trowbridge  (Wied.  Ann.  65,  1898)  give  the  following  transparencies  for 
a  i  cm.  thick  plate  in  %  : 


X 

9 

10 

12 

!3 

14 

15 

16 

17 

18 

19 

20.7 

23-7A* 

% 

99-5 

99-5 

99-3 

97.6 

93-i 

84.6 

66.1 

51.6 

27.5 

9.6 

0.6 

o. 

i  iiutiwi     i  A.  UTO*  «^*«    3*    »  y^^r  I    o  o 

231,86%;  210,77%;  186,70%. 
Metallic  reflection  at  0.110/1,  0.156,  51.2,  and  87/*. 
Sylvine :  Transparency  of  a  i  cm.  thick  plate  (Trowbridge,  Wied.  Ann.  60,  1897). 


lx 

9 

IO 

98.8 

II 

12 

13 

14 

15 

16 

17 

18 

19 

20.7 

23-7M 

L 
[_%_ 

IOO. 

99.0 

99-5 

99-5 

97-5 

95-4 

93-6 

92. 

86. 

76. 

58. 

15- 

Metallic  reflection  at  0.1141*,  0.161,  61.1,  100. 
Fluorite :  Very  transparent  for  the  ultra-violet  nearly  to  O.I/A. 
Rubens  and  Trowbridge  give  the  following  for  a  i  cm.  plate  (Wied.  Ann.  60,  1897) : 


X 

8ju 

9 

IO 

ii 

I2/i 

% 

84.4 

54-3 

16.4 

I.O 

O 

Metallic  reflection  at  24/4,  31.6,  40/1. 

Iceland  Spar:   Merritt  (Wied.  Ann.  55,   1895)  gives  the  following  values  of  k  in  the  formula 
i  =  i0e-kd  (d  in  cm.) : 
For  the  ordinary  ray : 


X 

1.02 

1-45 

1.72 

2.07 

2.  II 

2.30 

2.44 

2-53 

2.60 

2.65 

2-74A* 

k 

0.0 

0.0 

0.03 

0.13 

0.74 

1.92 

3.00 

1.92 

1.  21 

1.74 

2.36 

X 

2-83 

2.90 

2-95 

3-04 

3-30 

3-47 

3.62 

3.80 

3-98 

4-35      4.52 

4-83^ 

k 

1.32 

0.70 

i.  80 

4.71 

22.7 

19.4 

9.6 

18.6 

CO 

6.6    i    14.3 

6.1 

For  the  extraordinary  ray  : 


X 

2.49 

2.87 

3.00 

3.28 

3.38 

3-59 

3.76 

3-90 

4.02 

4.41 

4-67^ 

•  k 

0.14 

0.08 

0.43 

1.32 

0.89 

1.79 

2.04 

1.17 

0.89 

1.07 

2.40 

X 

4.91 

5-04 

5-34 

5-5°M 

k 

1.25 

2.13 

4.41 

12.8 

Quartz  :  Very  transparent  to  the  ultra-violet ;  Pfliiger  gets  the  following  transmission  values  for 

a  plate  i  cm.  thick:  at  0.222/4,  94.2%;  0.214,  92  ;  0.203,  83-6 ;  0.186,  67.2%. 

Merritt  (Wied.  Ann.  55,  1895)  gives  the  following  values  for  k  (see  formula  under  Iceland  Spar) : 
For  the  ordinary  ray  : 


X 

2.72 

2.83 

2-95 

3-07 

3-T7 

3-38 

3.67 

3.82 

3.96 

4.12 

4.50/1 

k 

O.2O 

0-47 

0-57 

0.31 

O.2O 

0.15 

1.26 

1.61 

2.04 

3-41 

7-3° 

For  the  extraordinary  ray  : 


X 

2.74 

2.89 

3.00 

3.08 

3.26 

343 

3-52 

3-59 

3-64 

3-74 

3-9i 

4.19 

4-36/t 

k 

o.o 

O.I  I 

o-33 

0.26 

O.I  I 

0.51 

0.76 

1.88 

1.83 

1.62 

2.22 

3-35 

8.0 

For  A>7  /^becomes  opaque,  metallic  reflection  at  8.50/1,  9.02,  20.75-244/4,  then  trans- 
parent again. 

The  above  are  taken  from  Kayser's  "  Handbuch  der  Spectroscopie,"  vol.  iii. 
SMITHSONIAN  TABLES. 


TABLES  217-218. 
TRANSMISSIBILITY   OF    RADIATION. 

TABLE  217.  —  Color  Screens. 


201 


The  following  light-filters  are  quoted  from  Landolt's  "  Das  optische  Drehungsvermogen,  etc."  1898. 
Although  only  the  potassium  salt  does  not  keep  well  it  is  perhaps  safer  to  use  freshly  prepared 
solutions. 


Thick- 

Grammes  of 

Optical  cen- 

Color. 

ness. 

Water  solutions  of 

substance 

tre  of  band. 

Transmission  . 

mm. 

in  100  c.cm. 

M 

Red 

u 

20 
20 

Crystal-violet,  5BO 
Potassium  monochromate 

O.OO5 
IO. 

0.6659 

j  begins  about  0.7  i8/t. 
I  ends  sharp  at  0.639/1. 

Yellow 

20 

Nickel-sulphate,  NiSO^aq. 

30. 

0.5919 

o.6i4-o.574/t, 

15 

Potassium  monochromate 

IO. 

" 

15 

Potassium  permanganate 

O.O2C 

Green 

20 

Copper  chloride,  CuCl2.2aq. 

60. 

0-5330 

0.540-0.505/1 

Bright  ( 
blue  ) 

20 
2O 
2O 

Potassium  monochromate 
Double-green,  SF 
Copper-sulphate,  CuSO^aq. 

IO. 
O.O2 

X5- 

0.4885 

j  0.526-0.494  and 
|  0.494-0.458/4 

Dark     ( 

20 

Crystal-violet,  5BO 

0.005 

0.4482 

0.478-0.410/4 

blue  \ 

20 

Copper  sulphate,  CuSO^aq. 

J5- 

TABLE  218.  -Color  Screens. 

The  following  list  is  condensed  from  Wood's  Physical  Optics  : 

Methyl  violet,  4R-  (Berlin  Anilin  Fabrik)  very  dilute,  and  nitroso-dimethyl-aniline  transmits  0.365/1*. 

Methyl  violet  -f-  chinin-sulphate  (separate  solutions),  the  violet  solution  made  strong  enough  to 

blot  out  0.4359/1,  transmits  0.4047  and  ,0.4048,  also  faintly  0.3984. 
Cobalt  glass  -f-  aesculin  solution  transmits  0.4359/1. 
Guinea  green  B  extra  (Berlin)  -\-  chinin  sulphate  transmits  0.4916/1. 
Neptune  green  (Bayer,  Elberfeld)  +  chrysoidine.     Dilute  the  latter  enough  to  just  transmit  0.5790 

and  0.5461 ;  then  add  the  Neptune  green  until  the  yellow  lines  disappear. 
Chrysoidine  -f-  cosine  transmits  0.5790/1.     The  former  should  be  dilute  and  the  cosine  added  until 

the  green  line  disappears. 
Silver  chemically  deposited  on  a  quartz  plate  is  practically  opaque  except  to  the  ultra-violet  region 

0.3160-0.3260  where  90%  of  the  energy  passes  through.     The  film  should  be  of  such  thickness 

that  a  window  backed  by  a  brilliantly  lighted  sky  is  barely  visible. 
In  the  following  those  marked  with  a  *  are  transparent  to  a  more  or  less  degree  to  the  ultra-violet: 

*  Cobalt  chloride  :  solution  in  water,  —  absorbs  O.5O-.53/*;  addition  of  CaCl2  widens  the  band  to 
0.47-. 50.     It  is  exceedingly  transparent  to  the  ultra-violet  down  to  0.20.     If  dissolved  in  methyl 
alcohol  -j-  water,  absorbs  O-5O-.53  and  everything  below  0.35.     In  methyl  alcohol  alone  0.485- 
0.555  ar>d  below  0.40/1. 

Copper  chloride :  in  ethyl  alcohol  absorbs  above  0.585  and  below  0.535  >  ni  alcohol  -f-  50%  water, 

above  0.595  and  below  0.37/1. 
Neodymium  salts  are  useful  combined  with  other  media,  sharpening  the  edges  of  the  absorption 

bands.    In  solution  with  bichromate  of  potash,  transmits  O-535-.565  and  above  0.60/1,  the  bands 

very  sharp  (a  useful  screen  for  photographing  with  a  visually  corrected  objective). 
Praesodymium  salts  :  three  strong  bands  at  0.482,  .468,  .444.     In  strong  solutions  they  fuse  into  a 

sharp  band  at  o.^S'-^Sl^-     Absorption  below  0.34. 
Picric  acid  absorbs  0.36-42/1,  depending  on  the  concentration. 
Potassium  chromate  absorbs  O.4O-.35,  O-3O-.24,  transmits  0.23/1. 

*  Potassium  permanganate:  absorbs  0.5  5  5-.  50,  transmits  all  the  ultra-violet. 

Chromium  chloride :  absorbs  above  0.57,  between  0.50  and  .39,  and  below  0.33/1.     These  limits 

vary  with  the  concentration. 
Aesculin  :  absorbs  below  0.363/1,  very  useful  for  removing  the  ultra-violet. 

*  Nitroso-dimethyl-aniline :  very  dilute  aqueous  solution  absorbs  O.49--37  and  transmits  all  the 
ultra-violet. 

Very  dense  cobalt  glass  -f-  dense  ruby  glass  or  a  strong  potassium  bichromate  solution  cuts  off 

everything  below  0.70  and  transmits  freely  the  red. 
Iodine :  saturated  solution  in  CS%  is  opaque  to  the  visible  and  transparent  to  the  infra-red. 

SMITHSONIAN  TABLES. 


2O2 


TABLES  21  9,  219A. 
TRANSMISSIBILITY  OF  RADIATION, 

TABLE  219.  —  Color  Screens.    Jena  Glasses. 


Kind  of  Glass. 

Maker's 
No. 

Color. 

Region  Transmitted. 

Thick- 
ness, 
mm. 

TroQ 

Only  red  to  o  6it  .         ... 

1 

ACQm 

Red     .         .... 

(  Red,  yellow  ;  in  thin  layers  also 

2 

2a 
3 

Uranium    .    .    . 
Nickel    .    .    .     . 

459 
454m 
455m 

A  I  A111 

Bright  yellow   .    .     . 

I  Bright  yellow,  fluo- 
"j      resces. 

Bright  yellow-brown 
Yellow-green 

|      blue  and  violet. 
i  Red,  yellow,  green  to  Eb  ;   in  ) 
\      thin  layer  also  blue                 } 

(  Red,  yellow,  green  (weakened),  ) 
(      blue  (very  weakened)             } 
Yellowish-green    

16. 

ii. 

10. 

4 

433111 

Greenish-yellow   .     . 
Green      .                   . 

Red,  green;  from  0.65-.  50^    .     .     . 
Green,  yellow,  some  red  and  blue  . 

5- 

2-7 

45 

Chromium  . 

Al6m 

Yellow-green   .     .     . 

Yellowish-green,  some  red    .     .     . 
Green                

2-5 

Green-filter     .     . 

437- 

Dark  green  .... 

Green  (in  thin  sheets  some  blue)   . 

5- 

P 

4j 

Blue  as  CuSO* 

Green  blue  violet    

C-I2 

HI 

Blue  violet           .....         . 

c 

Cobalt 

424m 

Blue    

(  Blue,  violet,  blue-green  (weak-  } 
\      ened),  no  red                            \ 
Blue,  violet,  extreme  red  .... 

2-5 
4-c 

13 

Nickel    .     .    .     . 
Violet    .     .    .     . 
Gray  

450IU 
452"1 
444m 

Dark  violet  .... 
)  Gray,  no  recog-  ) 

Violet  (G-H),  extreme  red    .     .     . 
Violet  (G-H),  some  weakened  .     . 

6 

£t 

in 

5m 

j      nizable  color     ) 

All  parts  of  the  spectrum  weakened 

0.1-3 

See  "  0ber  Farbglaser  fiir  wissenschaftliche  und  technische  Zwecke,"  by  Zsigmondy,  Z.  fur  In- 
strumentenkunde,  21,  1901  (from  which  the  above  table  is  taken),  and  "  Cber  Jenenser  Licht- 
filter,"  by  Grebe,  same  volume. 
(The  following  notes  are  quoted  from  Everett's  translation  of  the  above  in  the  English  edition  of 

Hovestadt's  "  Jena  Glass.") 
Division  of  the  spectrum  into  complementary  colors : 

ist  by  2728  (deep  red)  and  2742  (blue,  like  copper  sulphate). 
2nd  by  454™  (bright  yellow)  and  447111  (blue,  like  cobalt  glass). 
3rd  by  433m  (greenish-yellow)  and  424'"  (blue). 
Thicknesses  necessary  in  above :  2728,  1.6-1.7  mm. ;  2742,5;  454IU,  16;  447™,  1.5-2.0;  433'", 

2.5-3.5;  424m,  3  mm. 

Three-fold  division  into  red,  green  and  blue  (with  violet) : 
2728,  1.7  mm. ;  4i4m,  10  mm.;  447m,  1.5  mm.,  or  by 
2728,  1.7  mm.  ;  436"',  2.6mm. ;  447'",  1.8  mm. 

Grebe  found  the  three  following  glasses  specially  suited  for  the  additive  methods  of  three-color 
projection : 

2745,  red ;  438m,  green;  447™,  blue  violet ; 

corresponding  closely  to  Young's  three  elementary  color  sensations. 
Most  of  the  Jena  glasses  can  be  supplied  to  order,  but  the  absorption  bands  vary  somewhat  in 

different  meltings. 
See  also  "Atlas  of  Absorption  Spectra,"  Uhler  and  Wood,  Carnegie  Institution  Publications,  1907. 

TABLE  2 19a.- Water  Vapor. 
Values  of  a  in  I  =  I0  e  ad,  d  in  c.  m.  I0;  I,  intensity  before  and  after  transmission. 


Wave-length  /*, 

.186 

•193 

.200 

.210 

.220 

.230 

.240 

.200 

.300 

415 

a 

.0688 

.0165 

.009 

.Oo6l 

.0057 

.0034 

.0032 

.0025 

.0015 

.00035 

Wave-length  \L, 

•43° 

•45° 

.487 

•500 

•550 

.600 

.650 

•779 

.865 

•945 

a 

.00023 

.0002 

.0001 

.OO02 

.0003 

.OOl6 

.0025 

.272 

.296 

•538 

First  9;  Kreusler,  Drud.  Ann.  6,  1901,;  next  Ewan,  Proc.  R.  Soc.  57,  1894,  Aschkinass,  Wied  Ann.  55,  1895;   ^ast  3i 

Nichols,  Phys.  Rev.  i,  i. 
See  Rubens,  Ladenburg.  Verb.  D.  Phys.  Ges.  1911,  for  extinction  coefs.,  reflective  power  and  index  of  refraction,  i  jx 

to  18  /x. 

SMITHSONIAN  TABLES. 


203 


TABLES   220,   221  .-ROTATION   OF   PLANE   OF   POLARIZED   LIGHT. 

TABLE  220.  —  Tartaric  Acid  ;  Camphor  ;  Santonin  ;  Santonlo  Acid;  Cane  Sugar. 

A  few  examples  are  here  given  showing  the  effect  of  wave-length  on  the  rotation  of  the  plane  of  polarization.  The 
rotations  are  for  a  thickness  of  one  decimeter  of  the  solution.  The  examples  are  quoted  from  Landolt  &  Born- 
stein's  "Phys.  Chem.  Tab."  The  following  symbols  are  used  :  — 

/=  number  grams  of  the  active  substance  in  100  grams  of  the  solution. 

c=  solvent 

q-=.  active  "  cubic  centimeter  " 

Right-handed  rotation  is  marked  -}-,  left-handed  —  . 


Line  of 

Wave-length 
according  to 

Tartaric  acid,*  CuH6O6, 
dissolved  in  water. 

Camphor,*  C10H16O, 
dissolved  in  alcohol. 

Santonin.t  C15H18O3, 
dissolved  in  chloroform. 

spectrum. 

Angstrom  in 
cms.  X  io6. 

g—  50  to  95, 
temp,  rr  24°  C. 

q  =  50  to  95, 
temp.  =  22.9°  C. 

g  =  75  to  96.  5, 
temp.  —  20°  C. 

B 

68.67 

—  140°.  I     +  0.2085  ? 

C 
D 
E 

65.62 
58.92 
52.69 

+  2°.748  +  0.09446  ? 

+  1.950+0.13030? 
+  0.153  +  0.17514? 

38°.  549  —  0.0852? 
51.945  —  0.0964? 
74.331—0.1343? 

—  149.3    +0.1555? 
—  2O2-7    +0.3086? 
—  285.6    +  0.5820  ? 

F2 

51.83 
51.72 
48.61 

—  0.832  +  0.19147? 
—  3-598  +  0.23977? 

79-348  —  0.1451? 
99.601  —  0.1912? 

—  302.38  +  0.6557  ? 
—  365.55  +  0.8284  ? 

e 

43-83 

—  9.657  +  0.31437? 

149.696  —  0.2346  ? 

534-98+I.5240? 

Santonin,t  C15H18O3,  * 
dissolved  in  alcohol. 
c=i.  782. 
temp.  =  20°  C. 

Santonin,t  C15H18O8, 

Santonicacid,t 

dissolved  in 
chloroform. 
£  =  27.192. 
temp.  =  20°  C. 

Cane  sugar,}: 
C12H22On, 
dissolved  m 
water. 
/  =  io  to  30. 

dissolved  in 
alcohol. 
c  =  4.046. 
temp.  = 

20°  C. 

dissolved  in 
chloroform 
c  =3-  1-30.5- 
temp.  = 

20°  C. 

B 

68.67 

—  110.4° 

442° 

484° 

-49° 

47°-56 

C 

65.62 

—  118.8 

5°4 

549 

—  57 

52.70 

D 

58.92 

—  161.0 

693 

754 

—  74 

60.41 

E 

52.69 

—  222.6 

991 

1088 

—  105 

84.56 

bi 

5I-83 

—  237.1 

1053 

1148 

—  112 

— 

b2 

— 

— 

87.88 

F 

48.61 

—  261.7 

1323 

1444 

—  137 

101.18 

e 

43-83 

—  380.0 

201  1 

2201 

—  197 

— 

G 

43-°7 

— 

— 

— 

131.96 

g 

42.26 

— 

2381 

26lO 

—  230 

*  Arndtsen,  "  Ann.  Chim.  Phys."  (3)  54,  1858. 

t  Narini,  "  R.  Ace.  dei  Lincei,"  (3)  13,  1882. 

t  Stefan,  "  Sitzb.  d.  Wien.  Akad."  52,  1865. 

TABLE  221.  -Sodium  Chlorate;  Quartz. 


Sodium  chlorate  (Guye,  C.  R.  108,  1889). 

Quartz  (Soret  &  Sarasin,  Arch,  de  Gen.  1882,  or  C.  R.  95,  1882).* 

Spec- 
trum 
line. 

Wave- 
length. 

Temp. 

Rotation 
per  mm. 

Spec- 
trum 
line. 

Wave- 
length. 

Rotation 
per  mm. 

Spec- 
trum 

line. 

Wave- 
length. 

Rotation 
per  mm. 

a 

71.769 

i5°-o 

2°.o68 

A 

76.04 

i2°.668 

Cd9 

36.090 

63°.628 

B 

67.889 

17.4 

2.318 

a 

71.836 

14.304 

N 

35-8l8 

64.459 

C 

1     D 

65-073 
59-085 

2O.6 

18.3 

2-599 
3.104 

B 

68.671 

15-746 

Cd10 
0 

34.655 
34.406 

69.454 
70-587 

E 
F 

53-233 
48.912 

1  6.0 
11.9 

3.841 
4-587 

C 

65.621 
58-95I 

17.318 

21.684 

Cdn 

34-015 

72.448 

G 

45-532 

IO.I 

5-331 

Da 

21.727 

P 

33.600 

74-571 

G 

42.834 

14.5 

6.005 

Q 

32.858 

78.579 

H 

40.714 

13-3 

.   6.754 

E 

52.691 

27.543 

Cdi2 

32.470 

80.459 

L 
M 

38.412 
37-352 

14.0 
10.7 

7-654 
8.100 

F 
G 

48.607 
43.072 

32.773 

42.604 

R 

3I-798 

84.972 

N 
P 

Q 

35-8I8 
33.931 
32.341 

12.9 

I2.I 

8.861 
9.801 
10.787 

h 
H 

41.012 
39-681 

47.481 

5I-I93 

Cd17 
Cd18 
Cd23 

27.467 
23.125 

121.052 
143.266 
190.426 

R 
T 

30-645 
29.918 

12.8 

11.921 
12.424 

K 

39-333 

52.155 

Cd24 

22.645 

201.824 

Cd17 

28.270 

12.2 

13.426 

L 

38.196 

55-625 

Cd25 

2L935 

220.731 

Cd18 

25-038 

1  1.6 

14.965 

M 

37.262 

58.894 

Cd26 

21.431 

235-972 

*  The  paper  is  quoted  from  a  paper  by  Ketteler  in  "  Wied.  Ann."  vol.  21,  p.  444-    The  wave-lengths  are  for 
the  Fraunhoier  lines,  Angstrom's  values  for  the  ultra  violet  sun,  and  Cornu's  values  for  the  cadmium  lines. 

SMITHSONIAN  TABLES. 


204 


TABLE  222. 
NEWTON'S  RINGS. 


Newton's  Table  of  Colors. 

The  following  table  gives  the  thickness  in  millionths  of  an  inch,  according  to  Newton,  of  a  plate  of  air,  water,  and 
class  corresponding  to  the  different  colors  in  successive  rings  commonly  called  colors  of  the  first,  second,  third, 


glass  corresponding  to  the 
etc.,  orders. 


Color  for  re- 
flected light. 

Color  for 
transmitted 
light. 

Thickness  in 

Color  for  re- 
flected light. 

Th  ckness  in 

millionths  of  an 

millionths  of  an 

1 

inch  for  — 

I 

Color 
for  trans- 
mitted 
light. 

inch  for  — 

Si 

A 

4J 

. 

. 

1 

1 

• 

7e 

rt 

< 

* 

5 

< 

£ 

o 

I. 

Very  black 

_ 

°-5 

0.4 

O.2 

Yellow  .    . 

Bluish 

Black    . 

, 

White  .     . 

I.O 

0-75 

0-9 

green 

27.1 

20-3 

T7-5 

Beginning 

Red. 

— 

29.0 

21.7 

18.7 

of  black  . 

— 

2.0 

J-5 

J-3 

Bluish 

red' 

— 

32.0 

24.0 

20.7 

Blue      . 

t 

Yellowish 

red  .     . 

2.4 

1.8 

'•5 

IV. 

Bluish 

White  . 

Black  .     . 

5-2 

3-9 

34 

green    . 

— 

24.0 

25-5 

22.O 

Yellow  . 

Violet      . 

7.1 

5-3 

4.6 

Green 

Red    . 

35-3 

26.5 

22.7 

Orange 

, 

— 

8.0 

6.0 

4.2 

Yellowish 

Red.     . 

Blue    .    . 

9.0 

6.7 

5.8 

green     . 

— 

36.0 

27.0 

23.2 

Red. 

. 

Bluish 

II. 

Violet  . 

, 

White     . 

II.  2 

34 

7.2 

green 

40-3 

30.2 

26.0 

Indigo  . 

— 

12.8 

9.6 

8.4 

Blue      . 

t 

Yellow    . 

14.0 

10.5 

9.0 

V. 

Greenish 

Green  . 

. 

Red     .     . 

I5-1 

"•3 

9-7 

blue 

. 

Red    . 

46.0 

34-5 

39-7 

Yellow  . 

Violet      . 

16.3 

1-2.2 

10.4 

Red. 

.    . 

— 

52-5 

39-4 

34-o 

Orange 

. 

— 

17.2 

13.0 

"•3 

Bright  red 

Blue    .     . 

18.2 

x3-7 

11.8 

VI. 

Greenish 

Scarlet  . 

— 

19.7 

14.7 

12.7 

blue 

. 

— 

58.7 

46 

38.0 

Red. 

. 

— 

65.0 

48.7 

42.0 

III. 

Purple  . 

, 

Green 

2  I.O 

15-7 

!3-5 

Indigo  . 

— 

21.  1 

17.6 

14.2 

VII. 

Greenish 

Blue      . 
Green   . 

• 

Yellow    . 
Red     .     . 

23.2 
25.2 

J7-S 
18.6 

T 
16.2 

blue  .     . 
Reddish 

— 

72.0 

53-2 

45-8 

white 

— 

71.0 

57-7 

494 

The  above  table  has  been  several  times  revised  both  as  to  the  colors  and  the  numerical 

values.     Professors  Reinold  and  Rucker,  in  their  investigations  on  the  measurement  of  the 

thickness  of  soap  films,  found  it  necessary  to  make  new  determinations.   They  give  a  shorter 
series  of  colors,  as  they  found  difficulty  in  distinguishing  slight  differences  of  shade,  but 

divide  each  color  into  ten  parts  and  tabulate  the  variation  of 

thickness  in  terms  of  the  tenth 

of  a  color  band.     The  position  in  the  band  at  which  the  thickness  is  given  and  the  order  of 

color  are  indicated  by  numerical  subscripts.    For  example  :  RI  5  indicates  the  red  of  the  first 
order  and  the  fifth  tenth  from  the  edge  furthest  from  the  red  edge  of  the  spectrum.     The 

thicknesses  are  in  millionths  of  a  centimeter. 

1 

Color. 

Posi- 
tion. 

Thick- 
ness. 

y 

1 

o 

Color. 

Posi- 
tion. 

Thick- 
ness. 

Color. 

O 

Posi- 
tion. 

Thick- 
ness. 

I. 

Red*    . 

Rl5 

28.4 

Red*    . 

R35 

76.5 

VI.    Green    . 

Ge  o 

141.0 

Bluish 

Green* 

GO  5 

147.9 

II. 

Violet   . 

V25 

3°-5 

red*  . 

BR35 

8l.5 

Red  .     . 

RGO 

154.8 

Blue  .     . 

B25 

35-3 

Red*    . 

R65 

162.7 

Green    . 

G25 

40.9 

IV. 

Green"  . 

G4  o 

84.I 

Yellow  * 

Y25 

454 

« 

G45 

89-3 

VII.    Green    . 

G70 

170.5 

Orange  * 

O25 

49.1 

Yellow 

Green*. 

G75 

178.7 

Red  .     . 

RS  5 

52.2 

green  * 

yc45 

96.4 

Red  .     . 

RTO 

186.9 

Red*    . 

R4  5 

105.2 

Red*    . 

R?5 

193.6 

III. 

Purple  . 

P35 

55-9 

Blue  .     . 

B3  0 

57-7 

V. 

Green    . 

GS  o 

III-9 

VIII.    Green    . 

GS  0 

200.4 

Blue*   . 

B35 

60.3 

Green  *  . 

G55 

II8.8 

Red  .     . 

Rso 

2II-5 

Green    . 

G35 

65.6 

Red  .     . 

RS  o 

126.0 

Yellow  * 

Yfl 

71.0 

Red*     . 

R55 

!33-5 

*  The  colors  marked  are  the  same  as  the  corresponding  colors  in  Newton's  table. 
SMITHSONIAN  TABLES. 


TABLE  223. 
CONDUCTIVITY  FOR  HEAT. 


205 


The  coefficient  k  is  the  quantity  of  heat  in  small  calories  which  is  transmitted  per  second  through 
a  plate  one  centimeter  thick  per  square  centimeter  of  its  surface  when  the  difference  of  tempera- 
ture between  the  two  faces  of  the  plate  is  one  degree  Centigrade.  The  coefficient  k  is  found  to 
vary  with  the  absolute  temperature  of  the  plate,  and  is  expressed  approximately  by  the  equation 
kt  —  ks  [i  +  a  (t  —  /0)].  k0  is  the  resistance  at  /0,  the  lower  temperature  of  the  bracketed  pairs 
in  the  table,  kt  that  at  temperature  /  and  a  is  a  constant. 


'C 

'C 

Substance. 

t 

*, 

a 

o 

Substance. 

* 

kt 

o 

Ji 

"3 

p 

Aluminum    .     .  < 

18 

0.480  I 

.OOO3O 

2 

Carborundum  .     .     . 
Slate            .          .     . 

- 

00050 
.0036 

I 

( 
Antimony     .     .  • 

0 
IOO 

.0442  i 

.0396  J 

—  .001041 

, 

Soil  dry  
"      wet       .     .     . 

- 

.00033 
.0016 

II 
II 

Bismuth  .     .     .  • 

18 

IOO 

.0194  ) 

.0161  ) 

—  .OO2I 

2 

Diatomic  earth    ;     . 
Fire-brick    .... 

_ 

.00013 
.00028 

12 

12 

Brass  (yellow)  .  • 

0 
100 

.2041  J 
.2540  J 

.002445 

I 

Granite  .     .    j  from 

( 

_ 

.00510 
.00550 

i6 

«     (red)  .     .  | 
Cadmium      .     .  < 

o 

IOO 

18 

IOO 

.2460  ( 

.2827  ( 

.222 
.215  J 

.001492 
—  .00038 

I 

2 

Lime                •     •     • 

- 

.00029 
.00016 
.00045 

12 

Magnesia    .    |  ^ 
MarbleSjlime-  f 

Constantin    .     .  j 
6oCu+4oNi  .  I 

Copper    .... 

18 

IOO 

18 

IOO 

.5402  1 
.6405  J 
.9l8( 
.908  j 

.00227 
—  .00013 

2 
2 

stone,    cal-jf 
cite,     com--{ 
pact     dolo- 
mite .     .     . 

— 

.00470 
.00560 

}« 

German  silver  .  | 

0 
IOO 

.0700  ) 
.0887  ( 

.002670 

I 

Micaceous  flagstone  : 
along  cleavage  .     . 

_ 

.00632 

6 

Iron  (cast)    .    .  < 

18 

IOO 

.108  i 
.108  f 

—  .0001 

2 

across  cleavage     . 

: 

.00441 

6 

8 

"   (wrought)    | 

18 

IOO 

.144  ) 
.142  j 

—  .0001 

2 

Paraffine   .    .     .    .< 

o 

IOO 

.00021 
.00168 

9 
9 

Lead    ....  | 

18 

IOO 

.083 
.076  f 

—  .0001 

2 

Pasteboard.     .     .     . 
Plaster  of  Paris  .     . 

_ 

.00045 
.00070 

J 

|  Mercury  .     .     .  < 

o 

.0148  i 

•0055 

4 

"       "     "  powder 
Quartz         .... 

— 

.0026 

ii 

12 

( 

\  Magnesium  .     . 
j  Manganin 

i2Mn    .     .     .) 

0-100 

18 

ICO 

.3760 

.5186) 
.6310  j 

+.0026 

2 

Sand  (white  dry)  .     . 
Sandstone  and  (  ,M 
hardgriJfrt°om 

(dry).     .     .(    ' 

- 

.00093 

•00545 
.00565 

6 

H 

!  Nickel      .     .     . 

18 

1420 

_ 

2 

Sawdust  

_ 

.00012 

8 

Palladium     .     . 

18 

.  1  C^4.\J 

.1683 

_ 

2 

Serpentine       (Corn- 

Platinum .     .     .  j 

18 

IOO 

.1664  ) 

•J733) 

+.00051 

2 

wall  red)       .     .     . 
Slate: 

— 

.00441 

6 

Steel  (hard)  .     . 

- 

"75620 

- 

5 

along  cleav-    from 

- 

.00550 

u 

«'     (soft)    .    . 

— 

,  .1110 

— 

5 

age  ...       to 

— 

.00650 

I- 

|  Silver  .     .     .    .  | 

18 

IOO 

1.006) 
.992  J 

—  .00017 

2 

across  cleav-    from 
age  .     .     .      to 

- 

.00315 
.00360 

H 

|  Tin  ] 

0 
IOO 

.1528  ) 

.1423  f 

—.000687 

I 

Snow,  compact  layers 
Strawboard      .     .     . 

_ 

.00051 
.00033 

Wood's  alloy    . 

_ 

.0319 

_ 

4 

Vulcanite    .     .     '     . 

— 

.00087 

10 

Zinc     .    .    .    .  j 

18 

IOO 

.2619  ) 

—  .00016 

2 

Vulcanized      j  from 
rubber  (soft)  j    to 

: 

.00034 
.00054 

6 
6 

i  Concrete  (cinder) 

- 

.00081 

- 

- 

Wax  (bees)      .     .     . 

- 

,00009 

8 

(stone) 

— 

.0022 

— 

3 

Wood,  fir  : 

parallel  to  axis  .     . 

- 

.00030 

8 

perpendicular      to 

axis  .    •     .    .     . 

— 

.00009 

8 

I  Lorenz.          4  H.  F.  Weber.          6  H.  L.  &  D.f          8  G.  Forbes.          10  Stefan. 

2  J-\-D*.         5  Kohlrausch.             7  Hjeltstrom.           9  R.Weber.           n  Lees-Chorlton. 

3  Norton.                                                                                                               12  Hutton-Blard. 

*  Jaeger  and  Diesselhorst. 
SMITHSONIAN  TABLES. 


t  Herschel,  Labour,  and  Dunn  (British  Association  Committee). 


206  TABLE  224. 

THERMAL  CONDUCTIVITIES  AT  HIGH  TEMPERATURES. 


Material. 

Authority. 

Temperature 
Centigrade 

Thermal  Conductivity 
Calories  per  sec.  per 

Degrees. 

deg.  C.  per  cm.  cube. 

Nickel 

Angell  i 

300 

.126 

400 

.117 

600 

.088 

700 

.069 

800 

.068 

IOOO 

.064 

1200 

.058 

Aluminum 

Angell1 

100 

•49 

2OO 

•IS 

300 

.64 

400 

.76 

600 

I.OI 

Iron 

Hering 

100-727 

.202 

100-912 

.184 

100-1245 

.191 

Copper 

Hering 

loo-  197 

1.043 

100-268 

.969 

IOO-37O 

•93  i 

TOO  -  541 

.902 

100-837 

.858 

Graphite 

Hering 

loo-  390 

.338 

(Artificial) 

100-546 

•324 

100-720 

•306 

100-914 

.291 

Hansen  * 

30  -  2830 

.162 

2800  -  3200 

.002 

maximum,      minimum. 

90-  no 

•55            -45 

1  80-  22O 

•44              -34 

350-450 

•35             -26 

5OO  -  7OO 

.31                   .22 

Amorphous 

Hansen  2 

37  -  163 

.028                .003 

Carbon 

170-330 

.027                .004 

240-523 

.020                .003 

283  ~  597 

.OI  I                 .OO4 

Hering 

100-360 

.089 

100-751 

.124 

100  -  842 

.129 

Graphite  brick 

Wologdine 

300  -  700 

.024 

Carborundum  brick 

150-  12OO 

.0032  to  .027 

Magnesia  brick 

50-1130 

.0027  to  .0072 

Gas  retort  brick 

ioo-  1125 

.0038 

Building  and  terra 

cotta 

15-  iioo 

.0018  to  .0038 

Silica  brick 

IOO-  IOOO 

.002    to  .0033 

Stoneware  mixtures 

« 

70-  1000 

.0029  to  .0053 

Porcelain  (Sevres) 

« 

165-1055 

.0039  to  .0047 

Fire  clay  brick 
Limestone 

« 
Poole  » 

125-  I22O 
40 

.0032  to  .0054 
.0046  to  .0057 

IOO 

.0039  to  .0049 

35° 

.0032  to  .0035 

Granite 

Poole* 

IOO 

.0045  to  .0050 

200 

.0043  to  .0097 

500 

.0040 

Angell,  Phys.  Rev.  33,  p.  421,  1911;  Clement,  Egy,  Eng.  Exp.  Univers.  of 
111.,  Bui.  36,  1909;  Dewey,  Progressive  Age,  27,  p.  772,  1909  ;  Hering,  Trans. 
Am.  Inst.  Elect.  Eng.  1910;  Poole,  Phil.  Mag.  24,  p.  45,  1912;  Wologdine, 
Bull.  Soc.  Encouragement,  in,  p.  879,  1909  ;  Electroch.  and  Met.  Ind.  7,  pp. 

383,  433,  1909;  Woolson,  Eng.  News,  58,  p.  166,  1907  ;  heat  transmission 
by  concretes.    Actual  values  not  given;  Hansen,  Trans.  Amer.  Electrochem. 

Soc.  16,  p.  329,  1909;  Richards,  Met.  and  Chem.  Eng.  n,  p.  575,  1913. 

1  Taken  from  Angell's  curves. 

2  Values  calculated  from  results  expressed  in  other  units.     The  max.  and  min,  do  not  relate  to 
variability  in  material,  but  to  possible  errors  in  the  method. 

3  Taken  from  Poole's  curves. 

SMITHSONIAN   TABLES. 


TABLES  225-228.  207 

CONDUCTIVITY  FOR  HEAT. 

TABLE  225.  -Various  Substances.  TABLE  226.  — Water  and  Salt  Solution!. 


Au- 

Substance. 

kt 

thor- 

o 

ity. 

Asbestos  paper     . 
Blotting  paper  .    . 
Carbon    .... 

0 

.00043 

.00015 
.000405 

5 

5 

i 

Portland  cement  . 

- 

.00071 

5 

Cork   .     . 

o 

OOO7I7 

Cotton  wool     .     . 
Cotton  pressed 

o 

.000043 
.000033 

I 

Chalk.     .     .     . 

-~ 

OO2OOO 

2 

Ebonite   . 

49 

.OOO37O 

2 

Felt     

o 

000087 

j 

Flannel  (dry)    .     . 

0 

.00012 

I 

(  from 

__  , 

.0011        ) 

s  (to     ... 

_ 

.0023        \ 

3 

OOOO87 

- 

Haircloth     .    .     . 

_ 

.000042 

i 

Xce      ...'.{ 

— 

.00223 
.00568 

i 

4 

Leather,  cow-hide 

- 

.00042 

5 

"         chamois  . 

- 

.00015 

5 

Linen            . 

OOO2  I 

Silk     

.OOOOQS 

c 

Caen  stone  (build-( 
ing  limestone)    \ 

- 

•00433 

2 

C  ale's  sandstone  / 
(freestone)     .     J 

- 

.00211 

2 

i  G.  Forbes.            4  Neumann. 

2  H.,  L.,  &  D.*       5  Lees-Chorlton. 

3  Various. 

Substance. 

Density. 

t 

0 

kt 

Au- 
thor- 
ity. 

Water     .     . 
« 

1.160 
1.026 

1.054 

1.  100 

1.180 

1:136 

0 

9-15 

4 
18 

44 

10-18 
20.5 
20.5 

21 

4-5 

4-5 

.002 
.00120 
.00136 
.OOI29 
.00157 
.00124 

.OOIlS 
.00116 
.00267 
.OOI26 
.00128 
.00130 
.OOIlS 
.OOII5 

I 
2 
2 
3 

4 
5 

2 

i 

5 
5 
5 

2 
2 

Solutions  in 
water. 

CuS04 
KC1    . 
NaCl  . 
H2S04 

ZnSO4          ! 

i  Bottomley.                4  Graetz. 
2  II.  F.  Weber.           5  Chree. 
3  Wachsmuth.             o  Winkelmann. 

TABLE  227.  -  Organic  Liquids. 


TABLE  228.  -  Gases. 


Substance. 

t 

o 

kt 

Xiooo 

a 

o 

"3 

Acetic  acid  .    .    . 
Alcohols  :  amyl    . 
ethyl    . 
methyl 
Benzole    .... 
Carbon  disulphide 
Chloroform  .     .     . 
Ether       .... 

9-15 

5 

9-i5 
9-i5 

13 
13 

.472 
.328 
423 

495 
•333 
•343 

•303 
•637 
•395 
425 
•355 
•325 
44 

0.12 

O.OII 
0.0067 

2 

3 
3 

2 
2 
4 

Glycerine     .     .    . 
Oils  :  olive   .     .     . 
castor      .     . 
petroleum    . 
turpentine   . 
Vaseline  .... 

I  H.  F.  Weber.          3  Wachsmuth. 
2  Graetz.                     4  Lees. 

Substance. 

t 

o 

kt 

Xioooo 

a 

1 

Air    

o 

.t;68 

OOIQO 

I 

Argon    .... 

O 

.389 

.OO26O 

2 

Ammonia  .     .    . 
Carbon  monoxide 

0 
0 

.458 
499 

.00548 

I 

I 

"      dioxide    . 

0 

•307 

- 

I 

Ethylene     .     .     . 
Helium  .... 
Hydrogen  .     .     . 
Methane     .    .    . 

o 
o 

0 

7-8 

•395 
3-39 
3.27 
.647 

.00445 
.00318 
.00175 

I 

2 

I 
I 

Nitrogen     .     .    . 
Nitrous  oxide      . 

7-8 
7-8 

•524 

.00446 

I 
I 

Oxygen  .... 

7-8 

•563 

— 

I 

i  Winkelmann. 

2  Schwarze. 

*  Herschel,  Lebour,  and  Dunn  (British  Association  Committee). 


SMITHSONIAN  TABLES. 


208 


TABLE  229. 
DIFFUSIVITIES. 


The  diffusivity  of  a  substance  =  h2  =  k/cp,  where  k  is  the  conductivity  for  heat,  c  the  spe- 
cific heat  and  p  the  density.   (Kelvin.)  The  values  are  mostly  for  room  temperatures,  about  i8°C. 


Material. 

DifEusivity. 

Material. 

Diffusivity. 

0826 

Coal              .     .     . 

O  OO'7 

.I7O 

OO72 

.0678 

"          (stone)            .          .     . 

0058 

"          (light  slag)     .... 

.OO6 

Cadmium     

4O7 

.OOI7 

Copper   

1.  1  7-3 

Ebonite  .     .          .         . 

OOIO 

Gold                                         .     . 

I  182 

Glass  (ordinary)            ... 

OO57 

Iron  (wrought,  also  mild  steel) 

O.I  71 

•w<~'j/ 
•OI  ^ 

Iron  (cast,  also  i%  carbqn  steel) 

.121 

Ice      

.OI  12 

Lead 

277 

Limestone                                 . 

OOQ'' 

§3 

Marble  (white)     

.OOQO 

Mercury  

.O727 

Paraffin  ...               . 

.00098 

Nickel     

.1  52 

Rock  material  (earth  aver.)  . 

.0118 

.240 

"            "       (crustal  rocks)    . 

.0064 

Platinum      

.24.7 

Sandstone        ....          . 

.OI  7.7 

Silver                ...              .    . 

I  77.7 

Snow  (fresh) 

OO77. 

Tin      

0.407 

Soil  (clay  or  sand,  slightly  damp) 

.00  c 

Zinc    

.402 

Soil  (very  dry)      . 

OO7I 

Air      

.I7Q 

Water 

OOI4 

,OO7t; 

Wood  (pine,  cross  grain) 

OOO68 

Brick  (average  fire) 

OO74 

"       (    "     with       "    ) 

OO'''? 

"     (     "       building)    .    .    . 

.OO5O 

Taken  from  "An  Introduction  to  the  Mathematical  Theory  of  Heat  Conduction,"  Ingersoll  and  Zobel,  1913. 
SMITHSONIAN  TABLES. 


TABLE  230. 
HEAT   OF  COMBUSTION. 

Heat  of  combustion  of  some  common  organic  compounds. 
Products  of  combustion,  CO2  or  SO2  and  water,  which  is  assumed  to  be  in  a  state  of  vapor. 


209 


Substance. 

Small  calories 
per  gram 
of  substance. 

Authority. 

11027 

Thomsen.    3 

Alcohols  :  Amyl 

V  O 
89S8 

Favre  and  Silbermann. 

Ethyl          ... 

7183 

«       «             « 

Methyl       . 

5307 
QQ77 

«              U                           tt 

Stohmann,  Kleber,  and  Langbein. 

Coals  :  Bituminous     .        . 

yy/  1 

7400-8500 

Various. 

Anthracite 

7800 

Average  of  various. 

Lignite  .... 

6900 

<«         «       « 

Coke      .        .        .~~    . 

7000 

«         «       « 

Carbon  disulphide 

3244 

Berthelot. 

Dynamite,  75%  .... 

I20X) 

Roux  and  Sarran. 

Gas  :  Coal  gas   .... 

580O-IIOOO 

Mahler. 

Illuminating 

5200-5500 

Various. 

Methane    .... 

13063 

Favre  and  Silbermann. 

Naphthalene     . 

9618-9793 

Various. 

Gunpowder         .        .        .        . 

720-750 

« 

Oils:  Lard          .... 

9200-940O 

H 

Olive         .... 

9328-9442 

Stohmann. 

Petroleum,  Am.  crude 

II094 

Mahler. 

"             "     refined    . 

1  1045 

<r 

Russian  . 

I0800 

« 

Woods  :  Beech  with  12.9  %  H2O 

4168 

Gottlieb. 

Birch    "     11.83      " 

4207 

« 

Oak      "     13.3 

3990 

«« 

Pine      "     12.17      " 

4422 

« 

SMITHSONIAN  TABLES. 


2io  TABLE  231. 

HEAT  VALUES  AND  ANALYSES  OF  VARIOUS  TYPES  OF  FUEL. 

(a)  Coals. 


Coal. 

e 

0 

3$ 

•i* 

•88 

.£"£ 

4 

B 

a 

| 

1 

c 

1 

it 

jjj 

>2 

^cj 

O) 

>> 

X 

0 

* 

O 

$i 

rfi 

T  :„„;*-  f  Low  grade  .    . 
L'Snlte  }  High  grade  .     . 

38.81 

25.48 
27.44 

27.29 

29.62 

8.42 
9-56 

•97 
.94 

7.09 
6.77 

37-45 

•50 
.67 

45-57 
40-75 

3526 

3994 

6347 
7189 

Sub-bitu-  (  Low  grade    . 
minous  (  High  grade  . 

22.71 

15-54 

34.78 
33-03 

36.60 

46.06 

5-37 

'.58 

6.14 

5.89 

52.54 
60.08 

1.03 
1.05 

34-09 
27.03 

9207 

10557 

Bituminous  {  H^gmde 

11.44 
3-42 

33-93 
34.36 

43-92 

58.83 

10.71 
3-39 

4-94 
.58 

5-39 

60.06 
77.98 

1.  02 

1.29 

17.88 

7852 

10958 
14134 

Semi-bitu-  (  Low  grade  . 
minous    (  High  grade  . 
Semi-anthracite.     .    .     . 

2.07 

14-5 
14-57 
9.81 

75-5 
78.20 
78.82 

7-3 
3-97 
9-30 

•99 
•54 
1.74 

4.76 
3.62 

80.65 
84.62 
80.28 

1.82 

1.  02 

1.47 

5-09 
3-59 

7845 
8166 
7612 

14121 
14699 
13702 

Anthradte|^JhSgrraaddee' 

2.76 

3-33 

2.48 
3-27 

82.07 
84.28 

12.69 
9.12 

•54 
.60 

79.22 
8i.35 

.68 
•79 

4.64 
5.06 

6987 
7417 

12577 
13351 

(D)  Peats  (air  dried). 


From 

Vol. 
Hydro- 
Carbon. 

Fixed 
Carbon. 

Ash. 

Sul- 
phur. 

Hydro- 
gen. 

Carbon. 

Nitro- 
gen. 

Oxygen. 

Calories 
per 
gram. 

B.T.U.'s 

per 
pound. 

Franklin  Co.,  N.  Y. 
Sawyer  Co.,  Wis. 

67.10 
56.54 

28.99 
27.92 

3-91 
15-54 

-'5 
.29 

5-93 

4.71 

57-17 
51.00 

1.48 
1.92 

3I-36 
26.54 

5726 
4867 

10307 
876l 

(c)  Liquid  Fuels. 


Fuel. 

Specific  Gravity 
at  15°  C 

Calories  per  gram. 

British  Thermal  Units 
per  pound. 

.684-.6Q4 

I22IO-I222O 

21078—21006 

.7IO-  77O 

11100-11400 

IQo8o-2OS2O 

Kerosene     

7QO—  8OO 

I  IOOO—  I  I2OO 

19800—20160 

Fuel  oils,  heavy  petroleum  or 
refinery  residue 

060—  O7O 

I  O2OO—  I  O  ^OO 

18360-18900 

Alcohol,   fuel    or  denatured 
with  7-9  per  cent  water  and 
denaturing  material  .     .    . 

.8I96-.8202 

6440-6470 

11592-11646 

Table  compiled  by  U.  S.  Geological  Survey. 


SMITHSONIAN  TABLES. 


TABLE  232. 

CHEMICAL  AND  PHYSICAL  PROPERTIES  OF  FIVE   DIFFERENT 
CLASSES   OF    EXPLOSIVES. 


211 


Explosive. 

Specific  gravity. 

Number  of  large  calories  developed  j 
by  i  kilogram  of  the  explosive. 

j! 

"O  C 

8,2 

o  « 

1 

Unit  disruptive  charge  by  ballistic  1 
pendulum. 

Rate  of  detonation. 
Cartridges  ij  in.  diam. 

1 

8 

ii 
it 

1 

Q 

Length  of  flame  from  100  grams. 

Cartridge  ij  in.  transmitted  explo-  1 
sion  at  a  distance  of 

Products  of  combustion  from  200  1 
grams;  gaseous,  solid,  and  liquid,  j 
respectively. 

a, 

L 

<c'I 

C   * 

11 

3% 
P 
1 

•J* 

O 

h 

11 

5° 

1 

I 

O 

1 

O 

(A)  Forty-per-centnitro- 
glycerin  dynamite 

(B)  FFF  black  blasting 
powder 

(C)  Permissible     explo- 
sive; nitroglycerin 
class 

(D)  Permissible     explo- 
sive ;    ammonium 
nitrate  class 

(E)  Permissible     explo- 
sive; hydrated  class 

1.22 
1.25 
I.IO 

0.97 

I22I.4 

789.4 
760.5 
992.8 
6lO.6 

8235 
4817 
5912 
7300 
6597 

227* 

374t 
458* 

301* 
279* 
434* 

4688 
469.41 
3008 

3438§ 
2479 

•358 

925- 
.471 

.483 
.338 

24.63 
54.32 
27.79 
25.68 
17.49 

12 

4 
3 

88.4 
79-7 
14.5 

1544 
126.9 

4.III 

103.9 
65.1 
154 

89.8 
27.5 
75-5 

86.1 
56.0 
33-0 

25 
25 
IOOO 

800 

Over 

IOOO 

Chemical  Analyses. 

(A)  Moisture    

0.91 
39.68 
42.46 
13.58 
3-37 

0.80 
70.57 

17-74 
10.89 

7.89 
24.02 
36.25 

9.2O 
2I.3I 
0.97 
0.36 

(D)] 

] 
] 

i 

(E)  J 

J 

i 
< 
< 

j 

] 

Moisture 
A.mmon] 
Sulphur 
Starch   . 
Wood  pi 
Doisonot 
Vlanganc 

0.23 
83.10 
0.46 
2.61 

1.89 
2.54 
2.64 
6.53 

9.94 

1.75 

11.98 

19.65 

um  nitrate 

Sodium  nitrate  

Wood  pulp     

ilp     . 
is  ma 
se  pe 

(B)  Moisture     

tter   

roxide 

Sodium  nitrate   

Moisture 
Vitroglyc 

(C)  Moisture    

-prin 

\mmonium  nitrate 
>and 

Sodium  nitrate    
Wood  pulp  and  crude  fibre  from 
grams      

3oal  ..... 

:iay  

\mmonium  sulphate 
Sine  sulphate  (7HO) 
^otassium  sulphate 

Starch    

Calcium  carbonate  

*  One  pound  of  clay  tamping  used.  t  Two  pounds  of  clay  tamping  used.  $  Rate  of  burning. 

§  Cartridges  if  in.  diam.  ||  For  300  grammes. 

Compiled  from  U.  S.  Geological  Survey  Results,  —  "  Investigation  of  Explosives  for  use  in  Coal  Mines,  1909." 
SMITHSONIAN  TABLES. 


212 


TABLE  233. 


HEAT   OF 


Heat  of  combination  of  elements  and  compounds  expressed  in  units,  such  that  when  unit  mass  of  the  substance  is 

units,  which  will  be  raised  in  temperature 


Substance. 

Combined 
with  oxygen 
forms  — 

Heat 
units. 

Combined 
with  chlorine 
forms  — 

Heat 
units. 

Combined 
with  sulphur 
forms  — 

Heat 
units. 

o 

J3 
=  £> 
<* 

Calcium     .... 

CaO 

3284 

CaCl2 

4255 

CaS 

2300 

I 

Carbon  —  Diamond  . 

C02 

7859 

— 

— 

— 

2 

«                   « 

CO 

2I4I 

— 

- 

— 

— 

3 

"      —Graphite  . 

CO2 

7796 

- 

- 

- 

- 

3 

Chlorine    .... 

C120 

—  254 

— 

— 

— 

- 

i 

Copper      .... 

Cu2O 

321 

CuCl 

tpO 

- 

- 

i 

"           .... 

CuO 

585 

CuCl8 

8l9 

CuS 

I58 

i 

« 

" 

593 

- 

— 

4 

Hydrogen* 

H2O 

34J54 

HC1 

22000 

H2S 

2250 

3 

« 

" 

34800 

— 

— 

— 

— 

5 

« 

(i 

34417 

— 

— 

— 

— 

6 

Iron  

FeO 

J353 

FeCl2 

1464 

FeSH2O 

428 

3 

«i 

_ 

FeCl8 

1714 

— 

— 

3 

Iodine       .        . 

I206 

177 

_ 

— 

— 

Lead          .... 

PbO 

243 

PbCl2 

400 

PbS 

98 

Magnesium       .        . 
Manganese 

MgO 
MnOH2O 

6077 
1721 

MgCl2 
MnCl2 

6291 
2O42 

MgS 
MnSH2O2 

3T9i 
841 

Mercury    .... 

Hg20 

105 

HgCl 

206 

- 

- 

H 

HgO 

«53 

HgCl2 

310 

HgS 

84 

Nitrogen* 

N2O 

-654 

- 

"          .... 

NO 

-1541 

— 

— 

— 

— 

H 

NO2 

—  143 

— 

- 

— 

- 

Phosphorus  (red) 

P205 

5272 

- 

- 

- 

- 

(yellow) 

« 

5747 

- 

- 

- 

- 

7 

«                   « 

" 

5964 

— 

— 

— 

— 

i 

Potassium 

K2O 

1745 

KC1 

2705 

K2S 

1312 

8 

Silver         .... 

AgjO 

27 

AgCl 

271 

Ag2S 

24 

i 

Sodium      .... 

Na2O 

3293 

NaCl 

4243 

Na2S 

1900 

8 

Sulphur     .... 

S02 

2241 

- 

- 

- 

i 

« 

(i 

2165 

— 

— 

— 

— 

2 

Tin    .        '.        '.        '.         '. 

SnO 

573 

SnCl2 

690 

- 

- 

4 

"..... 

_ 

SnCl4 

1089 

_ 

_ 

7 

Zinc  

ZnO 

1185 

_  • 

_ 

_ 

_ 

4 



I3H 

ZnCl2 

1495 

— 

— 

i 

Substance. 

Combined 
withS  +  O4 
to  form  — 

Heat 
units. 

Combined 
with  N  -f  O, 
to  form  — 

Heat 
units. 

Combined 
withC  +  O, 
to  form  — 

Heat 

units. 

o 

JS     . 

ti  >» 
<•* 

Calcium     .... 

CaSO4 

7997 

Ca(N03)2 

5080 

CaC03 

6730 

I 

Copper      .... 

CuS04 

2887 

Cu(NO3)2 

I304 

— 

I 

Hydrogen 
Iron  

H2S04 
FeSO4 

96450 
4208 

HNO3 

Fe(NO3)2 

41500 
2134 

— 

: 

I 
I 

Lead          .        . 
Magnesium 

PbS04 
MgS04 

1047 
12596 

Pb(N08)a 

512 

PbCO3 

814 

I 

I 

Mercury    .... 

_ 

_ 

_ 

_ 

_ 

I 

Potassium 

K2S04 

4416 

KN03 

TJO6l 

K2C03 

3583 

I 

Silver         .... 
Sodium      .... 

Ag2S04 
Na2SO4 

776 
7119 

AgN03 
NaNO3 

266 

4834 

AgssCOs 
Na2CO3 

561 
5841 

I 
I 

Zinc  

ZnSO4 

3538 

— 

~ 

" 

I 

AUTHORITIES. 

i  Thomsen.        3  Favre  and  Silbermann.     5  Hess.                                          7  Andrews. 

2  Berthelot.       4  Joule.                                 6  Average  of  seven  different.      8  Woods. 

SMITHSONIAN  TABLES. 


Combustion  at  constant  pressure. 


TABLE  233  (continued). 


213 


COMBINATION. 


caused  to  combine  with  oxygen  or  the  negative  radical,  the  numbers  indicate  the  amount  of  water,  in  the  same 
from  o°  to  i°  C.  by  the  addition  of  that  heat. 


In  dilute  solutions. 

| 

Substance. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

-.£ 

<,•" 

Calcium 

CaOH2O 

3734 

CaCl2H20 

4690 

CaS  +  H20 

2457 

i 

Carbon  —  Diamond  . 

— 

— 

_ 

2 

«                  « 

_ 

_ 

_ 

— 

— 

_ 

3 

"      —Graphite   . 

- 

- 

- 

- 

- 

- 

3 

Chlorine     . 

— 

— 

— 

— 

— 

— 

i 

Copper 

• 

- 

- 

- 

- 

- 

i 

"            ... 

— 

— 

— 

— 

— 

— 

i 

« 

_ 

_ 

_ 

_ 

_ 

_ 

4 

Hydrogen  . 

- 

- 

- 

- 

- 

- 

3 

« 
•        •        *. 

: 

: 

_ 

_ 

_ 

_ 

I 

Iron  .... 

FeO+H20 

1  2  2O* 

FeCl2+H2O 

1785 

- 

- 

3 

« 

— 

— 

FeCl3 

2280 

— 

— 

3 

Iodine 

_ 

— 

_ 

— 

_ 

— 

Lead. 

_ 

_ 

PbCl2 

368 

_ 

_ 

Magnesium 
Manganese 

Mg02H2 

9°5°t 

MgCl2 
MnCl2 

7779 
2327 

MgS 

4784 

Mercury     . 

— 

— 

— 

— 

— 

« 

— 

— 

HgCl2 

299 

— 

— 

Nitrogen   . 

~ 

_ 

_ 

_ 

_ 

Phosphorus  (red) 

_ 

_ 

_ 

—  • 

— 

_ 

«'             (yellow)  . 

— 

— 

— 

— 

— 

— 

7 

«                  « 

— 

— 

_ 

_ 

_ 

— 

i 

Potassium  . 

K2O 

2  1  10* 

KC1 

2592 

K2S 

1451 

8 

Silver 

— 

— 

— 

— 

i 

Sodium 

Na20 

3375 

NaCl 

4190 

Na2S 

2200 

8 

Sulphur 

- 

- 

- 

- 

i 

"            ... 

_ 

_ 

_ 

_ 

_ 

_ 

2 

Tin    . 

- 

- 

SnCl2 

691 

- 

- 

7 

• 

— 

— 

SnCl4 

1344 

_ 

— 

7 

Zinc  .... 

_ 

_ 

_ 

_ 

_ 

4 

. 

~ 

— 

ZnCl2 

1735 

~ 

— 

i 

In  dilute  solutions. 

i 

Substance. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

Forms  — 

Heat 
units. 

D£ 

<!"" 

Calcium 

_ 

- 

Ca(N08)2 

5J75 

_ 

_ 

Copper 
Hydrogen  . 
Iron  .... 

CuSO4 
H2S04 
FeSO4 

3150 
105300 
42IO 

Cu(N08)2 
HNO. 

Fe(N08)3 

1310 
24550 
2134 

- 

- 

Lead. 

_ 

— 

Pb(N03)2 

475 

— 

— 

Magnesium 
Mercury     . 

MgS04 

13420 

Mg(N08)2 
Hg(N08)2 

8595 

_ 

_ 

Potassium  . 

K2SO4 

4324 

KN08 

2860 

— 

— 

Silver 
Sodium      . 

Ag2S04 
Na2SO4 

753 
7160 

AgN08 
NaN08 

216 
4620 

Na2CO8 

5995 

Zinc   .... 

ZnSO4 

3820 

Zn(N08)2 

2035 

~ 

AUTHORITIES. 

i  Thomsen.        3  Favre  and  Silbermann.      5  Hess.                                        7  Andrews. 

2  Berthelot.        4  Joule.                                 6  Average  of  seven  different.    8  Woods. 

Thomsen. 


f  Total  heat  from  elements. 


SMITHSONIAN  TABLES. 


214 


TABLE  234. 
LATENT    HEAT   OF   VAPORIZATION, 


The  temperature  of  vaporization  in  degrees  Centigrade  is  indicated  by  T ;  the  latent  heat  in  large  calories  per  kilo- 
gram or  in  small  calories  or  therms  per  gram  by  H;  the  total  heat  fromo0  C,  in  the  same  units  by  H' ,  The  pressure 
is  that  due  to  the  vapor  at  the  temperature  T. 


Substance. 

Formula. 

T 

H 

H' 

Authority. 

Acetic  acid  .... 

C2H402 

118° 

84.9 

- 

Ogier. 

Air       

- 

'    - 

5°-97 

- 

Fenner-Richtmyer. 

Alcohol:  Amyl    . 

C5H120 

131 

120 

- 

Schall. 

Ethyl   . 

M 

C2H6O 

78.1 

0 

205 
236 

255 
236 

Wirtz. 
Regnault. 

"... 

" 

5° 

— 

264 

" 

"... 

" 

IOO 

- 

267 

M 

"... 

" 

150 

- 

285 

U 

Methyl  . 

CH40 

64.5 

2.67 

307 

Wirtz. 

"... 

" 

0 

289 

289 

Ramsay  and  Young. 

"     . 

" 

5° 

— 

274 

u                                « 

"              . 

" 

IOO 

_ 

246 

<t                             u 

"... 

" 

150 

- 

206 

"                     " 

" 

" 

200 

_ 

T52 

«                                       M 

"              . 

" 

238.5 

- 

44.2 

"                                      " 

Ammonia     .... 

NH3 

7.8 

294.2 

_ 

Regnault. 

.... 

" 

II 

291.3 

— 

M 

. 

H 

16 

297.4 

— 

M 

. 

" 

i7 

296.5 

- 

" 

Benzene        .... 

C6H6 

80.  i 

92.9 

127.9 

Wirtz. 

Bromine        .... 

Br 

61 

45-6 

- 

Andrews. 

Carbon  dioxide,  solid  . 

C02 

_ 

_ 

138-7 

Favre. 

liquid 

" 

—25 

72.23 

Cailletet  and  Mathias. 

u                «                 « 

" 

0 

5748 

_ 

«                   <«                   M 

«                 «                  (1 

" 

12.35 

44-97 

- 

Mathias. 

t(                tt                 a 

•t 

22.04 

31.8 

— 

« 

"      .           . 

" 

29.85 

14.4 

- 

" 

"      • 

H 

30.82 

3-72 

- 

" 

"       disulphide 

CS2 

46.1 

83.8 

94-8 

Wirtz. 

<(                    u 

" 

0 

90 

90 

Regnault. 

« 

it 

IOO 

— 

100.5 

* 

• 

" 

140 

- 

102.4 

H 

Chloroform  .... 

CHC13 

60.9 

58.5 

72.8 

Wirtz. 

Ether    

C4H100 

34.5 

88.4 

r\r\  £ 

107 

« 

it 

" 

0 

rr\ 

9°-5 
94 

94 

Regnault. 

M 

N 

u 

5° 

115.1 

I 

^>  ">  rv  r* 

140 

23-95 

~ 

Favre  and  Silbermann. 

Mercury        .... 

Hg 

357 

65 

- 

Mean. 

Nitrogen      .... 

N 

—195.6 

47.65 

- 

Alt. 

Oxygen         .... 

O 

—182.9 

5°-97 

- 

« 

Sulphur  dioxide   . 

SO2 

0 

91.2 

_ 

Cailletet  and  Mathias. 

.        •        . 

" 

30 

80.5 

— 

«         «         <« 

. 

" 

65 

68.4 

- 

«         «         « 

Turpentine  .... 

Ci0H10 

1593 

74.04 

- 

Brix. 

Water  . 

Tj     ~ 

A 

1L%\J 

IOO 

535-9 

~ 

Andrews. 

** 

ffl 

TOO 

f\tt 

"D                   It 

L\J\J 

037 

ixegnauii. 

OMITHSONIAN    TABLES. 


TABLE  234  (continued^. 


215 


LATENT   HEAT  OF   VAPORIZATION.' 


Substance,  formula,  and 
temperature. 


1=  total  heat  from  fluid  at  o°  to  vapor  at  t°. 
r= latent  heat  at/0. 


Authority. 


Acetone, 
C3H60, 


Benzol, 
C6H6, 
7°  to  215°. 


Carbon  dioxide, 
CO2, 

—  25°  to  31°. 

Carbon  disulphide, 
CS2, 

—  6°  to  143°. 

Carbon  tetrachloride, 

ecu, 

I  8°  to  163°. 


Chloroform, 

CHC18, 
-5°  to  159°. 


Nitrogen,  N. 


Nitrous  oxide, 
N20, 

20°  tO  36°. 


Oxygen,  O. 


Sulphur  dioxide, 

SO2, 
o°  to  60°. 


Water,  H2O. 


/  =  140.5  -f  0.36644 1  —  0.000516  tz 
1=  139.9  -j-  0.23356  /  -f-  0.00055358  t2 
r=  139.9  —  0.27287  t  -j-  0.0001571 t2 


1=  109.0  +  0.24429 1 — 0.000131 5  fl 


118.485  (31  — t)  — 0.4707  (31  — f2) 


1  =  90.0  +  o.i 460 1 1  —  0.000412/2 

/  =  89.5  -f  0.16993  /  —  0.0010161  /2  +  0.000003424  fl 

r  =  89.5  —  0.06530  /  —  0.0010976  f2  -j-  0.000003424  t* 


/=  52.0  +  0.14625 1  —  0.000172/2 

/=  51.9  +  0.17867  /  —  0.0009599  fl  +  0.000003733  /" 

r  =  51.9  —  0.01931  /  —  0.0010505  f2  +  0.000003733  fl 


7=67.0  +  0.1375  t 

i= 67.0 + 0.14716 1 — 0.0000937  & 

r  =  67.0  —  0.08519  /  —  0.0001444  f2 


r  =68.85  — 0.2736  T 


r2=  131.75  (36.4  —  ^  —  0.928  (36.4  — 


r  =  60.67  —  0.2080  T 


r  =  91 .87  —  0.3842  /  —  0.000340  fl 


r=  94.210  (365  —  0  °'81249,  30°  —  100° 

r=  538.46  —  0.6422  (/ —  100)  —  0.000833  (f~~  loo)2, 

ioo°-i8o° 
r=  539.66 — 0.718  (/—  100),  I20°-i8o° 


Regnault. 
Winkelmann. 


Regnault. 


Cailletet  and 
Mathias. 


Regnault. 
Winkelmann. 


Regnault. 
Winkelmann. 


Regnault. 
Winkelmann. 


Alt. 


Cailletet  and 
Mathias. 


Alt. 


Mathias. 


Henning. 


*  Quoted  from  Landolt  &  Bornstein'i  "  Phys.  Chem.  Tab." 


SMITHSONIAN  TABLES. 


2l6 


TABLE  235. 
LATENT   HEAT  OF   FUSION, 


This  table  contains  the  latent  heat  of  fusion  of  a  number  of  solid  substances  in  large  calories  per 
kilogram  or  small  calories  or  therms  per  gram.     It  has  been  compiled  principally  from  Landolt 
and  Bernstein's  tables.     C  indicates  the  composition,  T  the  temperature  Centigrade,  and 
latent  heat. 


Substance. 

C 

T 

H 

Authority. 

Alloys:  3O.5?b  +  69-sSn    . 
36.9Pb  +  63.iSn    . 
63.7  Pb-f  36.38  n    . 
77.8Pb-J-  22.2811    . 
Britannia  metal,  gSn  -f-  iPb 
Rose's  alloy, 
24Pb  +  27.3Sn  +  48.7Bi 
Wood-sa,loy|¥.8Pb+;4.;Sn| 

PbSn4 
PbSn» 
PbSn 
Pb2Sn 

Al 

183 
179 

177-5 
176.5 
236 

98,8 

75-5 
658. 

17. 
15-5 
11.0 

9-54 
28.0* 

6.85 
8.40 
76.8 

Spring. 
« 

Ledebur. 
Mazzotto. 

H 

Glaser. 

NH3 

—  7  C. 

108. 

Massol. 

Benzole       .         .         . 

C6H6 
Br 

54 

—  7«1 

30.6 
16.2 

Mean. 
Regnault. 

Bi 

268 

12.64 

Person. 

Cd 

72O.7 

1366 

« 

Calcium  chloride 
Copper        .        .        . 
Iron,  Gray  cast  .... 
"     White  "    . 
«     Slag   

CaCl2  +  6H2O 
Cu 

28.S 
1083 

40.7 
42. 

23- 

33- 

CQ. 

«( 

Mean. 

Gruner. 
i« 

«« 

I 

II.  71 

Favre  and  Silbermann. 

Ice      

H2O 

o 

70  6^ 

(  Dickinson,  Harper, 

« 

o 

70.  en 

|      Osborne.t 
Smith  .J 

"    (from  sea-water)  . 
Lead   

\  H20  +  3.535  I 
|      of  solids      j 
Pb 
Hg 

-8.7 

327 
—  39 

54-0 

5.36 
282 

Petterson. 

Mean. 
Person. 

Naphthalene       .... 
Nickel         

.eg, 

79.87 

IA  7C 

35-62 

A    OA 

Pickering. 
Pionchon 

Pd 

I  US 

^6  i 

Violle 

Phosphorus         .... 

P 
Pt 

44.2 

I7CC 

J^O 

4-97 

27  2 

Petterson. 
Violle 

K 

625 

I  c  7 

Toannis 

Potassium  nitrate       .        . 
Phenol         

KN03 
C6H6O 

333-5 

2C.-I7 

48.9 

24.  Q7 

Person. 
Petterson 

Paraffin        

52  4O 

7  c  in 

Batelli 

Silver           

Ag 
Na 

..     4<j 
96l 

97 

2I.O7 

71.7 

Person. 
Toannis. 

"       nitrate    .... 
"       phosphate 

Spermaceti          .... 
Sulphur      
Tin      
Wax  (bees)         .... 
Zinc    

NaNO3 
(  Na2HPO4  1 
\   +  I2H20  f 

S 
Sn 

Zn 

305-8 
36-1 

43-9 
"5 
232 
61.8 

4.IQ 

64-87 

66.8 
36.98 

9-37 
14.0 

42.3 

28  17 

<« 

Batelli. 
Person. 

Mean. 
« 

«< 

•w«»J 

*  Total  heat  from  o°  C. 

U.  S.  Bureau  of  Standards,  19x3,  in  terms  of  15°  calorie. 
interaadonafvoH^n  electrfical  measurements,  assuming  mechanical  equivalent  =  4.187,  and  in  terms  of  the  value  of  the 

SMITHSONIAN  TABLES.      *• 


TABLE  236. 
MELTING-POINTS  OF  THE  CHEMICAL   ELEMENTS. 


2I7 


The  metals  in  heavier  type  are  often  used  as  standards. 

The  melting-points  are  reduced  as  far  as  possible  to  a  common  temperature  scale  which  is  the 
one  used  by  the  United  States  Bureau  of  Standards  in  certifying  pyrometers.  This  scale  is  de- 
fined in  terms  of  Wien's  law  with  Cg  taken  as  14500,  and  on  which  the  melting-point  of  platinum 
is  1755°  C  (Nernst  and  Wartenburg,  1751 ;  Waidner  and  Burgess,  1753 ;  Holborn  and  Valentiner, 
1770;  see  C.  R.  148,  p.  1177,  1909).  Above  noo°C,  the  temperatures  are  expressed  to  the 
nearest  5°  C.  Temperatures  above  the  platinum  point  may  be  uncertain  by  over  50°  C. 


Element. 

Melting- 
point. 

Remarks. 

Element. 

Melting- 
point. 

Remarks. 

Aluminum 

658  -J-  I 

Most      samples 

Manganese 

1260 

Burgess-  Wallenberg 

give  657  or  less 

Mercury 

-38-7 

Antimony 

630^1 

(Burgess). 
"Kahlbaum"  pu- 

Molybdenum 
Neodymium 

2535 
840 

Mendenhall-  Forsythe 
(Muthmann-  Weiss.) 

rity. 

Neon 

—  252 

Argon 

—  188 

Ramsay-T  ravers. 

Nickel 

M52 

Day,    Sosman,    Bur- 

Arsenic 

500 

gess,  Wallenberg. 

Barium 

850 

(Guntz.) 

Niobium 

T95o 

v.  Bolton. 

Beryllium 

<Ag 

Nitrogen 

—  211 

(Fischer-Alt.) 

Bismuth 

270 

Adjusted. 

Osmium 

About  2700 

(Waidner  -  Burgess, 

Boron 

j  >  2000  ) 
]<2500j 

Weintraub. 

Oxygen 

—  230? 

unpublished.) 

Bromine 

—  7-3 

Palladium 

I545±  15 

(  Waidner-Burgess, 

Cadmium 

321 

Range  :      320.7- 

Nernst  -Warten- 

320.9. 

burg.) 

Caesium 

26 

Range  :     26.37- 

25-3 

Phosphorus 

44.2 

Calcium 

805 

Adjusted. 

Platinum 

*755  ±  20 

See  Note. 

Chlorine 

—  IO2 

(Olszewski.) 

Potassium 

'  •**?   -r1— 

62.3 

Carbon 
Cerium 

03500) 
645 

Sublimes. 

Praesodymium 
Rhodium 

940 
1910 

(Muthmann-  Weiss.) 
(Mendenhall-Inger- 

Chromium 

>I520 

Burgess-Walten- 

soll.) 

berg 

Rubidium 

38-5 

Cobalt 

1478 

Burgess-  Wallen- 

Ruthenium 

1900  ? 

berg 

Samarium 

1300-1400 

(Muthmann-Weiss.) 

Copper 

Io83  ±  3 

Mean,  Holborn- 

Selenium 

217 

Saunders. 

Day,       Day- 

Silicon 

I42O 

Adjusled. 

Clement. 

Silver 

Q6I-1-I 

Adjusled. 

Erbium 

Sodium 

97 

Fluorine 

—  223 

(Moissan  -  De- 

Strontium 

Belween  Ca  and  Ba  ? 

war.) 

Sulphur 

113.5-119.5 

Various  forms.     See 

Gallium 

30.1 

Landoll-Bornstein. 

Germanium 

<Ag 

Tantalum 

2800 

Ad  justed  from  Waid- 

Gold 

1063-1-3 

Adjusted. 

ner-Burgess  =2910. 

Hydrogen 

—  -59 

Tellurium 

45i 

Adjusted. 

Indium 

J55 

(Thiel.) 

Thallium 

302 

Iodine 

114 

Range:  1  12-115. 

Thorium 

>i7oo<Pt 

v.  Wartenburg. 

Iridium 

2290 

Mendenhall  In- 

Tin 

231.9  i  .2 

gersoll. 

Titanium 

*795 

Burgess-  Wallenberg. 

Iron 

1530 

Burgess-  Wallen- 

Tungsten 

2950 

Mean,  Waidner-Bur- 

berg. 

gess  and  Warten- 

Krypton 

-169 

(Ramsay). 

burg. 

Lanthanum 

810 

(Mulhmann- 

Uranium 

Near  Mo 

Moissan. 

Weiss.) 

Vanadium 

1720 

Burgess-  Wallenberg. 

Lead 

327  -J-  0.5 

Xenon 

—  140 

Ramsay. 

Lithium 

186    " 

(Kahlbaum.  ) 

Zinc 

419^-0.5 

Magnesium 

651 

(Grube)  in  clay 

Zirconium 

>Si 

Troost. 

crucibles,  635. 

SMITHSONIAN  TABLES. 


218 


TABLE  237. 
BOILING-POINTS  OF  THE  CHEMICAL  ELEMENTS, 


Element. 

Range. 

Boiling- 
point. 

Observer;  Remarks. 

Aluminum 

0 

o 
I800. 

Greenwood,  Ch.  News,  100,  1909. 

Antimony 

- 

1440. 

<i             «         <t        «       « 

Argon 

_ 

-186.1 

Ramsay-Travers,  Z.  Phys.  Ch.  38,  1901. 

Arsenic 
« 

449-45° 

>36o. 

Gray,  sublimes,  Conechy. 
Black,  sublimes,  Engel,  C.  R.  96,  1883. 

« 

280-310 

- 

Yellow,  sublimes. 

Barium 
Bismuth 

1420-1435 

1430. 

Boils  in  vacuo,  Guntz,  1903. 
Barus,  1894;  Greenwood,  1.  c. 

Boron 

Volatilizes  without  melting  in  electric  arc. 

Bromine 

59-63 

61.1 

Thorpe,  1880  ;  van  der  Plaats,  1886. 

Cadmium 

778. 

Berth  el  ot,  1902. 

Caesium 

— 

670. 

Ruff-Johannsen. 

Carbon 

_ 

3600. 

Computed,  Violle,  C.  R.  120,  1895. 

«< 

_ 

- 

Volatilizes  withoutmeltingin  electric  oven,  Moisson. 

Chlorine 

_ 

-33-6 

Regnault,  1863. 

Chromium 

_ 

2200. 

Greenwood,  Ch.  News,  100,  1909. 

Copper 
1    Fluorine 

2100-2310 

2310. 
-I87. 

1.  c. 
Moisson-Dewar,  C.  R.  136,  1903. 

Helium 

_ 

-267- 

Computed,  Tracers  Ch.  News,  86,  1902. 

Hydrogen 

—  252.5-252.8 

—252.6 

Mean. 

Iodine 

_ 

>200. 

Iron 

_ 

2450. 

Greenwood,  1.  c. 

Krypton 

_ 

—  15'-7 

Ramsay,  Ch.  News,  87,  1903. 

Lead 

_ 

*525- 

Greenwood,  I.  c. 

Lithium 

_ 

1400. 

Ruff-Johannsen,  Ch.  Ber.  38,  1905. 

Magnesium 

_ 

1  1  20. 

Greenwood,  1.  c. 

Manganese 

_ 

1900. 

a              « 

Mercury 

_ 

357- 

Crafts;  Regnault. 

Neon 

_ 

—239. 

Dewar,  1901. 

Nitrogen 

—195.7-194.4 

—195- 

Mean. 

Oxygen 

—182.5-182.9 

—182.7 

« 

Ozone 

_ 

—119. 

Troost,  C.  R.  126,  1898. 

Phosphorus 

287-290 

288. 

Potassium 

667-757 

712. 

Per  man  ;  Ruff-Johannsen. 

Rubidium 

696. 

Ruff-Johannsen. 

Selenium 

664-694 

690. 

Silver 

— 

J955- 

Greenwood,  1.  c. 

Sodium 

742-757 

75°- 

Perman  ;  Ruff-Johannsen. 

Sulphur 

444.7-445 

444-7 

Mean. 

Tellurium 

1390. 

Deville-Troost,  C.  R.  91,  1880. 

Thallium 

- 

1280. 

v.  Wartenberg,  25  Anorg.  Ch.  56,  1908. 

Tin 

— 

2270. 

Greenwood,  1.  c. 

Xenon 

- 

—  109.1 

Ramsay,  Z.  Phys.  Ch.  44,  1903. 

Zinc 

916-942 

93°- 

SMITHSONIAN  TABLES. 


TABLE  238.  2 IQ 

DENSITIES  AND  MELTING  AND  BOILING  POINTS.  INORGANIC  COMPOUNDS. 


Substance. 

Chemical  Formula. 

Density 

about  20° 
C. 

Melting- 
point 

Vy. 

H 

Boiling- 
point 
C. 

Pres- 
sure 
mm. 

Authority.  1 

Aluminum  chloride     .     . 

A1C13 

_ 

190. 

I 

183° 

752 

I 

"          nitrate  .     .     . 

A1(N03)3+9H20 

— 

72.8 

2 

— 

_ 

Aluminum  oxide     .     .     . 

A12O8 

4.00 

2020 

II 

_ 

_ 

_ 

Ammonia             .          . 

NH3 

_ 

7<v 

•5 

—  i-J-7    C 

700 

7 

Ammonium  nitrate  .     .     . 

NH4N08 

1.72 

I.J 
165. 

3 

JJO 

/  *-"^ 

/ 

sulphate  .     . 

(NH4)2S04 

1.77 

I4O. 

4 

_ 

_ 

_ 

phosphite 

NH4H2PO8 

123. 

5 

- 

_ 

- 

Antimony  trichloride  .     . 

SbCl8 

3-06 

73- 

223. 

76o 

— 

"         pentachloride  . 

SbCls 

2-35 

3- 

ii 

102. 

68 

14 

Arsenic  trichloride  .     .     . 

AsCl3 

2.20 

—  18. 

8 

130  2 

760 

23  1 

Arsenietted  hydrogen  .     . 

AsH3 

- 

—"3-5 

6 

-54-8 

u 

6 

Barium  chloride      .     .     . 

BaCl2.2H2O 

3.10 

"3- 

9 

_ 

— 

"        nitrate    .... 

Ba(N08)2 

575- 

24 

— 

_ 

_ 

"        perchlorate     .     . 

Ba(C104)2 

- 

505- 

10 

- 

_ 

- 

Bismuth  trichloride     .     . 

BiCl3 

4.56 

232.5 

- 

440. 

760 

_ 

Boric  acid 

TT     TJf^) 

1.46 

_ 

"      anhydride  .... 

B3203 

ft*OJW 

1.79 

577- 

- 

_ 

_ 

_ 

Borax  (sodium  borate)     . 

Na2B4O7 

1.69 

561+ 

9 

— 

— 

— 

1  Cadmium  chloride  .     .     . 

CdCl2 

4-05 

560. 

25 

900.^ 

— 

9 

*'         nitrate     .     .     . 

Cd(NO3)2  +  4H2O 

2-45 

59-5 

2 

132. 

760 

4 

!  Calcium  chloride     .     .     . 

CaCl2 

2.2§ 

774- 

— 

"              "           ... 

CaCl2-f  6H2O 

1.68 

29.6 

- 

- 

_ 

- 

"        nitrate  .... 

Ca(N03)2 

2.36 

499- 

24 

— 

_ 

— 

"              " 

Ca(NO3)2  +  4H2O 

1.82 

42.3 

26 

_ 

_ 

_ 

Carbon  tetrachloride  .     . 

CC14 

1.59 

—24. 

22 

76.7 

760 

23 

"        trichloride  .     .     . 

C2C16 

1.63 

184. 

— 

"        monoxide  .    .    . 

CO 

—207. 

6 

—  190. 

760 

6 

"       dioxide  .... 

CO2 

- 

—57- 

3 

—  80. 

subl. 

- 

"       disulphide  .    .    . 

CS2 

1.26 

—  IIO. 

46.2 

760 

_ 

Chloric  acid                  . 

HC1O4+H2O 

1.81 

-  _ 

T  C 

Chlorine  dioxide     .     .     . 

C102 

—76! 

1  J 

3 

9-9 

731 

21 

Chrome  alum      .... 

KCr(SO4)2+i2H2O 

1.83 

89. 

16 

_ 

"        nitrate   .... 

Cr2(N03)6+i8H20 

37- 

2 

170. 

760 

2 

Cobalt  sulphate  .... 

CoSO4 

3-53 

16 

_ 

Cupric  chloride  .    .    .    . 

CuCl2 

3-05 

498. 

9 

- 

_ 

- 

Cuprous      "  

Cu2Cl2 

7.7 

A  2  T 

IOOO.-I— 

760 

Cupric  nitrate     .... 
Hydrobromic  acid  .     .     . 

Cu(N03)2  +  3H20 
HBr 

J  / 

2.05 

114.5 
—86.7 

2 

3 

170. 

700 
760 

2 

Hydrochloric     "... 

HC1 

- 

—111.3 

17 

—  83.1 

755 

17 

Hydrofluoric      "... 

HF1 

•99 

—92-3 

6 

—  36.7 

17! 

Hydriodic          "... 

HI 

—51.3 

17 

—  35-7 

760 

Hydrogen  peroxide     .     . 

H202 

i.  5 

—  2. 

18 

80.2 

47 

20  ! 

"          phosphide  .     . 

PH3 

_ 

—  132.  c 

6 

_ 

-  i 

"         sulphide      .     . 

H2S 

_ 

$6^ 

3 

—62. 

_ 

_ 

Iron  chloride  

FeCl3 

2.80 

"      nitrate    

Fe(NO*U  4-  oHoO 

i  68 

/l*7    -7 

2 

"      sulphate     .... 
Lead  chloride     .... 

j.  \,\  x^  vyg^g  -y™  \j  L  L%\j 

FeSO4+7H2O 

PbCl2 

Jf 

47.  £ 
64. 
500. 

16 
9 

900.-!- 

760 

- 

"     metaphosphate  .     . 

Pb(P03)2 

800. 

9 

_ 

Magnesium  chloride   .     . 

MgCl2 

2.18 

70S. 

9 

_ 

_ 

_ 

nitrate     .    . 

Mg(N03)2  +  6H20 

1.46 

90. 

2 

143- 

760 

2 

"          sulphate  .    . 
Manganese  chloride    .     . 

MgS04+5H20 
MnCl2  -f-  4H2O 

1.68 

2.OI 

16 

106. 

760 

19 

"         nitrate  .     .     . 

Mn(NO3)2  +  6H2O 

1.82 

26! 

2 

129. 

2 

"         sulphate    .     . 

MnSO4-f5H2O 

2.09 

54- 

16 

_ 

_ 

Mercurous  chloride    .     . 

Hg2Cl2 

7.10 

45°i 

_ 

_ 

_ 

_ 

Mercuric  chloride   .     .     . 

HgCl2 

542 

282. 

- 

305. 

- 

- 

i,  Friedel  and  Crafts;  2,  Ordway;  3,  Faraday;  4,  Marchand;  5,  Amat;  6,  Olszweski;  7,  Gibbs;  8,  Baskerville;  9, 
Carnelly;  10,  Carnelly  and  O'Shea;  n,Ruff;  13,  Wroblewski  and  Olszewski;  14,  Anschiitz  ;  15,  Roscoe;  16,  Tilden  ; 
17,  Ladenburg;  18,  Staedel;  19,  Clarke,  "Const,  of  Nature";  20,  Bruhl;  21,  Schacherl;  22,  Tamman;  23,  Thorpe; 


24,  Ramsay;  25,  Lorenz;  26,  Morgan. 
SMITHSONIAN  TABLES. 


2  2O 


TABLE  238  (continued). 

DENSITIES   AND    MELTING-   AND    BOILING-POINTS. 
INORGANIC    COMPOUNDS. 


Substance. 

Chemical  Formula. 

Density 
about 

20°  C. 

Vlelting- 
point  C. 

Authority.  I 

Boiling- 
point  C. 

Pres- 
sure 
mm. 

Authority.  1 

Nickel  carbonyl  .... 
"      nitrate      .... 

NiC404 
Ni(NO3)2  +  6H2O 

1.32 
2.05 

~25- 
56.7 

I 

2 

43° 
136.7 

760 

2 

"      oxide  

NiO 

6.69 

— 

— 

—  i 

"      sulphate  .... 

NiSO4+7H2O 

I.98 

99- 

3 

- 

- 

- 

i  Nitric  acid                          • 

HNO3 

1.52 

—  42. 

4 

86. 

760 

16  ; 

"       anhydride      .     .     . 

N205 

1.64 

3°- 

5 

48. 

« 

9 

"      oxide*  

NO 

_ 

—  i  SS- 

—  153. 

«« 

6 

"      peroxide  .... 

N2O4 

- 

J  J 

—  IO.I 

8 

24. 

76o 

Nitrous  anhydride  .     .     . 

N2O3 

— 

—82. 

7 

0.4; 

It 

-  i 

**       oxide 

N2O 

_ 

—  102.4 

8 

—89.8 

« 

8  i 

Phosphoric  acid  (ortho)  . 

H3P04 

1.88 

**T 

40-± 

VyX 

- 

Phosphorous  acid   .     .     . 

H3P03 

1.65 

72. 

— 

— 

- 

— 

Phosphorus  trichloride    . 

PC13 

1.61 

—  111.8 

10 

76. 

760 

19 

"          oxychloride    . 

POC18 

1.68 

+i-3 

— 

108. 

M 

— 

"          disulphide  .     . 

P8S6 

- 

297. 

12 

- 

<« 

- 

"          pentasulphide 
"         sesquisulphide 

P2S5 

P4S3 

2.IO 

275- 
168. 

13 

522. 
400. 

<« 

_  ' 

"          trisulphide 

P2S3 

— 

290.-]- 

14 

490. 

" 

25 

Potassium  carbonate   .     . 

K2C03 

2.29 

840.J- 

— 

— 

— 

"          chlorate      .     . 

KClOg 

2-34 

372. 

15 

- 

- 

- 

"          chromate    .     . 

K2Cr04 

2.72 

975- 

17 

— 

— 

— 

"          cyanide  .     .     . 

KCN 

1.52 

— 

— 

- 

— 

"          perchlorate     . 

KC1O4 

2.52 

610. 

15 

— 

— 

— 

"          chloride      .     . 

KC1 

1.99 

801. 

- 

- 

- 

"          nitrate    .     .     . 

KN08 

2.IO 

34L 

— 

— 

- 

- 

"          acid  phosphate 

KH2P04 

2-34 

96. 

3 

- 

- 

- 

"          acid  sulphate  . 

KHSO4 

2-35 

205. 

- 

- 

- 

Silver  chloride    .... 

AgCl    ' 

5-56 

45i- 

15 

— 

— 

— 

"      nitrate  

AgNO3 

4-3  <> 

208.7 

_ 

_ 

_ 

_ 

"      perchlorate   .     .     . 

AgC104 

^  OJ 

486. 

18 

- 

- 

- 

"      phosphate     .     .     . 

Ag3P04 

6.37 

849. 

15 

— 

— 

— 

"      metaphosphate  .     . 

AgP03 

482 

15 

- 

- 

- 

"      sulphate   .... 

Ag2S04 

5-45 

655-± 

— 

— 

— 

— 

Sodium  chloride      .     .     . 

NaCl 

2.17 

800. 

ii 

— 

— 

— 

"        hydroxide  .     .     . 

NaOH 

2.1 

318. 

27 

- 

- 

- 

"        nitrate    .... 
"        chlorate      .     .     . 

NaNO3 
NaClOs 

2.26 
2.48 

Ill: 

28 

_ 

•• 

_ 

"        perchlorate     .     . 

NaClO4 

482. 

18 

— 

— 

— 

"        carbonate  .     .     . 

Na2CO3 

2.48 

852. 

— 

— 

— 

— 

K               « 

Na2CO3+ioH2O 

1.46 

34. 

3 

- 

- 

- 

"        phosphate  .     .     . 

Na2HPO4+i2H2O 

i-54 

38. 

— 

— 

— 

"        metaphosphate   . 

NaP03 

2.48 

6i7. 

15 

- 

- 

- 

"     '   pyrophosphate    . 
"        phosphite  .     .     . 

Na4P2O7 
(H2NaP03)2+5H20 

2.45 

970. 
42. 

30 
20 

* 

_ 

_ 

"        sulphate     .     .     . 

Na2SO4 

2.67 

884. 

ii 

— 

— 

— 

«              « 

Na2SO4+  ioH20 

1.46 

32.38 

17 

— 

— 

— 

"        hyposulphite  .     . 
Sulphur  dioxide  .... 

Na2S203+5H20 
SO2 

i-73 

48.16 
—76. 

—  10. 

760 

_ 

Sulphuric  acid    .... 

H2SO4 

1.83 

10.4 

21 

338. 

N 

22 

«           « 

I2H2SO4+H2O 

—o-5 

22 

— 

— 

— 

"           "        .... 

H2SO4  +  H2O 

- 

8.5 

- 

- 

- 

- 

.  "  (pyro)     .    . 
Sulphur  trioxide  .... 

H2S2O7 
S08 

1.91 

35- 
J5- 

22 

46.2 

760 

_ 

Tin,  stannic  chloride  .     . 

SnCl4 

2.28 

—33- 

23 

114. 

« 

19 

"     stannous     "          .     . 

SnCl2 

_ 

250. 

24 

605. 

(( 

— 

Zinc  chloride       .... 

ZnCl2 

2.91 

365- 

29 

710. 

<( 

- 

«         « 

ZnCl2  +  3H2O 

6.5 

26 

_ 

_ 

_ 

"     nitrate  

Zn(NO3)2  +  6H2O 

2.06 

f  J 

•3Q.4 

•3 

I7i. 

760 

2 

"     sulphate     .    .    .    . 

ZnSO4  +  7H2O 

2.02 

O        T^ 
SO" 

o 
3 

O 

i,  Mond,  Langer,  Quincke ;  2,  Ordway ;  3,  Tilden  ;  4,  Erdmann ;  5,  R.  Weber ;  6,  Olszewski ;  7,  Birhaus ;  8,  Ram- 
say; q,  Deville;  10,  Wroblewski;  ii,  Day,  Sosman,  White;  12,  Ramme;  13,  Meyer;  14,  Lemoine ;  15,  Carnelly ;  16, 
Mitscherlich ;  17,  LeChatelier  ;  18,  Carnelly,  O'Shea;  ig,  Thorpe  ;  20,  Amat;  21,  Mendelejeff;  22,  Marignac ;  23, 
Besson  ;  24,  Clarke,  "  Const,  of  Nature  ";  25,  Isambert;  26,  Mylius;  27,  Hevesy;  28,  Retgers;  29,  Griinauer ;  30, 
Richards  and  others.  *  Under  pressure  138  mm.  mercury. 

SMITHSONIAN  TABLES. 


TABLES  239-240. 
TABLE  239. —Effect  of  Pressure  on  Meltlng-Polnt. 


221 


Substance. 

Melting-point 
at  i  kg/sq.  cm. 

Highest 
experimental 
pressure  : 
kg/sq.  cm. 

dt/dp 
at  i  kg/sq.  cm. 

A  t.  (observed) 
for 
looo  kg/sq.  cm. 

Reference. 

Hg 

-38.85 

I2OOO 

O.O05II 

S'f 

I 

K 

59-7 

2800 

.0136 

I3.8 

2 

Na 

97-4 

2800 

.0082 

8.2 

2 

Sn 

231.9 

2000 

.00317 

3-17 

3 

Bi 

270.9 

2OOO 

—  0.00344 

—  344 

3 

Cd 

320.9 

2OOO 

0.00609 

6.09 

3 

Pb 

3274 

200O 

.00777 

7-77 

3 

*  A  t  (observed)  for  10000  kg/sq.  cm.  is  50.8°. 

References.  —  i.  P.  W.  Bridgman,  "  Proc.  Am.  Acad."  47,  pp.  391-96,  416-19,  1911. 

2.  G.  Tammann,  "  Kristallisieren  und  Schmelzen,"  Leipzig,  1903,  pp.  98-99. 

3.  J.  Johnston  and  L.  H.  Adams,  "Am.  J.  Sci."  31,  p.  516,  1911. 

A  large  number  of  organic  substances,  selected  on  account  of  their  low  melting-points,  have 
also  been  investigated:  by  Tammann,  loc.  cit.\  G.  A.  Hulett,  "Z.  Physik.  Chem."28,  p.  629,  1899; 
F.  Korber,  ibid.,  82,  p.  45,  1913;  E.  A.  Block,  ibid.,  82,  p.  403,  1913.  The  results  for  water  are 
given  in  the  following  table. 


TABLE  240.  -Effect  of  Pressure  on  the  Freezing-Point  of  Water  (Bridgman*). 


Pressuret: 
kg/sq.  cm. 

Freezing-point. 

Phases  in  Equilibrium. 

I 

0.0 

Ice  I  —  liquid. 

1000 

—  8.8 

2000 

—  20.15 

1C 

2IIS 

—  22.O 

Ice  I  —  ice  III  —  liquid  (triple  point). 

3000 

—  18.40 

Ice  III  —  liquid. 

353° 
4000 

—  ly.O 
—  13-7 

Ice  III  —  ice  V  —  liquid  (triple  point). 
Ice  V  —  liquid. 

6OOO 

—   1.6 

a 

6380 
8000 

+  0.16 

12.8 

Ice  V  —  ice  VI  —  liquid  (triple  point). 
Ice  VI  —  liquid. 

12000 

37-9 

16000 

57-2 

« 

20000 

73-6 

« 

*  P.  W.  Bridgman,  "Proc.  Am.  Acad."  p.  47, 441-558,  1912. 
1 1  atm.  =  1.033  kg/sq.  cm. 


SMITHSONIAN  TABLES. 


222 


TABLES  241 -243.    MELTING-POINTS, 

TABLE  241.  — Melting-point  of  Mixtures. 


Metals. 

Melting-points,  C°. 

Reference.  1 

Percentage  of  metal  in  second  column. 

o% 

10% 

20% 

30% 

40% 

5°% 

60% 

70% 

80% 

90% 

100% 

Pb.  Sn. 

326 

295 

276 

262 

240 

220 

190 

I»5 

200 

216 

232 

i 

Bi. 

322 

290 

_ 

179 

MS 

126 

168 

205 

- 

268 

7 

Te. 

322 

710 

79° 

880 

917 

760 

600 

480 

410 

425 

446 

8 

Ag. 

328 

460 

545 

59° 

620 

650 

70S 

775 

840 

90S 

959 

9 

Na. 

360 

420 

400 

37° 

330 

290 

250 

200 

130 

96 

13 

Cu. 

326 

870 

920 

925 

945 

95° 

955 

985 

IOCS 

1020 

1084 

2 

Sb. 

326 

250 

275 

330 

395 

440 

49° 

525 

560 

600 

632 

16 

Al.  Sb. 

650 

75° 

840 

925 

945 

950 

970 

1000 

1040 

IOIO 

632 

»7 

Cu. 

650 

630 

600 

560 

540 

580 

610 

755 

930 

1055 

1084 

18 

Au. 

655 

675 

740 

800 

855 

915 

970 

1025 

1055 

675 

1062 

JO 

Ag. 

650 

625 

6i5 

600 

590 

58o 

575 

570 

650 

750 

954 

'7 

Zn. 

6S4 

640 

620 

600 

580 

560 

530 

Sio 

475 

425 

419 

ii 

Fe. 

653 

860 

1015 

II  IO 

i  '45 

"45 

1220 

1315 

1425 

1500 

'515 

3 

Sn. 

650 

645 

635 

625 

620 

605 

590 

570 

56o 

54o 

232 

r7 

Sb.  Bi. 

632 

610 

59<> 

575 

555 

540 

520 

470 

4°5 

330 

268 

16 

Ag. 

630 

595 

57° 

545 

520 

500 

505 

545 

680 

850 

959 

9 

Sn. 

622 

600 

570 

525 

4So 

430 

395 

350 

3io 

255 

232 

19 

Zn. 

632 

555 

5'o 

540 

570 

565 

540 

525 

5  10 

470 

419 

17 

Ni.  Sn. 

1455 

1380 

1290 

I2OO 

"35 

1290 

1305 

1230 

1060 

800 

232 

*7 

Na.  Bi. 

96 

425 

520 

590 

645 

690 

720 

730 

7*5 

570 

268 

13 

Cd. 

96 

125 

185 

245 

285 

325 

330 

340 

360 

390 

322 

13 

Cd.  Ag. 

322 

420 

520 

610 

700 

760 

805 

850 

895 

940 

954 

17 

Tl. 

321 

300 

285 

270 

262 

*58 

245 

230 

210 

235 

302 

H 

Zn. 

322 

280 

270 

295 

3i3 

327 

340 

355 

370 

390 

419 

ii 

Au.  Cu. 

1063 

910 

890 

895 

9°5 

925 

975 

1000 

1025 

1060 

1084 

4 

Ag. 

1064 

1062 

1061 

1058 

1054 

1049 

1039 

1025 

I006 

982 

963 

5 

Pt. 

1075 

1125 

1190 

1250 

1320 

1380 

1455 

1530 

1610 

1685 

1775 

20 

K.  Na. 

62 

i7-5 

—  10 

—3-5 

5 

ii 

26 

41 

58 

77 

97-5 

15 

Sf 

62.5 

133 

165 

188 

205 

90 
215 

no 

220 

135 
240 

162 
280 

265 
305 

301 

13 

'4 

Cu.  Ni. 

1080 

1180 

1240 

1290 

1320 

1335 

1380 

1410 

1430 

1440 

M55 

'7 

Ag. 

1082 

1035 

990 

945 

910 

870 

830 

788 

814 

875 

960 

9 

Sn. 

1084 

1005 

890 

755 

725 

680 

630 

580 

530 

440 

232 

12 

Zn. 

1084 

1040 

995 

930 

900 

880 

820 

780 

700 

580 

419 

6 

Ag.  Zn. 

959 

850 

755 

70S 

690 

660 

630 

610 

570 

505 

419 

n 

Sn. 

959 

870 

750 

630 

55° 

495 

45° 

420 

375 

300 

232 

9 

Na.  Hg. 

96.5 

90 

80 

70 

60 

45 

22 

55 

95 

215 

13 

1  Means,  Landolt-Bornstein-Roth  Tabellen.  ii 

2  Friedrich-Leroux,  Metal.  4,  1907.  12 

3  Gwyer,  Zs.  Anorg.  Ch.  57,  1908.  13 

4  Means,  L.-B.-R.  Tabellen.  14 

5  Roberts- Austen  Chem.  News,  87,  2,  1903.  15 

6  Shepherd  J.  ph.  ch.  8,  1904.  16 

7  Kapp,  Diss.,  Kbnigsberg,  1901.  17 

8  Fay  and  Gilson,  Trans.  Am.  Inst.  Min.  Eng.  Nov.  18 

1901. 

9  Heycock  and  Neville,  Phil.  Trans.  i8gA,  1897.  19 
10         "          "          "            "        "    I94A,  201,  1900.  20 


1903- 


Heycock  and  Neville,  J.  Chem.  Soc.  71,  1897. 
Phil.  Trans.  202A,    i, 
Kurnakow,  Z.  Anorg.  Chem.  23,  439,  1900. 
30,  86,  1902. 

30,    109,    IQ02. 

Roland-Gosselin,  Bui.  Soc.  d'Encour.  (5)    i,    1896. 
Gautier,  «       "  "         (5)    x,      •' 

Le  Chatelier,          "       "  "         (4)    10,   573, 

1895. 

Reinders,  Z.  Anorg.  Chem.  25,  113,  1896. 
Erhard   and   Schertel,   Jahrb.    Berg-u.    Hiittenw. 

Sachsen.  1879,  17. 


TABLE  242.  —Alloy  of  Lead,  Tin,  and  Bismuth. 


Per  cent. 

Lead  .     .     . 

32.0 

iS-5 
52-5 

25.8 
19.8 
54-4 

25-0 
15-0 
60.0 

43-0 
14.0 
43-o 

33-3 
33-3 
33-3 

10.7 
23-1 
66.2 

50.0 
33-0 
17.0 

35-8 
52.1 

12.  1 

20.  o 
60.0 

20.0 

70.9 
9.1 
20.0 

Tin     . 

Bismuth.     .    .     . 

Solidification   at 

96° 

101° 

125° 

128° 

MS0 

148° 

161° 

181° 

182° 

234° 

Charpy,  Soc.  d'Encours,  Paris,  1901. 


TABLE  243.  —  Low  Melting-point  Alloy. 


I 

*er  cent 

Cadmium  .... 
Tin 

10.8 

10.2 

I4.8 

»3-i 
11  8 

6.2 

7-' 

6.7 

Lead     

Bismuth    .... 

50.1 

50-4 

52.2 

48.8 

50.0 

53-2 

49-9 

Solidification    at 

65-5° 

67-5° 

68.5° 

68.5° 

76-5° 

89-5° 

95° 

Drewitz,  Diss.  Rostock,  1902. 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  244. 


223 


DENSITIES,    MELTING-POINTS,    AND    BOILING-POINTS    OF    SOME 
ORGANIC  COMPOUNDS. 

N.B.  —  The  data  in  this  table  refer  only  to  normal  compounds. 


Substance. 

Formula 

Temp. 

Den- 
sity. 

Melting- 
point 

Boiling-point. 

Authority. 

(a)  Paraffin  Series  :  CwH2W  +  2. 

Methane*    .     .     . 

CH4 

—164. 

0.415 

-184 

-165. 

Olszewski,  Young. 

Ethanet  .... 

O 

.446 

—171.4 

—93- 

Ladenburg,      " 

Propane  .... 

C3Hs 

O 

—195 

—45- 

Young,  Hainlen. 

Butane    .... 

C4H10 

0 

.60 

i. 

Butlerow,  Young. 

Pentane  .... 

CsHuj 

0 

•647 

— 

§3 

Thorpe,  Young. 

Hexane   .... 

CgHi4 

17- 

•663 

— 

Schorlemmer. 

Heptane  .... 

C7H16 

o 

.701 

- 

4 

Thorpe,  Young. 

Octane     .... 

CsHis 

0 

.719 

— 

I25-5 

«             « 

Nonane   .... 

CgH20 

0 

•733 

—51- 

150. 

Krafft. 

Decane    .... 
Undecane    .    .     . 
Dodecane    .     .     . 

CuH* 

0 

o 

0 

f 

.765 

—  12. 

173- 
195- 
214. 

ii 

Tridecane    .     .     . 

Ci3ri28 

0 

.771 

—6. 

234- 

" 

Tetradecane     .     . 

CI^HSO 

4. 

•775 

5. 

252. 

" 

Pentadecane     .     . 

CisH32 

IO. 

.776 

IO. 

270. 

« 

Hexadecane     .     . 

Ci6ri34 

18. 

•775 

18. 

287. 

" 

Heptadecane    .     . 

Ci7H36 

22. 

•777 

22. 

3°3- 

«« 

Octadecane      .     . 

Ci8H38 

28. 

•777 

28. 

" 

Nonadecane     .     . 

32- 

•777 

32- 

33°- 

" 

Eicosane.     .     .     . 

C20*142 

37- 

•778 

37. 

121.  § 

" 

Heneicosane    .     . 

C2iH44 

40. 

.778 

40. 

I29-§ 

«< 

Docosane     .     .     . 

C22H46 

44- 

.778 

44. 

i36.5§ 

« 

Tricosane     .     .     . 

C23I"l48 

48. 

•779 

48. 

142.  5§ 

" 

Tetracosane     .     . 
Heptacosane    .    . 

C24H5o 
C27Hs6 

£ 

•779 
.780 

fi 

2434 

I72.§ 

M 

Pentriacontane     . 

C3iHg4 

68. 

.781 

68. 

i99-§ 

M 

Dicetyl    .... 

082^66 

70. 

.781 

70. 

205.1 

« 

Penta-tria-contane 

C85H72 

75- 

.782 

75- 

33i4 

" 

(b)  Olefines,  or  the  Ethylene  Series  :  CnH2n. 

Ethylene 

C2H4 

_ 

0.6  10 

-169. 

—103. 

Wroblewski  or  Olszewski. 

Propylene 
Butylene  . 

C3H6 
C4H8 

—  ^-5 

•635 

—50.2 

Ladenburg,  Kriigel. 
Sieben. 

Amylone 
Hexylene 

C6H12 

0 

•7~6 

_ 

36- 

69. 

Wagner  or  Saytzeff. 
Wreden  or  Znatowicz. 

Heptylene 

C7H14 

19-5 

•703 

- 

Morgan  or  Schorlemmer. 

Octylene  . 

CsHig 

17- 

.722 

— 

I22.-I23. 

Moslinger. 

Nonylene 

CgH18 

20. 

.767 

- 

I40.-I42. 

Beilstein,  "  Org.  Chem." 

Decylene 

CioH2o 

— 

— 

— 

175. 

<«                           «                       0 

Undecylene 

CnH22 

20. 

•773 

- 

196.-!  97. 

U                        If                     « 

Dodecylene 

Ci2.H24 

—  31. 

•795 

—  31. 

2I2.-2I4. 

(I               <«            « 

Tridecylene 

Ci3H2e 

15. 

•774 

— 

233- 

Bernthsen. 

Tetradecylene 

CuH28 

—  12. 

•794 

—  12. 

Krafft. 

Pentadecylene 

Ci5iT3o 

— 

.814 

— 

247. 

Bernthsen. 

Hexadecylene 

C  16  H  82 

4- 

.792 

4- 

1554 

Krafft,  Mendelejeff,  etc. 

Octadecylene 

CisH36 

1  8. 

.791 

18. 

1794 

Krafft. 

Eicosylene  . 

C2oH40 

o 

.871 

- 

390.-400. 

Beilstein,  "  Org.  Chem." 

Cerotene 

C27Hs4 

— 

— 

58. 

— 

Bernthsen. 

Melene    .    . 

C80Heo 

" 

" 

62. 

' 

*  Liquid  at—  n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 

i  Boiling-point  under  15  mm.  pressure. 
§  In  vacuo. 


SMITHSONIAN  TABLES. 


224  TABLE  244  (continued). 

DENSITIES,   MELTING-POINTS,   AND   BOILING-POINTS   OF   SOME 
ORGANIC   COMPOUNDS. 


Substance. 

Chemical 
formula. 

Temp. 

Specific 
gravity. 

Melting- 
point. 

Boiling- 
point. 

Authority. 

(C)  Acetylene  Series  :  CnU2n_2, 

C2H2 

_ 

_ 

—  81. 

—  85- 

Villard. 

Allylene      

C3H4 

_ 

_ 

Ethylacetylene    .    .     . 

C4H6 

- 

- 

- 

+'18. 

Bruylants,  Kutsche- 

roff,  and  others. 

Propylacetylene  .    .    . 

C6H8 

_ 

— 

- 

48-50. 

Bruylants,  Taworski. 

Butylacetylene     .     .     . 

CgHio 

_ 

— 

— 

68.-70. 

Taworski. 

Oenanthylidene  .    .    . 

C7Hi2 

- 

- 

- 

IOO.-IOI. 

Beilstein,    and    oth- 

ers. 

Caprylidene    .... 

C8Hj4 

0. 

0.771 

- 

'33--I34- 

Behal. 

Undecylidene  .     .     .     . 

CnH2o 

— 

— 

2IO.-2I5- 

Bruylants. 

Dodecylidene      .     .    . 

CigH^ 

—  9- 

.810 

—  9- 

105.* 

Krafft. 

Tetradecylidene  .    .     . 
Hexadecylidene  .     .     . 

QeH3o 

+  6.5 
20. 

.806 
.804 

+  6.5 
20. 

I34-* 
1  60.* 

'<! 

Octadecylidene   .     .     . 

Q8H34 

30- 

.802 

30- 

184.* 

" 

(d)  Monatomic  alcohols  :  C^H2W_f_IOH. 

Methyl  alcohol 

CH3OH 

0. 

0.8  1  2 

_ 

66. 

Ethyl  alcohol  . 

C2H5OH 

0. 

.806 

—  130.1 

78. 

Propyl  alcohol 

C3H7OH 

o. 

.817 

_ 

97- 

From  Zander,  "  Lieb. 

Butyl  alcohol  . 

C4H9OH 

0. 

.823 

_ 

117. 

Ann."  vol.  224,  p.  85, 

Amyl  alcohol  . 

C5HnOH 

0. 

.829 

- 

138- 

and  Krafft,  "Ber." 

Hexyl  alcohol 

C6H13OH 

o. 

•833 

— 

vol.  16,  1714, 

Heptyl  alcohol 

C7H15OH 

0. 

.836 

- 

176. 

"     19,  2221, 

Octyl  alcohol  . 
Nonyl  alcohol 

C8H17OH 
C9H19OH 

0. 

o. 

•839 

.842 

—  5- 

195- 
213. 

"     23,2360, 

and  also  Wroblew- 

Decyl  alcohol 

CioH2jOH 

+  7. 

•839 

+  7- 

ski  and  Olszewski, 

Dodecyl  alcohol 

Ci2H25OH 

24. 

.831 

143.* 

"  Monatshefte," 

Tetradecyl  alcohol 

C14H29OH 

38. 

.824 

38. 

167.* 

vol.  4,  p.  338. 

Hexadecyl  alcohol 

C16H33OH 

.818 

5°' 

190.* 

Octadecyl  alcohol 

C18H37OH 

59- 

.813 

59- 

211.* 

(e)  Alcoholic  ethers  :  CnU2n+2O. 

Dimethyl  ether  .    .    . 

C2H60 

_ 

_ 

_ 

—  23.6 

Erlenmeyer,  Kreich- 

baumer. 

Diethyl  ether  .     . 
Dipropyl  ether    . 

C4Hi00 
C6H140 

4- 

0. 

0.731 
•763 

—  117 

+  34-6 
90.7 

Regnault,  Olszewski. 
Zander  and  others. 

Di-iso-propyl  ether 

C6H140 

0. 

•743 

— 

69. 

" 

Di-n-butyl  ether  . 

C8H180 

0. 

.784 

- 

141. 

Lieben,  Rossi,  and 

others. 

Di-sec-butyl  ether 

C8H180 

21. 

•756 

- 

121. 

Kessel. 

Di-iso-butyl     " 

C8H180 

IIT 

.762 

_ 

122. 

Reboul. 

Di-iso-amyl      " 
Di-sec-hexyl     " 

Ci0H22O 

0. 

•799 

— 

170.-!  7  5. 
203  .-208. 

Wurtz. 
Erlenmeyer  and 

Wanklyn. 

Di-norm-octyl  "      .    . 

Ci6H840 

17- 

.805 

- 

280.-282. 

Moslinger. 

(f  )  Ethyl  ethers  :  C,tH2n+2O. 

Ethyl-methyl  ether  . 

C8H8O 

0. 

0.725 

_ 

II. 

Wurtz,  Williamson. 

"     propyl      «      . 

C6H120 

20. 

0-739 

_ 

63.—  64. 

Chancel,  Briihl. 

"     iso-propyl  ether 

C5H120 

O. 

_ 

54- 

Markownikow. 

"     norm-butyl  ether 

C6H140 

O. 

.769 

_ 

92. 

Lieben,  Rossi. 

"     iso-butyl  ether 
"     iso-amyl  ether 

C6H140 
C7H160 

18. 

35 

— 

78.-8o. 

112. 

Wurtz. 
Williamson  and 

others. 

"    norm-hexyl  ether 

C8H180 

- 

- 

- 

I34--I37- 

Lieben,  Janeczek. 

'    norm-heptyl  ether 

C9H200 

1  6. 

.790 

— 

165. 

Cross. 

"    norm-octyl  ether 

17- 

•794 

— 

i82.-i84. 

Moslinger. 

*  Boiling-point  under  15  mm.  pressure. 

t  Liquid  at  — n.°  C.  and  180  atmospheres'  pressure  (Cailletet). 


SMITHSONIAN  TABLES. 


TABLE  244  (concluded). 

DENSITIES,  MELTING-POINTS,  AND  BOILING-POINTS  OF 
SOME  ORGANIC  COMPOUNDS. 

(g)  Miscellaneous. 


225 


Substance. 

Chemical  formula. 

Density  and 
temperature. 

Melting- 
point,  C. 

Boiling- 
point,  C. 

Authority. 

Acetic  Acid      .     . 

CH3COOH 

1.115         o° 

I6.7 

118.5 

Young  '09 

Acetone   .... 

CH3COCH3 

0.812          o° 

—94.6 

56.! 

Aldehyde      .     .     . 

C2H40 

0.806         o° 

—  1  2O. 

+  20.8 

Aniline     .... 

C6H5NH2 

1.038         o° 

—8. 

183.9 

Beeswax  .... 

0.96-1- 

62. 

Benzoic  Acid    .     . 

C7H602 

1.293          4 

121. 

249. 

Benzol      .... 
Benzophenone  .     . 

C6H6 
(C6H5)2CO 

0.879        20 
1.090        50 

J:58 

80.2 
305-9 

Young 
Holborn- 

Henning 

Butter       .... 

0.86-7 

3O.4- 

Camphor      .     .     . 

CioH160 

0.99          10 

176. 

209. 

Carbolic  Acid  .     . 

C6H6OH 

1.060        21 

43- 

182. 

Carbon  bisulphide 

CS2 

1.292         o 

—  no. 

46.2 

"         tetrachlor- 

ide    . 

CC14 

j   ^82            21 

-_ 

767 

Young 

Chlorbenzene   .     . 

C6H5C1 

I.  Ill             15 

—40. 

/<J./ 

132. 

Chloroform  .     .     . 

CHC13 

1.257          o 

—65- 

61.2 

Cyanogen     .     .     . 
Ethyl  bromide  .     . 

C2N2 
C2H5Br 

1-45          J5 

—35- 
—117. 

—  21. 
38.4 

„     chloride  .     . 

C2H5C1 

0.918         8 

—  141.6 

14. 

„      ether  .     .     . 

C4H100 

0.736         o 

—  118. 

34-6 

„     iodide      .     . 

C2H5I 

1.944        14 

72. 

Formic  acid      .     . 

HCOOH 

1.242          o 

8.6 

100.8 

Gasolene  .... 

0.684- 

70-90 

Glucose    .... 

CHO(HCOH)4CH2OH 

1.56 

146. 

Glycerine      .     .     . 

C3H803 

1.269          o 

20. 

290. 

lodoform      .     .     . 

CHI8 

2.25          25 

119. 

Lard    

38-=t 

Methyl  chloride    . 

CH3C1 

0.992   —24 

—103.6 

—24.1 

Methyl  iodide  .     . 

CH3I 

2.285        1S 

-64. 

42.3 

Napthalene  .     .     . 

/**     TT       .   /"*     TT 

^6^4    L-4O4 

1-152        15 

80. 

218.0 

Holborn- 

Henning 

Nitrobenzol  .     .     . 

C6H5O2N 

I-2I2          7.5 

5- 

211. 

Nitroglycerine  .     . 

C3H5N309 

1.60 

Olive  oil  .     .     .     . 

O.92 

300-zt 

Oxalic  acid  .     .     . 

C2H204-2H20 

1.68 

190. 

Paraffin  wax,  soft  . 

38-52 

350-390 

"     hard 

390-430 

Pyrogallol    .     .     . 

C6H3(OH)3 

1.46         40 

i33-  , 

293- 

Spermaceti  .     .     . 

45-i 

Starch      .... 

C6H1005 

1.56 

Sugar,  cane  .     .     . 

1.588           20 

160. 

Stearine  .... 

(CigHgJoaTsC^Hs 

0.925           65 

Tartaric  acid     .     . 

C4H606 

1-754 

Tallow,  beef     .     . 

40-45 

"       mutton     . 

44-45 

Toluene  .... 

C6H6CH3 

0.882        oo 

—92. 

in. 

Xylene(o)    .     .     . 

C6H4(CH3)2 

0.863        20 

—28. 

142. 

"     (m)    .     .     . 

" 

0.864        20 

54- 

140. 

«      (p)    .     .     . 

0.861        20 

15- 

138. 

SMITHSONIAN  TABLES. 


226  TABLE  245. 

TRANSFORMATION  AND   MELTING  TEMPERATURES  OF  LIME-ALUMINA- 
SILICA  COMPOUNDS  AND    EUTECTIC   MIXTURES. 

The  majority  of  these  determinations  are  by  G.  A.  Rankin.     (Part  unpublished.) 


Substance. 


%  CaO      A12O3        SiOs 


Transformation . 


Temp. 


CaSi08 
CaSiOs 
Ca2SiO4 


Ca3Si2O7 
Ca3SiO5    . 

Ca3Al2O6  . 
Ca5Al6Oi4 
CaAl2O4 


48.2  —  s1-8 

48.2  —  51.8 

65-  —  35- 

65-  —  35- 


Al2SiO6  . 
CaAl2Si2O8 
Ca2Al2SiO7 
Ca3Al2SiO8 


73-6 

62.2 
47.8 
35-4 
24.8 

20.  i 

40.8 
50-9 


37.8 
52.2 
64.6 
75.2 
62.8 
36.6 

37.2 

30.9 


26.4 


37.1 
43.3 

22.0 

18.2 


Melting 

o  to  j8  and  reverse 

Melting  

7  to  £  and  reverse 

£  to  a  and  reverse 

Dissociation  into  Ca2SiC>4  and 

liquid 

Dissociation  into  Ca2SiO4  and 

CaO 

Dissociation  into  CaO  and  liquid 

Melting 

Melting 

Melting 

Melting 

Melting 

Melting 

Dissociation  into  Ca2SiO4+ 

Ca2Al2SiO7  and  liquid    .     . 


1 540°  -J-2° 

1 2OO   -[-2 

2130  ^-10 
675  ±5 

I42O   4^-2 

H75  ±5 
1900  4-5 

1535  =Es 

J455  ±5 
1600  - -5 
1720  --10 
1816  iio 

1550  ±2 

1590  4^2 
1335  ±5 


EUTECTICS. 


EUTECTICS. 


Crystalline  Phases. 


CaSiO3,SiO2 

Ca,SiO3 

3CaO,2SiO2 

Ca,SiO4 

CaO. 

Al2SiO6,SiO2 

Al2SiO5,Al2Oj 

CaAl2Si2O8 

CaSiO3 

CaAl2Si2O8 

SiO2 

CaAl2Si2O8 

SiO2,CaSiO3 

Ca2Al2SiO7 

Ca2SiO4 

A1203 

CaAl2Si2O8 

CaAl2Si208 

Al2SiO5,SiO2 

Ca2Al2SiO7 

Ca8Al10Oi8 

Ca2Al2SiO7 

CaAl2O4 

Ca2Al2SiO7 

CaAl204 

Ca3Al10Oi8 

CaAl2Si2O8 

Ca2Al2SiO7 

Ca2Al2SiO7 

Ca8Si2O7 

CaSi03 

Ca2Al2SiO7 

CaSiO8 


%CaO   A1203      SiO2 


37-  —  63. 

54-5  —  45-5 

67-S  —  32-5 

34.1  18.6  47.3 
10.5  19.5  70. 

23.2  14.8  62. 
49-6  23.7  26.7 

19-3  39-3  414 

9.8  19.8  70.4 

35.  50.8  14.2 

37-8  52.9  9.3 

37-5  53-2  9-3 

30.2  36.8  33. 

47.2  1 1.8  41. 

45-7  13-2  41-1 


Melting 
Temp. 


Crystalline  Phases. 


2065^ 

1610 
1810 

1299 

1359 
1165 

1545 
1547 
1345 
1552 
1512 

IS05 
1385 
1310 
1316 


CaAl2Si2O8 

Ca2Al2SiO7 

CaSiO3 

CaAl2Si208 

Ca2Al2SiO7 

A1203 

Ca2SiO4 

CaAl2O4 

Ca5Al6014 


%CaO    A12O3    SiO2 


38.         20.         42. 
29-2     39-        3!-8 
49-5     43-7        6.8 


Melting 
Temp. 


1265° 


1780 


1335 


QUINTUPLE  POINTS. 


Ca2Al2SiO7 

Ca3SiO7 

Ca2SiO4 

Ca2Al2SiO7 

Ca2SiO4 

CaAl2O4 

CaAl2Si2O8 

A12O3 

Al2SiO6 


Ca2Al2SiO7 
A1203 


48.2  11.9  39.9 

48.3  42.  9.7 

IS-6  36.5  47-9 

31.2  44.5  24.3 


1335 
1380 
1512 
H7S 


QUADRUPLE  POINTS. 


3CaO.2SiO2 
2CaO.SiO2 


55-5      —       44-5 


I47S 


of  S 

SMITHSONIAN  TABLES. 


ints  is  S  to  10  units.    Geophysical  Laboratory.     See  also  Day  and  Sosman,  Am.  J. 


TABLE  246.  227 

LOWERING   OF   FREEZING-POINTS    BY   SALTS   IN    SOLUTION. 

In  the  first  column  is  given  the  number  of  gram-molecules  (anhydrous)  dissolved  in  1000  grams 
of  water  ;  the  second  contains  the  molecular  lowering  of  the  freezing-point ;  the  freezing-point 
is  therefore  the  product  of  these  two  columns.  After  the  chemical  formula  is  given  the  molecular 
weight,  then  a  reference  number. 


rt  ti 
g.  mol. 

g.  mol. 

If 

js  if 

g.  mol.                5'g 

g.  mol. 

11 

1000  g.  H2O           J  | 

looo  g   H2O 

1J 

1000  g.  H2O           -3  | 

looo  g.  H2O 

ll 

Pb(N03)2,  331-0:  1,2. 

0.0500 

3-47° 

0.4978                 2.O20 

MgCl2,  95.26  :  6, 

'4 

0.000362             5.5° 

.1000 

3-42 

.8lI2                   2.01 

O.OIOO 

5-i° 

.001204             5.30 

.2000 

3-32 

1.5233                   2.28 

.0500 

4-98 

.002805             5.17 

.500 

3-26 

BaCl2,  208.3:  3,6,  13. 

.1500 

4.96 

.005570            4-97 

I.OOO 

3-14 

O.OO2OO                5.5° 

.3000 

5.186 

.01737               4.69 

LiNO3,  69.07  :  9. 

.00498                5.2 

.6099 

5-69 

.5015                 2.99 

0.0398 

3-4° 

.0100             5.0 

KC1,  74.60:  9,  17-19. 

Ba(NO.s),,  261.5:  i. 

.1671 

3-35 

.0200                  4.95 

0.02910 

3-54° 

0.000383             5.6° 

.4728 

3-35 

.04805                4.80 

.05845 

3-46 

.001259             5.28 

1.0164 

3-49 

.100              4.69 

.112 

3-43 

.002681             5.23 

A12(S04)3,  342.4  : 

10. 

.200                     4.66 

•3J39 

.005422             5.13 

0.0131 

5-6° 

.500                     4.82 

.476 

3-37 

.008352             5.04  i 

.0261 

4.9 

.586                     5.03 

I.OOO 

3.286 

Cd(N03)2,  236.5:  3. 

-0543 

4.5 

.750                     5.2I 

1.989 

3-25 

0.00298               5.4° 
.00689               5.25 

.1086 
.217 

4-03 
3-83 

CdCl2,  183.3:  3,14. 
0.00299             5.0° 

3.269 
NaCl,  58.50  :  3,  20 

3-25 

,  12,  l6. 

.01997               5.18 

•04873           S-15 

CdSO4,  208.5:  i,  ii. 
0.000704            3.35° 

.00690            4.8 
.0200               4.64 

0.00399 
.01000 

3-7° 
367 

AgNO3,  167.0:  4,  5. 
0.1506                 3.32° 

.002685 
.01151 

3-05 
2.69 

.0541               4.11 
.0818             393 

.0221 

.04949 

3-55 
3-51 

.5001             2.96  : 

.03120 

2.42 

•214              3-39 

.1081 

348 

.8645             2.87 

•1473 

2-I3 

.429              3.03 

.2325 

3-42 

1.749              2.27 

.4129 

1.  80 

.858              2.71 

.4293 

3-37 

2-953               1-85 
3.856              1.64 
0.0560             3.82 
.1401             3.58 
.3490             3.28 

KN03,  101.9:  6,7. 
O.OIOO                3.5 

.0200                   3.5 
.0500                    3.41 
.IOO                      3.31 

•7501 
1-253 

0.00200 
.00398 
.00865 
.O2OO 
.0500 
.1000 

.200 

1.76 

1.86 

6,^12. 

5-3 

4-9 
4.76 
4.60 

4-32 
4.07 

1.072               2.75 

CuCl2,  134.5  :  9. 
0.0350               4.9° 
•1337               4-8l 
.3380               4.92 
.7149               5-32 
CoCl,,  129.9  :  9- 
0.0276               5.0° 
.1094               4.9 

.700 

NH4C1,  53-52  :  6, 
O.OIOO 

.0200 
•0350 

.1000 

.2000 
.4000 
.7000 

3-43 

3-50 
3-43 
3-396 
3-393 
3-4i 

.200                      3.19 
.250                      3.08 

.  soo               2.94 

•454 
CuSO4,  159.7:  IM 

O.OOO286 

,  ii. 

•2369               5-03 
•4399             5-30 
•538               5-5 

LiCl,  42.48  :  9,  15 
0.00992 
•0455 

3-7° 
3-5 

^                                        o 

.750               2.81 

.000843 

3.15 

CaCl,,  m.o:  5,  13-16. 

.09952 

3-53 

i.ooo               2.66 

.002279 

3-°3 

0.0100             5.1° 

.2474 

3-50 

NaN03,  85.09:  2,6,7 
0.0100             3.6° 

.006670 
.01463 

2.79 
2-59 

.05028            4.85 
.1006             4-79 

.5012 
•7939 

3.61 
3-71 

.0250             3.46 

.1051 

2.28 

.5077             5-33 

BaBr2,  297.3:  14. 

.0500           3.44 

.2074 

1-95 

.946              5-3 

O.IOO 

5-!° 

.2000                    3-345 

•4043 

1.84 

2.432             8.2 

.150 

4.9 

.500           3.24 

.8898 

1.76 

3.469            11.5 

.200 

5.00 

.5OI5             3.30 

MgSO4,  120.4:  i, 

4,  ii. 

3.829            14.4 

,500 

5.18 

i.ooo                3.15 

0.000675 

3-29 

0.0478            5.2 

AlBr3,  267.0  :  9. 

1.0030           3.03 

.002381 

3.10 

.153             4-91 

0.0078 

1.4° 

NH4N03,  80.11  :  6,  8. 

0.0100              3.6° 

.0250         3.50 

.01263 
.0580 
.2104 

2.72 
2.65 
2.23. 

•331              5.i5 
.612              5.47 
.998              6.34 

•0559 
.1971 

•4355 

1.2 
1.07 
1.07 

i  Hausrath,  Ann.  Phys.  9,  1902. 
a  Leblanc-Noyes,  Z.  Phys.  Ch.  6,  1890. 
3  Jones,  Z.  Phys.  Ch.  ii,  1893. 
4  Raoult,  Z.  Phys.  Ch.  2,  1888. 

ii  Kahlenberg,  J.  Phys.  Ch.  5,  1901. 
ia  Abegg,  Z.  Phys.  Ch.  20,  1896. 
13  Jones-Getman,  Am.  Ch.  J.  27,  looa. 
14  Jones-Chambers,  Am.  Ch.  J.  23,  1900. 

5  Arrhenius,  Z.  Phys.  Ch.  2,  1888. 
6  Loomis,  Wied.  Ann.  57,  1896. 

15  Loomis,  Wied.  Ann.  60,  1897. 
16  Roozeboom,  Z.  Phys.  Ch.  4,  1889. 

7  Jones,  Am.  Chem.  J.  27,  1902. 

17  Raoult,  Z.  Phys.  Ch.  27,  1898. 

8  Jones-Caldwell,  Am.  Chem.  J.  25,  1901. 
9  Biltz,  Z.  Phys.  Ch.  40,  1902. 
10  Jones-Mackay,  Am.  Chem.  J.  19,  1897. 

/  *~»—«;i~J    C-~™    T  -*«J^1*-RX^nefoir 

18  Roloff,  Z.  Phys.  Ch.  18,  1895. 
19  Kistiakowsky,  Z.  Phys.  Ch.  6,  1890. 
20  Loomis,  Wied.  Ann.  51,  1894. 

-\f  AWArVlr^ffAr'c    PViuci1/alic/»Vi_/*ViAmic/«ViA  T-iKnll^n 

SMITHSONIAN  TABLES. 


228  TABLE  246  (.continued). 

LOWERING   OF    FREEZING-POINTS    BY    SALTS    IN    SOLUTION  (continue^. 


g.  mol. 
looo  g.  H2O 

Molecular  1 
Lowering.  1 

g.  mol. 

Molecular  1 
Lowering.  1 

g.  mol 
looo  g.  H2O 

Molecular  1 
Lowering.  1 

g  mol. 

Molecular  1 
Lowering.  1 

1000  g.  H2O 

looo  g.  H2O 

CdBr2,  272.3  :  3,  14. 

KOH,  56.16:  i,  15,23- 

Na,SiO3,  122.5  :  15- 

0.472 

2.20° 

0.00324 
.00718 

5-'° 
4.6 

0.00352 
.00770 

3-60° 
3-59 

0.01052 
•05239 

b.4" 

5.86 

•944 
1.620 

2.27 
2.60 

.03627 

3-84 

.O2OO2 

3-44 

.1048 

5i? 

(COOH)2,  90.02:  4,15. 

.0719 

3-39 

.05006 

3-43 

.2099 

4.66 

O.OIOO2 

3-3° 

.1122 

3.18 

.IOOI 

3-42 

.5233 

3-99 

.02005 

3-i9 

.220 

2.96 

.2003 

3-424 

HC1,  36-46  : 

.05019 

3-°3 

440 
.800 

2.76 
2.59 

.230 
•465 

3-50 
3-57 

1-3,  6,  13,   iS,  22. 

0.00305         3.68° 

.1006 
.2022 

2.83 
2.64 

CuBr,,  223.5  :  9. 

0.0242 

c.i° 

CH3OH,  32.03:  24,25. 
0.0  1  00                 1.8° 

.00695 

.OIOO 

3.60 
3-6 

2.56 
2.3 

.0817 
.2255 
.6003 

J 

5-i 

S-27 
5-89 

.0301 
.2018 
1.046 

1.82 
1.811 
1.86 

.01703 
.0500 
.1025 

3-59 
3-59 
3-56 

C3HB(OH)3,  92.06 

O.O2OO 
.1008 

24,25. 
1.86° 
1.86 

CaBr2,  200.0:  14. 
0.0871               5.1° 
.1742               5.18 

•3484            5-3° 
.5226            5.64 

MgBr.,,  184.28  :  14. 

0.6517            5-4° 

.103                 5.16 
.207                 5.26 
•517                  5-85 
KBr,  ng.i  :  9,  21. 

0.0305            3-6i° 
.1850            3.49 
.6801            3.30 
.250             3.78 

3-41 
6.200 

C2HSOH,  46.04: 
1,12,  17 

0.000402 
.004993 
.OIOO 
.02892 
.0705 
.1292 
.2024 

•5252 
1.0891 
1.760 
3.901 
7.91 

1.88 
1.944 

,  24-27 
1.67° 
1-67 
1.81 
1.707 
1.85 
1.829 
1.832 

1-834 
1.826 

1.83 
1.92 

2.02 

.2000                j.y/ 
.3000                3.612 
.464                   3.68 
.516                   3-79 
1-003                   3.95 
1.032                   4-IO 
1.500                   4.42 
2.OOO                    4.97 
2.II5                    4-52 
3.000                    6.03 
3.053                    4-90 
4.065                    5-67 
4<657                    6.19 
HN03,  63.05:  3,  13,  15. 
0.02004             3.55° 
•05015             3.50 

.2031 

•535 
2.40 

5-24 

(C2H5)20,  74-08: 
O.OIOO 
.0201 
.IOII 
.2038 
Dextrose,  180.1: 
0.0198 
.0470 
.1326 
.4076 
1.  102 

1.85 
1.91 
1.98 
2-13 

24i.6° 
1.67 

1.72 
1.702 

24,  30. 
1.84° 
1.85 
1.87 
1.894 
1.921 

.500 

J-5° 

II.  II 

2.12 

.0510 

3-7i 

Levulose,  180.1  : 

24,  25. 

CdL,  366.1  :  3,  5,  22. 

18.76 

I.8l 

.1004 

348 

0.0201 

1.87° 

0.00210 

4-5° 

O.OI73 

1.  80 

.1059 

3-53 

.2050 

1.871 

.00626 

4.0 

.0778 

1.79 

.2015 

3-45 

•554 

2.OI 

.O2O62 

S-S2 

K2C03,  138.30:6 

.250 

3-50 

1.384 

2.32 

.04857 

2.70 

O.OIOO 

5-i° 

.500 

3.62 

2-77 

3-04 

.1360 

2-35 

.0200 

4-93 

I.OOO 

3.80 

CHO,  342.2  :  i,  24,  26. 

•333 

2.13 

.O5OO 

4.71 

2.000 

4.17 

0.000332 

1.90° 

.684 

2.23 

.IOO 

4-54 

3-OOO 

4.64 

.001410 

1.87 

.888 

2.51 

.200 

4-39 

H8P02,  66.0:  29. 

.009978 

1.86 

KI,  166.0  :  g,  2. 

Na2CO3,  106.10:  6. 

0.1260 

2.90° 

.O2OI 

1.88 

0.0651 

3-5° 

O.OIOO 

5.1° 

.2542 

2-75 

•1305 

1.88 

.2782 
.6030 

3-50 
3-42 

.O2OO 
.0500 

4-93 
4.64 

.5171 

1.071 

2-59 
2-45 

H2S04,  98.08  : 

'3,  20 

3!-3.v 

1.003 

3-37 

.1000 

4.42 

HPO,  82  o  :  4,  5. 

0.00461 

4.8° 

SrI2,  341.3:  22. 

.2000 

4.17 

0.0745 

3-s° 

.OIOO 

4.49 

0.054 

S-i° 

Na,SO3,  126.2  :  28 

.1241 

2.8 

.0200 

4-32 

.108 

5-2 

"0.1044 

4-51° 

.2482 

2.6 

.0461 

4.10 

.216 

5-35 

•3397 

3-74 

I.OO 

2.39 

.IOO 

3-96 

•327 

5-52 

.7080 

3-38 

H3P04,98.o:  6,  22. 

.200 

3-85 

NaOH,  40.06:  15 

Na2HPO4,  142.1  : 

22,  29. 

O.OIOO 

2.8° 

.400 

3-98 

O.O2OO2 

3-45° 

O.OIOOI 

5-o° 

.0200 

2.68 

I.OOO 

4.19 

.05005 
.1001 

3-45 
3-4i 

.02003 
.05008 

4.84 
4.60 

.0500 

.1000 

2.49 
2.36 

1.500 

2.OOO 

4.96 
5-65 

.2000 

3-407 

.1002 

4-34 

.2000 

2.25 

2.500 

6-53 

24  Loomis,  Z.  Phvs.  Ch.  32,  1900. 

25  Abegg,  Z.  Phys.  Ch.  15,  1X94. 

26  Nernst-Abegg,  Z.  Phys.  Ch.  15,  1894. 

SMITHSONIAN  TABLES. 


27  Pictet-Altschul,  Z.  Phys.  Ch.  16,  1895. 

28  Earth,  Z.  Phys.  Ch.  9,  1892. 

29  Petersen,  Z.  Phys.  Ch.  n,  1893. 

30  Roth.  Z.  Phys.  Ch.  43,  1903. 

31  Wildermann,  Z.  Phys.  Ch.  15,  1894. 

32  Jones-Carroll,  Am.  Ch.  J.  28,  1902. 

33  Jones-Murray,  Am.  Ch.  J.  30,  1903. 


TABLE  247.  229 

RISE  OF  BOILING-POINT  PRODUCED  BY  SALTS  DISSOLVED  IN  WATER.* 

This  table  gives  the  number  of  grams  of  the  salt  which,  when  dissolved  in  100  grams  of  water,  will  raise  the  boil- 
ing-point by  the  amount  stated  in  the  headings  of  the  different  columns.  The  pressure  is  supposed  to  be  76 
centimeters. 


Salt. 

i°C 

2° 

3° 

4° 

5° 

7° 

10° 

16° 

20° 

25> 

BaCl2  +  2H2O    . 

15.0 

31-1 

47-3 

63-5 

(7i.6g: 

ves  4° 

5  rise 

of  temp 

.) 

CaCl2 

6.0 

"•5 

16.5 

21.0 

25-0 

32.0 

41.5 

55-5 

69.0 

84-5 

Ca(N03)2  4-  2H20     . 

12.0 

25-5 

39-5 

53-5 

68.5 

IOI.O 

I52-5 

240.0 

J3J-5 

443-5 

KOH           ... 

4-7 

9-3 

13.6 

17.4 

20.5 

26.4 

34-5 

47-o 

57-5 

67-3 

KC2H3O2    . 

6.0 

12.0 

1  8.0 

24-5 

31.0 

44.0 

63-5 

98.0 

134.0 

I7L5 

KC1     .... 

9.2 

I6.7 

23-4 

29.9 

36-2 

48.4 

(574  gives  a  rise  of  8°.  5) 

K2CO3 

11.5 

22.5 

32.0 

40.0 

47-5 

60.5 

78.5 

103-5 

127.5 

152.5 

KC1O3 

13.2 

27.8 

44.6 

62.2 

KI       . 

15.0 

30.0 

45-0 

60.0 

74-o 

99-5 

134- 

185.0 

(220  gives  i8°.5) 

KN03 

15.2 

31.0 

47-5 

64-5 

82.0 

120.5 

188.5 

338.5 

K2C4H4O6  +  £H2O 

18.0 

36.0 

54-0 

72.0 

90.0 

126.5 

182.0 

284.0 

KNaC4H406       . 

17.3 

34-5 

51.3 

68.1 

84.8 

119.0 

171.0 

272.5 

390.0 

510.0 

KNaC4H406  4-  4H20 

25-0 

53-5 

84.0 

118.0 

157-0 

266.0 

554-o 

5510-0 

LiCl    .... 

3-5 

7.0 

IO.O 

12.5 

15.0 

2O.O 

26.0 

35-o 

42-5 

50.0 

LiCl  4-  2H2O      . 

6-5 

13.0 

19-5 

26.0 

32.0 

44-o 

62.0 

92.0 

123.0 

160.5 

MgCl2  +  6H2O  . 
MgS04  +  7H2O 

1  1.0 

22.O 
87-5 

33-o 
138.0 

44-o 
196.0 

55-o 
262.0 

77.0 

I  IO.O 

170.0 

241.0 

334-5 

NaOH 

4-3 

8.0 

"•3 

14-3 

17.0 

22.4 

30.0 

41.0 

51.0 

60.1 

NaCl  .... 

6.6 

12.4 

17.2 

21-5 

25-5 

33-5 

(40.7 

rives  8°.8  rise) 

NaNO3 

9.0 

18.5 

28.0 

38.0 

48.0 

68.0 

99-5 

156.0 

222.O 

NaC2H3O2  +  3H2O   . 

14.9 

30.0 

46.1 

62.5 

79-7 

118.1 

194.0 

480.0 

6250.0 

Na2S2O3      . 

14.0 

27.0 

39-o 

49-5 

59-0 

77.0 

104.0 

152.0 

214.5 

311.0 

Na2HPO4   . 

17.2 

34-4 

5*4 

68.4 

85-3 

Na2C4H406  +  2H2O  . 
Na2S2O3  4-  5H2O 

21.4 
23.8 

44-4 
50.0 

68.2 
78.6 

93-9 

108.1 

121.3 
139-3 

183.0 
216.0 

(237-3  gives  8 
400.0  1  1765.0 

°.4rise) 

Na2CO3  +  ioH2O      . 

34-i 

86.7 

177.6 

369.4 

1052.9 

1 

Na2B4O7  4-  ioH2O     . 
NH4C1 

39- 
6.5 

93-2 

12.8 

254.2 
19.0 

24.7 

(5555-5 
29.7 

gives  4°.  5  ri. 
39.6     56.2 

>C  88.5 

NH4NO3     . 

IO.O 

2O.O 

30.0 

41.0 

52-0 

74-o 

108.0 

172.0 

248.0 

337-0 

NH4SO4     . 

15.4 

30.1 

44-2 

58.0 

71.8 

99.1 

(115.3  gives  108.2) 

SrCl2  +  6H2O    . 

20.0 

40.0 

60.0 

81.0 

103.0 

150.0 

234.0 

524.0 

Sr(N03)2     . 

24.0 

45-o 

63.6 

81.4 

97.6 

C4H606       . 

17.0 

34-4 

52.0 

70.0 

87.0 

123.0 

177.0 

272.0 

374-0 

484.0 

C2H2O4  -f  2H2O 

I9.O 

40.0 

62.0 

86.0 

II2.O 

169.0 

262.0 

540-0 

1316.0 

50000.0 

C6H807  4-  H20 

29.0 

58.0 

87.0 

1  1  6.0 

145.0 

208.0 

320.0 

553-o 

952.0 

Salt.                    40°        60° 

80° 

100° 

120° 

140° 

160°       180° 

200°      240° 

CaCl2  .        .        .    137.5     222.0 

314.0 

KOH   .        .        .      92.5      121.7 

152.6 

185.0 

219.8 

263.1 

312-5     375-0 

444.4    623.0 

NaOH          .        .93.5     150.8 

230.0 

345-c 

526.3 

800.0 

1  333-o  2353.0 

6452.0        - 

NH4NO8      .        .    682.0    1370.0 

2400.0 

4099.0 

8547.0 

00 

C4H6O6        .        .    980.0   3774.0 

[infinity  gives  170) 

I 

*  Compiled  from  a  paper  by  Gerlach, 
SMITHSONIAN  TABLES. 


Zeit.  f.  Anal.  Chem."  vol.  26. 


230 


TABLE  248. 
FREEZING   MIXTURES.* 


Column  i  gives  the  name  of  the  principal  refrigerating  substance,  A  the  proportion  of  that  substance,  B  the  propor- 
tion  of  a  second  substance  named  in  the  column,  C  the  proportion  of  a  third  substance,  D  the  temperature  of  the 
substances  before  mixture,  E  the  temperature  of  the  mixture,  F  the  lowering  of  temperature,  G  the  temperature 
when  all  snow  is  melted,  when  snow  is  used,  and  H  the  amount  of  heat  absorbed  in  heat  units  (small  calories  when 
A  is  grams).  Temperatures  are  in  Centigrade  degrees. 


Substance. 

A 

B 

C 

D 

E 

F 

G 

H 

NaC2H3O2  (cryst.) 

85 

H2O-ioo 

_ 

10.7 

—  4-7 

154 

_ 

_ 

NH4C1  . 

3° 

«       « 

— 

'3-3 

—  5-1 

18.4 

— 

.- 

NaNO8. 

75 

«       « 

— 

13.2 

—  5-3 

18.5 

_ 

._ 

Na2S2O8  (cryst.)    . 

no 

"       " 

- 

10.7 

-8.0 

18.7 

_ 

- 

KI. 

140 

«       K 

— 

10.8 

—  11.7 

22.5 

- 

— 

CaCl2  (cryst.) 
NH4N08       . 

250 
60 

«          u 

— 

10.8 
13.6 

-12.4 
—  13.6 

23.2 

27.2 

- 

- 

(NH4)2S04   .        . 

25 

;;    50 

NH4N03-25 

26.0 

- 

_ 

NH4C1  . 

25 

"          " 

— 

— 

22.0 

— 

_ 

CaCl2    . 

25 

«    « 

«          <« 

_ 

_ 

20.0 

_ 

_ 

KN08    . 

25 

«    « 

NH4Cl-25 

- 

_ 

2O.O 

_ 

_ 

Na2SO4 

25 

"    " 

"        " 

_ 

_ 

19.0 

_ 

_ 

NaNO8. 

25 

«    « 

«        .< 

_ 

_ 

17.0 

_ 

_ 

K2S04  . 

10 

Snow  100 

_ 



—  1-9 

0.9 

_ 

Na2CO3  (cryst.)     . 

20 

«            « 

_ 

— 

—  2.O 

1.0 

_ 

_ 

KNO3    . 

13 

"            " 

- 

— 

—  2.85 

1.85 

- 

- 

CaCl2    . 

3° 

«<            « 

_ 

— 

—  IO-9 

9-9 

_ 

_ 

NH4C1  . 
NH4NO8 
NaNO8  . 

25 
45 
50 

«            «< 

: 

— 

-15-4 
—  16.75 
—  17-75 

14.4 

1575 
16.75 

- 

- 

NaCl     . 

33 

<«            « 

— 

— 

—  21-3 

20.3 

— 

— 

"       1.097 

- 

— 

—  37-0 

36.0 

—  37-0 

0.0 

"       1.26 

— 

— 

—  36.0 

35-o 

—  30.2 

17.0 

H2SO4+H2O 
(66.i%H2S04) 

«       2'32 

"  4-32 

- 

— 

—  35-0 
—  30.0 
—  25.0 

34-o 
29.0 
24.0 

—  25.0 
—  12.4 
—  7-0 

27.0 
133-0 
273.0 

u  7-92 

— 

— 

—  2O.O 

19.0 

—  3-1 

553-o 

"  13.08 

- 

— 

—  16.0 

15.0 

—  2.1 

967.0 

;;  0.35 

- 

0 

- 

0.0 

52.1 

I9 

- 

o 

- 

- 

—  19.7 

49-5 

.61 

— 

0 

— 

- 

—  39-0 

40-3 

CaCl2  +  6H20      - 

«    .70 
«    .81 

_ 

0 
0 

: 

_ 

—  54-9t 
—  40-3 

30.0 
46.8 

"     I-23 

- 

o 

- 

- 

—  21.5 

88.5 

"     2.46 

— 

0 

— 

— 

—  9.0 

192.3 

"     4-92 

- 

0 

- 

- 

—  4.0 

392-3 

Alcohol  at  4°       j 
Chloroform    . 

77 

"  73 
CO2  solid 

- 

o 

—30.0 
—72.0 

—  77-° 

- 

- 

Ether     . 

_ 

«       « 

_ 

_ 

_ 

_ 

_ 

Liquid  SO2    . 

- 

«       « 

'  _ 

__ 

—  82.0 

_ 

_ 

_ 

H;0-.75 

- 

20 

- 

- 

33-0 

•94 

— 

20 

—  4.0 

— 

— 

2I.O 

«             (« 
«(             « 

- 

10 

—  4.0 

- 

- 

34-o 

— 

5 

—  4.0 

— 

— 

40-5 

Snow     " 

_ 

o 

—  4.0 

_ 

_ 

122.2 

NH4NO3       . 

H2O-i.20 

- 

10 

—  14.0 

- 

- 

17.9 

Snow     " 

— 

0 

—  14.0 

— 

_ 

1  29.  c 

H2O-i.3i 
Snow     " 

- 

10 
0 

-I7-5J 

- 

- 

s 

10.6 
131.9 

H2O-3.6i 

- 

10 

—  8.0 

- 

_ 

0.4 

Snow     " 

o 

—  8.0 

: 

327.0 

To*.CoemPiled  fr°m  the  results  of  Cailletet  and  Colardeau,  Hammerl,  Hanamann,  Moritz,  Pfanndler,  Rudorf,  and 

t  Lowest  temperature  obtained. 
SMITHSONIAN  TABLES. 


TABLE  249.  23 1 

CRITICAL  TEMPERATURES,  PRESSURES,  VOLUMES,   AND  DENSITIES  OF 

GASES.* 

0  =  Critical  temperature. 
p=  Critical  pressure  in  atmospheres. 

$  =  Critical  volume  referred  to  volume  at  o°  and  76  centimeters  pressure. 
d  =  Critical  density  in  grams  per  cubic  centimeter. 

a,  b,  Van  der  Waals  constants  in  (p  +  ^ J     fv  —  bj 


i  +  at. 


Substance. 

e 

p 

* 

d 

aX  io« 

bXio« 

Observer 

Air          ... 

—  140.0 

39-0 

_ 

_ 

257 

1560 

I 

Alcohol  (C2H6O)  . 

243.6 

62.76 

0.00713 

0.288 

3769 

2 

«        (CH40)    . 

239-95 

78.5 

— 

— 

1898 

2992 

3 

Ammonia 

130.0 

15.0 

- 

- 

798 

1606 

4 

Argon     . 

-"74 

52-9 

- 

- 

259 

1348 

S 

Benzol    . 
Bromine 

288.5 
302.2 

47-9 

0.00605 

0.305 
1.18 

3726 
1434 

5370 
2020 

I 

Carbon  dioxide 

31-2 

73- 

0.0044 

0.46 

717 

1908 

- 

"        monoxide  . 

—141.1 

35-9 

— 

— 

275 

1683 

7 

"        disulphide 

277.7 

78.1 

. 

- 

2197 

3227 

8 

Chloroform     . 
Chlorine 

260.0 
141.0 

54-9 
83-9 

_ 

— 

2930 
"57 

445° 
2259 

9 

4 

Ether      '.        '.        '. 

146.0 
197.0 

93-5 

35-77 

0.01584 

0.208 

1063 
3496 

2050 
6016 

10 

ii 

tt 

194.4 

0.01344 

0.262 

3464 

6002 

3 

Ethane   . 

32.1 

49.0 

— 

— 

1074 

2848 

12 

Ethylene 

Si-1 

- 

- 

886 

2533 

- 

Helium  . 

<—  268.0 

— 

- 

5 

700 

13 

Hydrogen 
"          chloride  . 

—240.8 
5T-25 

14. 
86.0 

— 

~ 

1 

880 
1726 

14 
IS 

«                " 

52-3 

86.0 

— 

0.61 

I731 

4 

"          sulphide  . 

IOO.O 

88.7 

- 

- 

888 

1926 

i 

Krypton 
Methane 

-62.5 
—81.8 

54-3 
54-9 

_ 

"* 

462 
376 

1776 
1557 

5 
i 

" 

—95-5 

50.0 

— 

— 

357 

1625 

4 

Neon      . 

<—  205.0 

29. 

— 

— 

— 

- 

5>i3 

Nitric  oxide  (NO)  . 

—93-5 

71.2 

— 

— 

257 

1160 

i 

Nitrogen 

—  146.0 

35-o 

- 

0.44 

259 

1650 

i 

"        monoxide 

(N20) 

35-4 

75.0 

0.0048 

0.41 

720 

1888 

4,17 

Oxygen  . 
Sulphur  dioxide      . 

—  118.0 
155-4 

50.0 
78.9 

0.00587 

0.6044 
0.49 

273 
1316 

1420 
2486 

i 

Water    . 

358-1 

— 

0.001874 

0.429 

— 

— 

6 

"... 

374- 

217-5 

" 

1089 

1362 

16 

(1)  Olszewski,  C.  R.  98,  1884;  99,  1884;  100, 

1885;   Beibl.  14,  1890;  Z.  Phys.  Ch.  16, 
1893. 

(2)  Ramsay-Young,  Tr.  Roy.  Soc.  177,  1886. 

(3)  Young,  Phil.  Mag.  1900. 

(4)  Dewar,  Phil.  Mag.  18, 1884 ;  Ch.  News,  84, 

1901. 

(5)  Ramsay,  Travers,  Phil.  Trans.  16,  17, 1901. 

(6)  Nadejdine,  Beibl.  9,  1885. 

(7)  Wroblewski,  Wied.   Ann.   20,   1883 ;   Stz. 

Wien.  Ak.  91,  1885. 

(8)  Hannay,  Pr.  Roy.  Soc.  32,  1882. 


(9)  Sajotschewsky,  Beibl.  3,  1879. 
(10)  Knietsch,  Lieb.   Ann.   259,  1890. 
(n)  Batelli,  Mem.  Torino  (2),  41, 1890. 

(12)  Cardozo,  Arch.  sc.  physio,  1910. 

(13)  Kamerlingh-onnes,     Comno.    Phys.  tab. 

Leiden,    1908,   1909,    Proc.   Amst.  II, 
1908,  C.  R.  147,  1908. 

(14)  Olszewski,  Ann.  Phys.  17,  1905. 
II  fl  Ansdell,  Chem.  News,  41,  1880. 

(16)  Holborn,  Baumann  Ann.  Phys.  31,  1910. 

(17)  Cailletet,  C.  R.  102, 1886;  104,  1887. 


•Abridged  for  the  most  part  from  Landolt  and  Bernstein's  "Phys.  Chem.  Tab." 


SMITHSONIAN  TABLES. 


232 


TABLE  250. 
LINEAR    EXPANSION   OF  THE    ELEMENTS. 


In  the  heading  of  the  columns  /  is  the  temperature  or  range  of  temperature  ;  C  is  the  coefficient 
of  linear  expansion  ;  A\  is  the  authority  for  C;  Mis  the  mean  coefficient  of  expansion  between 
o°  and  100°  C. ;  a  and  0  are  the  coefficients  in  the  equation  /t  =  /0  (i  +  of  +  |8/2)f  where  /0  is 
the  length  at  o°  C.  and  /«the  length  at  t°  C.  j  A2  is  the  authority  for  o,  £,  and  M. 


Substance. 

t 

CXio* 

*i 

MY.  10* 

aX  io< 

/3  X  xo« 

A, 

Aluminum        .... 

40 
600 

0.2313 

.71  =;o 

1 
7 

0.2220 

- 

- 

2 

« 

—  191  to  -}-i6 

.1871: 

4 

.27C76 

O07O7 

t 

Antimony: 
Parallel  to  cryst.  axis  . 
Perp.  to  axis 
Mean    
Arsenic    
Bismuth  : 
Parallel  to  axis     . 
Perp.  to  axis 
Mean    
Cadmium         .... 
Carbon: 
Diamond      .... 
Gas  carbon  .... 
Graphite       .... 
Anthracite    .... 
Cobalt      

"" 

40 
40 
40 
40 

40 
40 
40 
40 

40 
40 
40 
40 
40 
40 

.1692 
.0882 
.1152 
•0559 

.1621 

.1208 
.1346 
.3069 

.0118 

.0540 
.0786 
.2078 
.1236 
1678 

i 
i 
i 

i 

i 
i 
i 

i 

i 
i 
i 
i 

i 

.1056 

.1316 
•3159 

1666 

.0923 

.1167 
.2693 

•0055 

1481 

.0132 

.0149 
.0466 

.00l6 

oiSc; 

6 

6 

6 

13 
6 

—  191  to  -}-i6 

I4OQ 

16070 

OO4O7 

C 

Gold         

40 

IAA.1 

IA7O 

T  -jrR 

i 

AQ 

4I7O 

j 

-i  JJ0 

Iron  : 
Soft       

4O 

.I2IO 

i 

Cast      .  -     . 

Wrought                       !        ! 
Steel     

40 

—  191  to  +16 

—  18  to  100 

4O 

.Io6l 
.0850 
.1140 
I  7^2 

i 

4 
7 

_ 

.11705 

no  1  7  1 

.005254 
OO8  7  76 

8 
8 

"    annealed 
Lead 

40 

AQ 

.1095 
2Q'M 

i 
i 

.I089 
•>7OQ 

.1038 
277 

.0052 

I 

Magnesium      .... 
Nickel      .... 

40 

4O 

.2694 

1  27Q 

i 
j 

,~/uy 

•*/J 
I  7d6o 

OO77I  ^ 

8 

u 

—  191  to  -f-i6 

.IOI2 

4. 

•WOJL:> 

4O 

o6^7 

Palladium         .... 
Phosphorus      .... 
Platinum  

40 
0-40 
40 

.1176 
1.2530 

I 

10 

- 

.11670 
08868 

.002187 

OOI  724 

8 
8 

Potassium        .... 
Rhodium          .... 
Ruthenium       .... 

0-50 
40 
40 
4O 

.8300 
.0850 
.0963 
.3680 

II 
I 

I 
I 

6604 

12 

4O 

0767 

j 

Silver       

4O 

.IQ2I 

18270 

OO47Q7 

8 

« 

—191  to  -4-i6 

I7O4 

4' 

Sulphur  : 
Cryst.  mean  .... 
Tellurium         .... 
Thallium 
Tin  

40 
40 
40 

4O 

.6413 

.1675 
.3O2I 
2"*  74 

j 

I.lSo 
.3687 

T">C)6 

2O77 

0267 

12 
12 

6 

Zinc  

4O 

'**Jn 

2918 

-7Q7(3 

''741 

O/774 

6 

1  Fizeau.  4  Henning.  8  Holborn-Day. 

2  Calvert,  Johnson  5  Dittenberger.  9  Benoit. 

and  Lowe.  6  Matthiessen.  10  Pisati  and  De 

3  Chatelier.  7  Andrews.  Franchis. 

The  above  table  has  been  partly  compiled  from  the  results  published  by  Fizeau.  "Comptes  Rendus,"  vol  68  and 

Mattlnessen,  "Proc.  Roy.  Soc.,"  vol.  15. 

The  Holborn-Day  and  Day  and  Sosman  data  are  for  temperatures  from  20°  to  1000°  C.  The  Dittenberger,  o°  to  600°  C. 
SMITHSONIAN  TABLES. 


11  Hagen. 

12  Spring. 

13  Day  and  Sos- 

man. 


TABLE   251. 

LINEAR   EXPANSION   OF   MISCELLANEOUS  SUBSTANCES. 


233 


The  coefficient  of  cubical  expansion  may  be  taken  as  three  times  the  linear  coefficient,    t  is  the  temperature  or  range 
of  temperature,  C  the  coefficient  of  expansion,  and  A  the  authority. 


Substance. 

i 

CX  10* 

A. 

Substance. 

i 

CXio* 

A. 

Brass  : 

Platinum-silver  : 

Cast     . 

O-IOO 

0.1875 

I 

lPt+2Ag 

O-IOO 

0.1523 

4 

Wire    . 

" 

0.1930 

I 

Porcelain 

20-790 

0.0411 

—       ... 

" 

-1  783--  1  93 

2 

Bayeux    . 

1000-1400 

0-0553 

20 

7i.5Cu+27.7Zn+ 

Quartz  : 

40 

0.1859 

3 

Parallel  to  axis     . 

0-80 

0.0797 

6 

7iCu-}-29Zn 

O-IOO 

0.1906 

4 

u             U         « 

—  19010  +  16 

.0521 

21 

Bronze  : 

Perpend."     «       ! 

0-80 

0.1337 

6 

3Cu+iSn    . 

16.6-100 

0.1844 

5 

Quartz  glass    . 

—  19010+16 

—.0026 

13 

"        " 

16.6-350 

0.21  16 

5 

Rock  salt 

40 

0.4040 

3 

«        « 

16.6-957 

0.1737 

5 

Speculum  metal 

O-IOO 

0.1933 

i 

86.3Cu+9.7Sn+ 

Topaz  : 

40 

0.1782 

3 

Parallel  to  lesser 

97.6^4-  LhtrT 

0-80 

0.1713 

0.1708 

6 
6 

horizontal  axis 
Parallel  to  greater 
horizontal  axis 

u 

0.0832 

0.0836 

8 
8 

Caoutchouc 

_ 

.657-.686 

2 

Parallel  to  verti- 

"... 

16.7-25.3 

0.770 

7 

cal  axis 

" 

0.0472 

8 

Constantine     . 

4-29 

0.1523 

Tourmaline  : 

Ebonite    . 

25-3-354 

0.842 

7 

Parallel   to  longi- 

Fluor spar  :  CaF2  . 

O-IOO 

0.1950 

8 

tudinal  axis 

" 

0.0937 

8 

German  silver 

" 

0.1836 

8 

Parallel    to   hori- 

Gold-platinum : 

zontal  axis 

" 

0.0773 

8 

2Au+iPt 

" 

0.1523 

4 

Type  metal 

16.6-254 

0.1952 

5 

Gold-copper  : 

Vulcanite 

0-18 

0.6360 

22 

2Au+iCu 

« 

0.1552 

4 

Wedgwood  ware     . 

O-IOO 

0.0890 

5 

Glass  : 

Wood  : 

Tube    . 

" 

0.0833 

i 

Parallel  to  fibre  : 

"... 

" 

0.0828 

9 

Ash  . 

" 

0.0951 

23 

Plate    . 

« 

0.0891 

10 

Beech 

2-34 

0.0257 

24 

Crown  (mean) 

« 

0.0897 

10 

Chestnut  . 

«« 

0.0649 

24 

"... 

50-60 

0.0954 

1  1 

Elm  . 

" 

0.0565 

24 

Flint     . 

It 

0.0788 

ii 

Mahogany 

" 

0.0361 

24 

Jena  ther-     16™  ) 
mometer  normal  j 

O-IOO 

0.081 

12 

Maple       . 
Oak  . 

M 

0.0638 

0.0492 

24 

24 

59m     . 

u 

—  191  to+i6 

0.058 
0.424 

I2J 

Pine  . 
Walnut     . 

" 

0.0541 

0.0658 

24 
24 

Gutta  percha  . 

20 

1-983 

14 

Across  the  fibre  : 

Ice  . 

—  20  tO  —  I 

0.51 

15 

Beech 

«« 

0.614 

24 

Iceland  spar  : 

Chestnut  . 

" 

0-325 

24 

Parallel  to  axis     . 

0-80 

0.2631 

6' 

Elm  . 

" 

0.443 

24 

Perpendicular    to 

Mahogany 

M 

0.404 

24 

axis 

" 

0.0544 

6 

Maple 

" 

0.484 

24 

Lead-tin  (solder) 

Oak  . 

" 

0.544 

24 

2Pb+iSn 

o-ioo 

0.2508 

i 

Pine  . 

" 

0.341 

24 

Magnalium 

12-39 

0.238 

16 

Walnut     . 

" 

0.484 

24 

Marble     . 

15-100 

0.117 

T7 

Wax:  White  . 

10-26 

2.300 

25 

Paraffin    . 

0-16 

1.0662 

18 

H 

26-31 

3.120 

25 

"... 

16-38 

1.3030 

iS< 

(I 

3^43 

4.860 

25 

"... 

38-49 

4.7707 

18 

H 

43-57 

15.227 

25 

Platinum-iridium 

loPt+iIr 

40 

0.0884 

3 

i  Smeaton.               8  Pfaff.                                  14  Russner.             20  Deville  and  Troost. 

2  Various.                  9  Deluc.                                  15  Mean.                  21  Scheel. 

3  Fizeau.                  10  Lavoisier  and  Laplace.     16  Stadthagen.         22  Mayer. 
4  Matthiessen.         n  Pulfrich.                               17  Frohlich.             23  Glatzel. 

5  Daniell.                 12  Schott.                                18  Rodwell.             24  Villari. 

6  Benoit.                  13  Henning.                             19  Braun.                 25  Kopp. 

7  Kohlrausch. 

SMITHSONIAN  TABLES. 


234 


TABLE  252. 
CUBICAL  EXPANSION  OF  SOLIDS, 


If  z>z  and  z>i  are  the  volumes  at  fa  and  t\  respectively,  then  vi  =  v\  (i  +  C&t),  C  being  the 
coefficient  of  cubical  expansion  and  A/  the  temperature  interval.  Where  only  a  single  temperature 
is  stated  C  represents  the  true  coefficient  of  cubical  expansion  at  that  temperature.* 


Substance. 

t  or  b.t 

CX  io< 

Authority. 

Antimony    
Beryl        ... 

0-100 
O—  IOO 

0.3167 

00105 

Matthiessen 
Pfaff 

Bismuth  

O-IOO 

o.  1048 

Matthiessen 

Copper    . 

O-IOO 

0.4008 

« 

Diamond      .... 

40 

O  O?>4 

Fizeau 

Emerald  . 

dO 

00168 

Galena 

O—  IOO 

o  cc8 

Pfaff 

Glass,  common  tube  .     . 
hard  
"        Jena,  borosilicate 
59  III     .    .     . 
"        pure  silica  .     .     . 
Gold 

O-IOO 
O-IOO 

20-100 

0-80 

O—  IOO 

V*JJP 

0.276 
0.214 

0.156 
0.0129 

O  44.1  1 

Regnault 

Scheel 
Chappuis 

Ice 

—  >-"O  •      •! 

Iron    

O—  IOO 

O   •j  C  CO 

Lead 

O—  IOO 

V'JJJV 

O  8lQQ 

Paraffin   

20 

*j'°jyy 

s88 

Platinum      
Porcelain,  Berlin  .     .     . 
Potassium  chloride  .     . 
nitrate     .     . 
"            sulphate  .     . 
Quartz     
Rock  salt    

O-IOO 

20 

O-IOO 
O-IOO 
20 
O-IOO 
CQ—  6O 

5*oo 

0.265 
0.0814 

1.094 
1.967 

1.0754 
0.3840 

Dulong  and   Petit 
Chappuis  and  Harker 
Playfair  and  Joule 

Tutton 
Pfaff 

PnlfrirVi 

Rubber 

20 

A  8? 

Silver 

O    IOO 

4.07 

arQ-jr 

Sodium    

20 

553J 

2  I  l(*)A 

EfTQ_pn 

Stearic  acid  ... 

•37  8—  /ie  e 

8 

Sulphur,  native     .     .     . 
Tin      

oj>0  <+jo 
i3-2-5°-3 

O—  IOO 

O-IOO 

o  8028 

*  For  tables  of  cubical  expansion  complete  to  1876,  see  Clark's  Constants  of  Nature,  Smithsonian  Collections,  289. 
SMITHSONIAN  TABLES. 


TABLE  253. 
CUBICAL  EXPANSION  OF  LIQUIDS, 


235 


If  V0  is  the  volume  at  o°  then  at  t°  the  expansion  formula  is  Vt  =  Vp  (i  +  at+  ftp  -f  7^). 
The  table  gives  values  of  o,  /3  and  7  and  of  C,  the  true  coefficient  of  cubical  expansion,  at  20° 
for  some  liquids  and  solutions.  A/  is  the  temperature  range  of  the  observation  and  A  the 
authority. 


Liquid. 

AJ 

a  xo8 

ft  I0« 

yio" 

Cl03 

at  20° 

A 

Acetic  acid 
Acetone 
Alcohol  : 
Amyl 
Ethyl,  30%  by  vol.      . 
"       50%        " 
"      99-3%    "        • 
500  atmo.  press. 
'«     3000      " 
Methyl     

16-107 
o-S4 

—15-80 
18-39 

0-39 
27-46 
0-40 
0-40 
0-61 
11-81 
o-59 

18-25 
17-24 
—34-60 
0-50 
0-50 
0-76 
0-63 
-15-38 

o-33 

O-IOO 

0-33 

16-25 
36-157 

24-120 
0-29 
11-40 

0-30 
0-30 
—9-106 
o-33 

1.0630 
1.3240 

8.9001 
0.2928 
0.7450 
I.OI2 

0.866 
0.524 
1.1342 
1.17626 
1.06218 

0.07878 
0.42383 
1.13980 
0.940 
0.581 
1.18384 
1.10715 
1.51324 
0-4853 

0.4460 
0.18182 
0.6821 
1.4646 

0.2695 
0.8340 

0.8994 
0.3640 

0-3599 

0.2833 

0.5758 
0.9003 
—  0.06427 

0.12636 

3.8090 

0.6573 
10.790 

1.85 

2.20 

L3635 
1.27776 
1.87714 

4.2742 
0.8571 
1.37065 

0.89881 
4.66473 
2.35918 
0.4095 

O.2I5 
0.0078 
I.I405 

3-o93J9 

2.080 
0.10732 

1.396 
1.237 
1.258 

2.580 
—0.432 
J-9595 
8-5053 

1.0876 
-0.87983 

1.18458 
—11.87 
0.730 

0.8741 
0.80648 
—  0.30854 

I.9I225 

1-35*35 

-1.74328 
4.00512 

—  0.539 
1.6084 

0.4446 

—0.44998 
6.7900 

1.071 
1.487 

0.902 
1.  12 

I.I99 
1.237 
I.I32 

0.250 
0.458 

1.218 

1.236 

*-m 

1.656 

0.505 

0-455 
1.8186 
0.721 
i.  608 

0-353 
1.090 

0-955 
0.414 
0.410 

0.387 
0-558 
0-973 
0.207 

3 
3 

4a 
6 
6 
6 

i 
i 

5a 
5a 

2      ! 

7 
7 
4a 
i 

4b 
4b 
4a 
8 

9 
13 

10 

14 

7 
ii 

12 

9 
9 
9 

?b 

13 

Benzol    .              .... 

Bromine  

Calcium  chloride  : 
5.8%  solution    .     .     . 
40.9%        "         •     •    • 
Carbon  disulphide    .     .     . 
500  atmos.  pressure 
3000      " 
Carbon  tetrachloride    .     . 
Chloroform           • 

Ether  

Hydrochloric  acid  : 
33.2%  solution  .... 
Mercury           .                   . 

Olive  oil  
Pentane  

Potassium  chloride  : 
24.3%  solution  .... 
Phenol     

Petroleum  : 
Density  0.8467  .... 
Sodium  chloride  : 
20.6%  solution  .... 
Sodium  sulphate  : 
24%  solution     .... 
Sulphuric  acid  : 
10.9%  solution  .... 

I  CO  O%                 ... 

Turpentine  . 

Water 

AUTHORITIES. 
i.  Amagat:  C.  R.  105,  p.  1120;  1887.                   9.  Marignac:  Lieb.  Ann.,  Supp.  VIII,  p.  335  ; 
2.  Thorpe  :  Proc.  Roy.  Soc.  24,  p.  283;  1876.                    1872. 
3.  Zander:  Lieb.  Ann.  225,  p.  109;  1884.            10.  Spring:  Bull.  Brux.  (3)  3,  p.  331  ;  1882. 
4.  Pierre:  a.  Lieb.  Ann.  56,  p.  139;  1845.           IX-  Pinette:  Lieb.  Ann.  243,  p.  32;  1888. 
b.  Lieb.  Ann.  80,  p.  125;  1851.          12.  Frankenheim  :    Pogg.   Ann.   72,   p.  422; 
5.  Kopp:  a.  Lieb.  Ann.  94,  p.  257;  1855.                       1847. 
b.  Lieb.  Ann.  93,  p.  129;  1855.            13.  Scheel:  Wiss.  Abh.  Reichsanstalt,  4,  p.  i; 
6.  Recknagel  :  Sitzber.  bayr.  Ak.  p.  327,   2                   1903. 
Abt.  ;  1866.                                                    14.  Thorpe  and   Jones:    J.   Chem.  Soc.  63, 
7.  Drecker  :  Wied.  Ann.  34,  p.  952  ;   1888.                     p.  273  ;  1893. 
8.  Emo:  Ber.  Chem.  Ges.  16,  1857;  1883. 

SMITHSONIAN  TABLES. 


236 


TABLE    254. 
COEFFICIENTS  OF  THERMAL  EXPANSION, 

Coefficients  of  Expansion  of  Gases. 
Pressures  are  given  in  centimeters  of  mercury. 


Coefficient  at  Constant  Volume. 

Coefficient  at  Constant  Pressure. 

Coeffi- 

8 

Coeffi- 

g 

Substance. 

Pressure 
cm. 

cient 
X 

1 

Substance. 

Pressure 
cm. 

cient 
X 

1 

100. 

& 

IOO. 

K 

Air         ... 

.6 

.37666 

i 

Air         ... 

76. 

.3671 

3 

M 

1.3 

•37172 

M 

. 

257. 

•3693 

"                          ' 

10.0 

.36630 

u 

"    0°-IOO°     . 

IOO.I 

.36728 

2 

"      !     .     . 

254 

.36580 

" 

Hydrogen   o°-ioo° 

IOO.O 

.36600 

• 

"      ... 

75-2 

.36660 

" 

"... 

200  Atm. 

•332 

9 

"   0°-IOO°     . 

100.  1 

•36744 

2 

"... 

400     " 

-295 

"            ... 

76.0 

.36650 

3 

" 

600     " 

.261 

" 

"                      .          • 

200.0 

H 

H 

800     " 

.242 

" 

M 

2OOO. 

.38866 

" 

Carbon  dioxide 

76. 

•37To 

3 

"            ... 

1  0000. 

.4100 

" 

«      0°-20° 

51.8 

.37128 

2 

Argon    . 

ci«7 

.3668 

4 

"        «     o°-40° 

51.8 

.37100 

" 

Carbon  dioxide      . 

76.0 

•36856 

3 

"           '       0°-IOO° 

51.8 

•37073 

" 

"        " 

1.8 

.36753 

•       0°-20° 

99-8 

.37602 

" 

"        " 

5-6 

.36641 

" 

'       0°-IOO° 

99.8 

•37410 

" 

14 

74-9 

.37264 

" 

'       0°-20° 

137-7 

•37972 

" 

"    0°-20° 

51.8 

•36985 

2 

'       0°-IOO° 

137-7 

•37/03 

" 

"  o°-40° 

51.8 

.36972 

" 

•<        "    o°-7.5° 

2621. 

.1097 

6 

"    0°-IOO° 

51.8 

.36981 

" 

"  64°-  i  00° 

2621. 

•6574 

JM 

"    0°-20° 

99.8 

•37335 

" 

Carbon  monoxide  . 

76. 

.3669 

3 

"    0°-IOO° 

99-8 

.37262 

" 

Nitrous  oxide 

76. 

•3719 

"    0°-IOO° 

IOO.O 

•37248 

5 

Sulphur  dioxide     . 

76. 

•39°3 

u 

Carbon  monoxide  . 

76. 

.36667 

3 

"             « 

98. 

•3980 

M 

Helium  . 

56.7 

.3665 

4 

o°-ii9° 

76. 

.4187 

IO 

Hydrogen  i6°-i32° 

.0077 

6 

Water.      ;  |£~|j£ 

7£ 

.4189 

M 

"        i5°-i32° 

.025 

•3623 

M 

76. 

.4071 

" 

i2°-i85° 

47 

•3656 

" 

vapor      o  ortrto 

(J   —  -iUU 

76. 

•3938 

U 

M 

•93 

.37002 

i 

lo°-247° 

76. 

•3799 

" 

"... 

II.  2 

.36548 

" 

(i 

76.4 

•36504 

" 

0°-IOO° 

Nitrogen    13°-  13  2° 

IOO.O 

.06 

.36626 
.3021 

2 

6 

Thomson  has  given,  Encyc.  Brit.  "  Heat," 
the  following  for  the  calculation  of  the  ex- 

9°-i33° 

0°-20° 
0°-IOO° 

Oxygen  n°-i32°    . 

:;    ,9°o:;32:  • 

•53 

100.2 
IOO.2 
76. 
.007 

•25 

.3290 
.36754 
•36744 
.36682 
.4161 
.3984 

•3&-7T 

U 

2 

\ 

pansion,  E,  between  o°  and  100°  C.  Expansion 
is  to  be  taken  as  the  change  of  volume  under 
constant  pressure  : 
Hydrogen,  E  =  .3662(1  —  .00049  V/v), 
Air,             E  =  .3662(1  —  .0026  V  /v), 
Oxygen,      h  =  .3662(1  —  .0032   V/v), 

u 

•51 

T  n 

•3°3I 
•2668? 

Q 

Nitrogen,    E  =  .3662(1  —  .0031    V  /v  , 

M 

1.9 
18.5 

•3DO53 

o 

CO2             .£  =  .3662(1  —  .0164   V/v). 

a 

75-9 

36681 

" 

V/v  is  the  ratio  of  the  actual  density  of  the 

Nitrous  oxide 

76 

[3676 

3 

gas  at  o°  C  to  what  it  would  have  at  o°  C  and 

Sulph'r  dioxide  SO2 

76. 

•3845 

u 

i  Atm.  pressure. 

I  Meleander,  Wied.  Beibl.  14,  1890;  Wied.           5  Chappuis,  Arch.  sc.  phys.  (3),  18,  1892. 

Ann.  47,  1892.                                                      6  Baly-Ramsay,  Phil.  Mag.  (5),  38,  1894. 

2  Chappuis,  Trav.  Mem.  Bur.  Intern.  Wts.           7  Andrews,  Proc.  Roy.  Soc.  24,  1876. 

Meas.  13,  1903.                                                    8  Meleander,  Acta  Soc.  Fenn.  19,  1891. 

3  Regnault,  Ann.  chim.  phys.  (3)5,  1842.               9  Amagat,  C.  R.  in,  1890. 
4  Keunen-Randall,  Proc.  R.  Soc.  59,  1896.         10  Him,  Theorie  mec.  chaleur,  1862. 

SMITHSONIAN  TABLES. 


237 


TABLES  255-257. 

MECHANICAL  EQUIVALENT   OF    HEAT. 

TABLE  255.  —  Summary. 

Taken  from  J.  S.  Ames,  L 'equivalent  mecanique  de  la  chaleur,  Rapports  pre'sentes  au  congres 
international  du  physique,  Paris,  1900. 


Name. 

Method. 

Scale. 

Result. 

Temp.  °C. 

Joule 

Mechanical 

A  177 

16  c 

Mechanical 

^•A/  J 

4IQP 

*»*o 

IO 

•lyj 
4.187 

*S- 

4.181 

20. 

4.176 

2  5- 

Mechanical 

47872 

calory. 

Griffiths  .... 

Electrical   .     . 

(  Latimer-Clark  =  1.4342  vat  i5°C. 

4.198 

IS 

£2t 

/ 

4.192 

20. 

IT 

(  International  Ohm 

4.187 

25- 

(  Latimer-Clark  =  i.434ov.  at  15°  ) 

Schuster-Gannon 

Electrical  Eit. 

\    C.,  Elec.  Chem.  Equiv.  Silver  > 

4.1905 

I9.I 

(   =0.001  1  i8g                                  ) 

Callendar-Barnes 

Electrical  Eit. 

Latimer-Clark  =  I.4342V.  at  15°  C. 

4.179 

40. 

TABLE  256.-Reduced  to  Gram-calory  at  20°  0.  (Nitrogen  thermometer). 


Joule       . 

4.169  X 
4.181 

io7  ergs 
«<      « 

4.i69X  io7  ergs. 
4.181        "      « 

Rowland     .     .     . 

Griffiths.     .     .     . 

4.192 

«      « 

4.184 

«      «< 

Schuster-Gannon 

4.189 

«      « 

4.181 

«      <« 

Callendar-Barnes 

4.186 

<«      « 

4.178 

««      <« 

*  Admitting  an  error  of  i  part  per  1000  in  the  electrical  scale. 

The  mean  of  the  last  four  then  gives 

1  small  (20°  0)  calory  =  4.181  XlO7  ergs. 

i  small  (15°  C)  calory  —  4.185  X  io7  ergs  assuming  sp.  ht.  of  water  at  2o°=o.99go. 


TABLE  257 .—  Conversion  Factors  lor  Units  of  Work. 


Joules 
Watts  X 
sec. 
Volt-amp, 
per  sec. 

Small  15° 
Calories. 

Ergs. 

Kilo- 
gram- 
meters. 

Foot-poundals. 

Foot-pounds. 

i  joule  =  i  watt 
X  second 

I 

0.2389 

I0f 

i 

F 

2373 

^n 

gt 

i  small    15°    cal- 
ory = 

4.185 

I 

4.185  Xio7 

4.183 
g* 

99-31 

99.31 
gt 

i  erg  = 

10-7 

0.2389  Xio-7 

i 

xo-7 
g* 

2373  X  io-7 

2|p  x  io-7 

i  kilog.-meter  = 

g* 

0.2389g* 

g*Xio? 

I 

23-73E* 

23-73 

, 

.04214 

.01007 

421400. 

.04214 
g* 

i 

i 
gt 

i  loot-poundal  — 

i  foot-pound  = 

.O42i4gt 

.oioo7gt 

42i40ogt 

.04214 

gt 

i 

*  g  =  9.80  m.  per  sec.  per  sec.  at  latitude  45°,  sea  level, 
t  g  =  32. 2  ft.  per  sec.  per  sec.    "      "         "      "      " 


SMITHSONIAN  TABLES. 


238 


TABLE  258. 
SPECIFIC  HEAT  OF  THE  CHEMICAL  ELEMENTS, 


Element. 

Range  *  of 
Temperature, 
°C. 

Specific 
heat. 

»  8 

Element. 

Range  *  of 
Temperature, 

Specific 
heat. 

«  s 

Aluminum 

—  250 

0.1428 

i 

Iodine 

9-98 

00541 

25 

" 

0 

.2089 

" 

Iridium 

—  i86-  +  i8 

.0282 

26 

» 

IOO 

.2226 

" 

" 

18-100 

•°323 

" 

" 

250 

.2382 

" 

Iron,  cast  . 

20-100 

.1189 

27 

" 

|00 

•2739 

" 

"      wrought   . 

15-100 

.1152 

28 

M 

10-100 

.2122 

43 

. 

I  000-  I  200 

.1989 

" 

Antimony  . 

15 

.0489 

2 

<<            « 

500 

.176 

H 

" 

IOO 

•°5°3 

" 

"    hard-drawn 

0-18 

.0986 

29 

« 

200 

.0520 

" 

«       «         « 

20-100 

.1146 

" 

Arsenic,  gray    . 

O-IOO 

.0822 

3 

"              .        . 

—  185-  +20 

•0958 

4 

black  . 

O-IOO 

.0861 

Lanthanum 

O-IOO 

.0448 

15 

Barium 

—  l85-  +20 

.068 

4 

Lead 

15 

.0299 

2 

Bismuth    . 

—  186 

.0284 

'      •        > 

IOO 

.0311 

• 

. 

0 

.0301 

6 

u 

300 

•0338 

" 

. 

75 

.0309 

" 

"     '  fluid        ! 

10310 

•0356 

30 

. 

2O-IOO 

.0302 

7 

"         "  . 

"  360 

.0410 

" 

fluid  . 

280-380 

•0363 

8 

M 

18-100 

.03096 

43 

Boron 
Bromine,  solid  . 

O-IOO 

_78  20 

•3°7 
.0843 

9 
10 

Lithium     . 

16-256 

—  IOO 

.03191 
•5997 

fluid  . 

13-45 

.107 

ii 

"           . 

O 

•7951 

" 

Cadmium  . 

21 

•0551 

2 

" 

50 

.9063 

" 

. 

IOO 

.0570 

0 

" 

IOO 

1.0407 

" 

(i 

2OO 

•0594 

II 

" 

190 

J-3745 

" 

Caesium     . 

300 
0-26 

.0617 
.0482 

12 

Magnesium 

M 

—185-  +20 

60 

O.222 
.2492 

4 
7 

Calcium    . 

—185  f-20 

4 

" 

325 

•3235 

H 

M 

Carbon,  graphite 

0-181 
—5° 

.170 
.114 

13 
14 

• 

625 

2O-IOO 

•4352 
.2492 

, 

«              « 

.160 

Manganese 

60 

.1211 

1 

«              « 

977 

.467 

" 

325 

.1783 

1 

"       diamond 

—50 

•0635 

H 

. 

2O-  IOO 

.1211 

1 

" 

+  11 

•"3 

" 

—  IOO 

.0979 

3J 

"            " 

985 

•459 

" 

O 

.1072 

Cerium 

O-IOO 

.0448 

15 

" 

IOO 

•1143 

" 

Chlorine,  liquid 
Chromium 

0-24 

—200 

.2262 
.0666 

16 

17 

Mercury    . 

—185-  +20 
O 

.032 
•03346 

4 
3f 

" 

O 

.1039 

" 

"           . 

85 

.0328 

"         . 

IOO 

.1121 

" 

. 

IOO 

.03284 

2 

" 

600 

.1872 

u 

« 

250 

.03212 

" 

Cobalt       1 

—185-  +20 
500 

.086 
.1452 

4 
18 

Molybdenum     . 

—  185-  +20 
60 

.062 
.0647 

4 
7 

"                  . 

1000 

.204 

" 

" 

475 

.0750 

" 

<c 

—182-  +15 

.0822 

19 

" 

20-100 

.0647 

H 

. 

15-100 

.1030 

Nickel       . 

—185-  +20 

.092 

4 

Copper 

17 

.0924 

2 

M 

IOO 

.1128 

18 

« 

IOO 

.0942 

« 

" 

300 

.1403 

" 

.        . 

1^238 

.09510 

43 

*' 

500 

.1299 

" 

M 

900 

.1259 

20 

" 

IOOO 

.l6o8 

M 

" 

.0868 

21 

" 

18-100 

.109 

26 

Gallium,  liquid  . 

23-100 

to  113 

.0940 
.680 

22 

Osmium     . 
Palladium  . 

19-98 

-i86-+i8 

.03  1  1 

.0528 

10 

26 

"        solid    . 

12-23 

.079 

22 

"         ,        . 

O-IOO 

.0592 

24 

Germanium 
Gold  . 

O-IOO 
—  185-  +20 

•0737 
•033^ 

23 

4 

Phosphorus,  red 

0-1265 

0-51 

.0714 
.1829 

33 

. 

O-IOO 

.0316 

24 

"      yellow 

!3-36 

.202 

M 

Indium 

O-IOO 

.0570 

13 

• 

—  186-+20 

,.7S 

4 

See  opposite  page  for  References.        See  Table  260  for  supplementary  data. 

*  Where  one  temperature  alone  is  given,  the  "  true  "  specific  heat  is  given ;  otherwise,  the  "  mean  "  specific  heat. 
SMITHSONIAN  TABLES. 


TABLES  258  (continued)  -259. 
SPECIFIC    HEAT. 

TABLE  258.  — Specific  Heat  of  the  Chemical  Elements  (continued). 


239 


Element. 

Range  *  of 
Temperature,  °C. 

Specific 
Heat. 

Refer- 
ence. 

Element. 

Range  *  of 
Temperature,  °C 

Specific 
Heat. 

Refer- 
ence. 

Platinum    . 

—  I86-+I8 

0.0293 

26 

Sulphur     .... 

-I88-+I8 

0.137 

36 

" 

o-ioo 

.0323 

24 

rhombic  . 

0-54 

.1728 

33 

•• 

IOO 

.0275 

34 

monoclin  . 

0-52 

.1809 

«• 

500 

.0356 

35 

liquid  .     . 

H9-I47 

•235 

2 

" 

700 

.0368 

Tantalum     .    .     . 

—  185-+20 

.033 

4 

*• 

900 

.0380 

H 

1400 

0.043 

«•           \ 

I  IOO 

.0390 

Tellurium     .    .     . 

-I88-+I8 

.047 

36 

«• 

1500 

.0407 

crys.  .     . 

15-100 

.0483 

37 

)) 

500 

.0335 
.0358 

Thallium  .... 

—  185-+20 

2O~IOO 

.038 

4 

« 

1500 

.0368 

Thorium  .... 

O-IOO 

.0276 

38 

•p  ,      .  * 

jgr  1~2O 

T'TA 

- 

Tin  

—  196  79 

.0486 

26 

ouTcf-          ' 

•  I/1-' 

4 

—  76  (_  jg 

IvJlOCllUni      . 

Ruthenium 

IO—97 
O-IOO 

.0611 

13 

"  cast     .... 

21-109 

.0551 

30 

Selenium    . 

-i88-+i8 

.068 

36 

"  fluid    .... 

250 

.05799 

18 

Silicon 

—  I85-+  20 

.123 

4 

"      "       .... 

IIOO 

.0758 

" 

-39-8 

.1360 

14 

Titanium.    .    .    . 

—  185-+  20 

.082 

4 

• 

+  57-1 

.1833 

" 

**         .... 

O-IOO 

.1125 

39 

«    '         | 

232 

.2029 

•• 

Tungsten  .... 

—  185-+20 

.036 

4 

Silver 

-186  —  79 

.0496 

26 

"         .... 

O-IOO 

•0336 

40 

. 

-79-+  18 

•0544 

" 

"         .... 

IOOO 

0.044 

— 

t 

o-ioo 

.0559 

13 

Uranium  .... 

0-98 

.028 

41 

- 

23 

.05498 

2 

Vanadium     .    .    . 
Zinc.    .    .    . 

O-IOO 
—  192—  +2O 

•  0836 

40 

27 

' 

soo 

.0581 

2O—  IOO 

,OQ3  1 

"»   e  T 

*J 

•I 

O—  IOO 

13 

800 

f~ 

18 

« 

IOO 

OCKI 

2 

'fluid  '. 

on*?—  T  ton 

O748 

M 

300 

•  uyo-i 
•  1040 

Sodium  .    . 

yu  /    iiuu 
—  185-+20 

'253 

4 

Zirconium     .    .    . 

O-IOO 

.0660 

42 

1  Bontschew. 

2  Naccari,  Atti  Torino,  23,  1887-88. 

3  Wigand,  Ann.  d.  Phys.  (4)  22,  1907. 

4  Nordmeyer-Bernouli,  Verh.  d.  phys.  Ges.  9,  1907 ;  10, 

1908. 

5  Giebe,  Verh.  d.  phys.  Ges.  5,  1903. 

6  Lorenz,  Wied.  Ann.  13,  1881. 

7  Stucker,  Wien.  Ber.  114,. 1905. 

8  Person,  C.  R.  23,  1846;  Ann.  d.  chim.  (3)21,  1847; 

24, 1848. 

9  Moisson-Gautier,  Ann.  chim.  phys.  (7)  17,  1896. 

10  Regnault,  Ann.  d.  chim.  (3)  26,  1849  ;  63,  1861. 

11  Andrews,  Pog.  Ann.  75,  1848. 

12  Eckardt-Graefe,  Z.  Anorg.  Ch.  23,  1900. 

13  Bunsen,  Pogg.  Ann.  141,  1870;  Wied.  Ann.  31,  1887. 

14  Weber,  Phil.  Mag.  (4)  49,  1875. 

15  Hillebrand,  Pog.  Ann.  158,  1876. 

16  Knietsch. 

17  Adler,  Beibl.  27,  1903. 

18  Pionchon,  C.  R.  102-103,  1886. 

19  Tilden,  Phil.  Trans.  (A)  201,  1903. 

20  Richards,  Ch.  News,  68,  1893. 

21  Trowbridge,  Science,  8,  1898. 

*  When  one  temperature  alone  is  given,  the  "  true  "  specific  heat  is  given  ;  otherwise,  the  "  mean  "  specific  heat. 
Compiled  in  part  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabelleu. 


22  Berthelot,  Ann.  d.  chim.  (5)  15,  1878. 

23  Pettersson-Hedellius,  J.  Pract.  Ch.  24,  1881. 

24  Violle,  C.  R.  85,  1877;  87,  1878. 

25  Regnault,  Ann.  d.  chim.  (2)  73,  1840;  (3)  63,  1861. 

26  Behn,  Wied.  Ann.  66,  1898 ;  Ann.  d.  Phys.  (4)  i,  1900. 

27  Schmitz,  Pr.  Roy.  Soc.  72,  1903. 

28  Nichol,  Phil.  Mag.  (5)  12,  1881. 

29  Hill,  Verh.  d.  phys.  Ges.  3,  1901. 

30  Spring,  Bull,  de  Belg.  (3)  n,  1886;  29,  1895. 

31  Laemmel,  Ann.  d.  Phys.  (4)  16,  1905. 

32  Barnes-Cooke,  Phys.  Rev.  16,  1903. 

33  Wiegand,  Fort.  d.  Phys.  1906. 

34  Tilden,  Pr.  Roy.  Soc.  66,  1900,  71,  1903 ;  Phil.  Trans. 

(A)  194,  1900;  201,  1903. 

35  White,  Phys.  Rev.  28,  1909. 

36  Dewar,  Ch.  News,  92,  1905. 

37  Kopp,  Phil.  Trans.  London,  155,  1865. 

38  Nilson,  C.  R.  96,  1883. 

39  Nilson- Pettersson,  Zt.  phys.  Ch.  i,  1887. 

40  Mache,  Wien.  Ber.  106,  1897. 

41  Blumcke,  Wied.  Ann.  24,  1885. 

42  Mixter-Dana,  Lieb.  Ann.  169,  1873. 

43  Magnus,  Ann.  d.  Phys.  31,  1910. 


TABLE  259.  — Specific  Heat  of  Water  and  of  Mercury. 


Specific  Heat  of  Water. 

Specific  Heat  of  Mercury. 

Temper- 
ature,°C. 

Barnes. 

Rowland. 

Barnes- 
Regnault. 

Temper- 
ature,°C. 

Barnes 

Barnes- 
Regnault. 

Temper- 
ature,°C. 

Specific 
Heat. 

Temper- 
ature,°C. 

Specific 
Heat. 

—5 

I.OI55 

_ 

_ 

60 

0.9988 

0.9994 

0 

0.03346 

90 

0.03277 

o 

1.0091 

1.0070 

1.0094 

65 

.9994 

1  .0004 

5 

.03340 

IOO 

.03269 

+  5 

1.0050 

1.0039 

1.0053 

70 

1.  0001 

1.  0015 

10 

.03335 

no 

.03262 

10 

1.0020 

1.0016 

1.0023 

80 

1.0014 

1.0042 

15 

.03330 

120 

.03255 

15 

1  .0000 

1.  0000 

1.0003 

90 

1.0028 

1.0070 

20 

•03325 

130 

.03248 

20 

0.9987 

•9991 

0.9990 

IOO 

1.0043 

I.OIOI 

25 

.03320 

140 

.03241 

25 

.9978 

.9989 

.9981 

120 

1.0162 

30 

.03316 

ISO 

.0324 

30 

.9973 

•9990 

•9976 

140 

— 

1.0223 

35 

.03312 

170 

.0322 

35 

•9971 

•9997 

.9974 

160 

- 

1.0285 

40 

.03308 

190 

.0320 

40 

•9971 

1.0006 

•9974 

1  80 

— 

1.0348 

50 

.03300 

210 

.0319 

45 

•9973 

I.OOI8 

•9976 

200 

— 

1.0410 

60 

.03294 

— 

50 

•9977 

1.0031 

.9980 

220 

- 

1.0476 

70 

.03289 

- 

- 

55 

.9982 

1.0045 

.9985 

" 

: 

80 

.03284 

' 

" 

Barnes's  results  :  Phil.  Trans.  (A)  199,  1902;  Phys.  Rev.  15,  1902;  16,  1903.     (H  thermometer.) 

Bousfield,  Phil.  Trans.  A  211,  p.  199,  1911.  Barnes-Regnault's  as  revised  by  Peabody  ;  Steam  Tables. 

The  mercury  data  from  o°  C  to  80,  Barnes-Cooke  ( H  thermometer);  from  90°  to  140,  mean  of  Winklemann,  Naccari 

and  Milthaler  (air  thermometer);  above  140°,  mean  of  Naccari  and  Milthaler. 


SMITHSONIAN  TABLES. 


240 


TABLES  260,  261 . 
TABLE  260.  —  Additional  Specific  Heats  of  the  Chemical  Elements. 


Element. 

Temperature. 

Sp.  Heat. 

"If 

Element. 

Temperature. 

Sp.  Heat. 

j! 

Aluminum 

—240.6° 

0.0092 

I 

Lithium      .    . 

—  191  80 

0.521 

2 

—  190.0 

.0889 

" 

—78-0 

•595 

M 

—  190  82 
—76  1 

.1466 
.1962 

2 

Manganese 

—  188  —  79 

.629 

.0820 

It 

4 

+  16  —  hioo 

.2122 

3 

—79-+  15 

.1091 

" 

+16-4-304 

.2250 

Mercury,  sol. 

—77  —  42 

.0329 

2 

Boron    .     .     . 
Bromine     .     . 

—191—78 
—  76-0 
—  192  —  80 

.0707 
.1677 
.O7O2 

2 

4 

liq. 
Potassium 

-3^—3 
—  191  —  80 
—78-0 

•0334 
.1568 
.1666 

<t 
u 

2 

Carbon,  graph. 

—191  —  79 

•0573 

2 

Sodium      .     . 

—191  —  83 

.243 

" 

—  76-0 

•1255 

" 

—77-0 

.276 

" 

—  Ache,  graph. 

—244.0 

.005 

6 

Zinc       .    .    . 

—  190  —  82 

.0792 

M 

—186.0 

.027 

u 

—  76-2 

.0906 

M 

—  Diamond    . 

—79  —  3 

.0720 

2 

Iron       .    .    . 

0-4-200° 

•1175 

5 

Copper       .     . 

—249-5 

•0035 

I 

0-4-300 

.1233 

u 

—185.0 

.0532 

" 

o  —  1-400 

.1282 

14 

—190  —  83 

.0720 

2 

0-4-500 

.1338 

" 

-76-0 

.0878 

" 

0-4-600 

.1396 

U 

+  15-4-238 

.0951 

3 

o  —  (-700 

.1487 

" 

Iodine    .     .    . 

—90-4-17 

.0485 

4 

0-4-800 

•J597 

M 

—191  —  80 

•0454 

" 

o  —  [-900 

.1644 

u 

Lead      .    .    . 

—77—3 

.0303 

2 

0  —  f-IOOO 

•J557 

K 

4-18-4-100 

.0310 

3 

o-4-iioo 

•!534 

It 

+  16-4-256 

.0319 

M 

i.  Nernst,  Lindemann,  1910,  1911.                    4.  Estreicher,  Straniewski,  1912. 

2.  Kosef,  Ann.  der  Phys.  36,  1911.                    5.  Harker  —  Proc.  Phys.  Soc.,   London,  19, 
3.  Magnus,  Ann.  der  Phys.  31,                              p.  703,  1905.  Fe  =  .oiC,  .O2Si,  .038,  .04?, 
1910.                                                                      trace  Mn. 

TABLE  261.  —Mean  Specific  Heats  of  Quartz,  Silica  Glass,  and  Platinum  from  zero,  C.,  to  the  tem- 
perature named. 

The  mean  specific  heats  of  quartz  above  550°  are   here  increased  by   the  heat  (2.3  calories)  of 
the  inversion  at  575°.     The  accuracy  is  probably  better  than  2  per  mille. 


Interval. 

Quartz. 

Silica  Glass. 

Platinum. 

Obs.—  calculated  for  Pt. 

0-100° 

.1870 

.1845 

__ 

^_ 

0-300° 

.2169 

.2124 

.03283 

.00000 

0-500° 

.2382 

•2303 

•03363 

4-  .000  1  2 

0-550° 

.2441 

— 

— 

0-600° 

.2520 

— 

— 

— 

0-700° 

•255.S 

•2433 

.03424 

-{-.00005 

0-900° 

.2608 

.2523 

.03487 

.00000 

0-1100° 

.2654 

•03551 

—  .00004 

0-1300° 

~ 

.03620 

—  .00003 

The  results  for  Platinum  follow  the  formula  : 

Sp.  Heat  =  .03174  4-  .000    0034  6  very  closely.     If  the  formula  were  strictly  correct  the  true 
specific  heat  at  any  temp,  would  be  :  .03174  +.000  006  86,  which  is  probably  true  to  i%  as  it  is. 

Determinations  by  W.  P.  White.    Geographical  Laboratory. 
SMITHSONIAN  TABLES. 


TABLES  262-263. 
TABLE  262.  -Specific  Heat  of  Various  Solids.* 


241 


Solid. 

Temperature 

$c. 

Specific  Heat. 

Authority,  t 

Alloys  : 
Bell  metal                         ;        

ic-g8 

00858 

R 

o 

.08001 

L 

"       yellow    

o 

.08831 

« 

80  Cu-f-2o  Sn    

14-08 

.0862 

R 

88.7  Cu-f  11.3  Al       
German  silver  
Lipowitz  alloy:   24.97  Pb  +  10.13  Cd  +  5°-66  Bi 
+  14.24  Sn         .... 
"            " 
Rose's  alloy  :  27.5  Pb+48.9  61+23.6  Sn 

Wood's  alloy  :   25.85  Pb  +  6.99  Cd  +  52.43  Bi  + 

14-73  Sn  
"           "        (fluid)       

20-100 
O-IOO 

5-50 

100-150 
—77-20 

20-89 
5-50 

100-150 

.10432 
.09464 

•0345 
.0426 

.0356 
.0552 

.0352 

.O42O 

Ln 
T 

M 
« 

S 

«« 

M 
a 

Miscellaneous  alloys  : 
17.5  Sb+29-9  Bi-j-i8.7  Zn+33-9  Sn 
37.1  Sb-j-62-9  Pb      

20-99 
10-08 

.05657 
.03880 

R 

mo  Pb+6o.i  Bi 

^  y 

IO-QQ 

.O7l6s 

P 

«     (fluid)      

144—  7t;8 

.01  soo 

« 

63.7  Pb+36.3  Sn       
46.7  Pb+53-3  Sn       
63  8  Bi+36.2  Sn       

12-99 
10-99 

2O-QQ 

.04073 
.04507 

.04001 

R 

« 

46.9  Bi+53.i  Sn                .   *     
Gas  coal        

20-99 
20-1040 
19-100 

.04504 

•3I45 

«« 
W 

"      French  hard  thermometer         .... 
"      crown         
"      flint    

10-50 
10-50 

!i6i 
.117 

Z 

H  M 
« 

Ice        

—  !88  252 

.146 

D 

« 

_78  1  88 

.285 

«« 

n 

India  rubber  (Para)      
Paraffin          

—  18  78 

P-IOO 
—  2O  r-7. 

/--* 
463 

.481 
.3768 

M 

G-T 
R  W 

i    J 
—  IQ  h2O 

•  t>2Cl 

« 

« 

O-2O 

J    •> 
.6970 

« 

<( 

7S-4O 

.622 

B 

«       fluid  

66-63 

.712 

« 

2O-IOO 

.7712 

A  M 

TABLE  263.  — Specific  Heat  of  Various  Liquids.' 


Liquid. 

Temper- 
ature °C. 

Specific 
Heat. 

Author- 
ity. 

Liquid. 

Temper- 
ature °C. 

Specific 
Heat. 

Author- 

ity.t 

Alcohol,  ethyl  . 

—  20 

0 

0-5053 
•S48 

R 

Nitrobenzole 
Napthalene,  CioH8 

28 
80-85 

0.362 
.396 

A 

B 

"             "... 

40 

.648 

" 

t« 

90-95 

.409 

"        methyl 

5-10 

•590 

" 

Oils  :  castor  . 

434 

W 

Anilin       .... 

15-20 
15 

.601 

G 

citron  . 
olive    . 

li 

438 

.471 

H  W 

"           .... 

30 

.520 

M 

sesame 

- 

.#7 

W 

"           .... 

5° 

•529 

turpentine 

0 

.411 

R 

Benzole,  C6He. 

10 

•340 

H-D 

Petroleum 

21-58 

•511 

Pa 

"         .... 

40 

423 

M 

Toluol,  C6H8 

IO 

.364 

H-D 

tt 

65 

.482 

" 

" 

65 

490 

" 

Diphenylamine,  C^HnN 

53 
65 

.464 
.482 

B 
it 

CaCl2,  sp.gr.  1.14 

•534 
.764 

DMG 

Ethyl  ether 

o 

•529 

R 

a            ft        K 

o 

•775 

" 

Glycerine 

15-50 

E 

«            tt        « 

+  20 

.787 

M 

Nitrobenzole    . 

14 

•350 

A 

"                "        1.20 

—  20 

.695 

*  These  specific  heat  tables  are  compiled  partly  from  more  extended  tables  in  Landolt-Bornstein-Meyerhoffer's  Tables. 
t  For  references  see  Table  263,  page  242. 
SMITHSONIAN  TABLES. 


TABLES  263 
TABLE  263.  —Specific  Heat  of  Various  Liquids. 


Liquid. 

Tempera- 
ture °C. 

Specific 
Heat. 

Author- 
ity. 

Liquid. 

Tempera-]  Specific 
ture°C.  j   Heat. 

Author- 
ity. 

CaCl2,  sp.  gr.  1.20  . 

O 

0.712 

DMG 

KOH  +  30  H2O  . 

18 

0.876 

TH 

U                               »4                   (« 

+  20 

•725 

el 

"       +  100    "      . 

18 

•975 

" 

"               1.26. 

—  2O 

.651 

u 

NaOH  +  50  H20 

18 

.942 

" 

«                              it                   « 

O 

.663 

U 

«        +100     "   . 

18 

•983 

u 

«(                              «                   «< 

+  20 

.676 

11 

NaCl  +  10  H2O  . 

18 

.791 

tt 

CuSo4+5oH2O     ! 

12-15 

.848 

Pa 

"       +200     "      . 

18 

.978 

u 

"        +200    " 

12-14 

•951 

u 

Sea  water,  sp.  gr.  1.0043 

17-5 

.980 

4< 

••      +400  "         . 

I3-1  7 

•975 

14 

"         "      1.0235 

17.5 

•938 

" 

ZnS04+50  H20    . 

20-52 

.842 

Ma 

«        "         "      1.0463 

17-5 

•903 

« 

"         +200    "         . 

20-52 

•952 

A,  Abbot.                        DMG,  Dickinson,  Mueller,  and  George.           T,  Tomlison. 

AM,  A.  M.  Mayer.          H-D,  de  Heen  and  Deruyts.                               S,  Schiiz. 

B,  Batelli.                        HM,  H.  Meyer.                                                     Th,  Thomsen. 

D,  Dewar.                        L,  Lorenz.                    P,  Person.                          W,  Wachsmuth. 

E,  Emo.                           Ln,  Luginen.               Pa,  Pagliani.                     Wn,  \Vinkelmann. 

G,  Griffiths.                     M,  Mazotto.                R,  Regnault.                     Z,  Zouloff. 

G-T,  Gee  and  Terry.      Ma,  Marignac.            RW,  R.  W.  Weber. 

TABLE  264.  -Specific  Heat  of  Minerals  and  Rocks. 


Substance. 

Tempera- 
ture °  C. 

Specific 
Heat. 

Refer- 
ence. 

Substance. 

Tempera- 
ture °  C. 

Specific 
Heat. 

Refer- 
ence. 

Andalusite 

O-IOO 

0.1684 

I 

Rock-salt 

J3~45 

0.219 

6 

Anhydrite,  CaSO4 

0-100 

•!753 

I 

Serpentine    . 

16-98 

.2586 

2 

Apatite  .... 
Asbestos 

15-99 
20-98 

.1903 
•I9S 

2 

3 

Siderite 
Spinel  . 

9-98 

15-47 

•J934 
.194 

I 

Augite  .... 

20-98 

•J931 

3 

Talc      . 

20-98 

.2092 

3 

Barite,  BaSO4 

10-98 

.1128 

4 

Topaz  . 

O-IOO 

.2097 

i 

Beryl      .... 

l$-99 

.1979 

2 

Wollastonite 

I9-51 

.178 

6 

Borax,  Na2B4O7  fused 

16-98 

.2382 

4 

Zinc  blende,  ZnS  . 

o-ioo 

.1146 

i 

Calcspar,  CaCO3  . 

0-50 

.1877 

i 

Zircon  . 

21-51 

.132 

6 

«               « 

O-IOO 

.2005 

i 

Rocks  : 

"         "     ! 

0-300 

.2204 

i 

Basalt,  fine,  black 

I2-IOO 

.1996 

6 

Casiderite,  SnO8    . 

16-98 

•0933 

4 

««                   44                   « 

20-470 

.199 

9 

Corundum 

9-98 

-.1976 

4 

««                   <(                   (« 

470-750 

•243 

9 

Cryolite,  Al2Fl6.6NaF  . 

16-99 

.2522 

2 

«                U                {< 

750-880 

.626 

9 

Fluorite,  CaF2 

J5~99 

.2154 

4 

««            «            « 

880-1190 

•323 

9 

Galena,  PbS  . 

O-IOO 

.0466 

5 

Dolomite     . 

20-98 

.222 

3 

Garnet   .... 

16-100 

•1758 

2 

Gneiss 

17-99 

.I96 

10 

Hematite,  Fe2Os  . 

lS-99 

.1645 

2 

" 

17-213 

.214 

10 

Hornblende  .         .         . 

20-98 

•  i952 

3 

Granite 

12-100 

.192 

7 

Hypersthene  . 

20-98 

.1914 

3 

Kaolin 

20-98 

.224 

3 

Labradorite 

20-98 

.1949 

3 

Lava,  Aetna 

23-IOO 

.201 

ii 

Magnetite 

18-45 

.156 

6 

«          « 

31-776 

•259 

ii 

Malachite,CuoC  O4.H2O 

J5-99 

.1763 

2 

"       Kilauea    . 

25-100 

.197 

ii 

Mica  (Mg)      . 

20-98 

.2061 

3 

Limestone  . 

15-100 

.216 

12 

11     (K)        .        .        . 

20-98 

.2080 

3 

Marble 

O-IOO 

.21 

— 

Oligoclase 

20-98 

.2048 

3 

Quartz  sand 

20-98 

.191 

3 

Orthoclase 

T5~99 

.1877 

Sandstone  . 

— 

.22 

Pyrites,  copper 
Pyrolusite,  MnO2  . 
Quartz,  SiO2 
«<          « 

J5-99 

17-48 

I2-IOO 

.1291 

2 

6 

7 

i  Lindner.       6  Kopp.           n"  Bartoli. 
2  Oeberg.        7  Joly.             12  Morano. 

«          « 
«          « 

O 

350 

400-1200 

•T737 
.2786 

•305 

8 
8 

3  Ulrich.          8  Pionchon. 
4  Regnault.     9  Roberts-Austen,  Riicker. 
5  Tilden.        10  R.  Weber. 

Compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLE  265. 
SPECIFIC   HEATS   OF   GASES   AND   VAPORS. 


243 


Substance. 

Range  of 
Temp.°C. 

Sp.  Ht. 
Constant 
Pressure. 

Authority. 

Range  of 
Temp.°C. 

Mean 
Ratio  of 
Specific 
Heats. 

Cp/Cr. 

Authority. 

Acetone,  C3H6O  . 

26-IIO 

0.3468 

Wiedemann. 

"             " 

27-179 

0.3740 

" 

<«             « 

129-233 

0.4125 

Regnault. 

Air         .        .        ! 

—30-  +  10 

0.2377 

" 

5-14 

1.4025 

Lummer  and 

M 

O-IOO 

0.2374 

" 

Pringsheim. 

« 

O-2OO 

0-2375 

« 

« 

2O-44O 

0.2366 

Holborn  and 

« 

20-630 

0.2429 

Austin. 

« 

20-800 

0.2430 

" 

Alcohol,'  C2H5OH 

IO8-22O 

0-4534 

Regnault. 

53 

I-I33 

Jaeger. 

«             it 

— 

_ 

100 

I-I34 

Stevens. 

«       C2H8OH 

101-223 

0.4580 

Regnault. 

100 

L256 

M 

Ammonia 

23-IOO 

0.5202 

Wiedemann. 

o 

1.3172 

Wullner. 

u 

27-2OO 

0-5356 

M 

IOO 

1.2770 

" 

(t 

24-216 

°-5I25 

Regnault. 

Argon    .... 

20-90 

0.1233 

Dittenberger. 

0 

1.667 

Niemeyer. 

Benzole,  C6H6 

34-H5 

0.2990 

Wiedemann. 

20 

1.403 

Pagliani. 

«                          U 

If              « 

35-180 
II6-2I8 

o-3325 
0-3754 

Regnault. 

60 

99-7 

1.403 

1.105 

Stevens 

Bromine 

83-228 

0-0555 

" 

20-388 

1.293 

Strecker. 

" 

IQ-388 

0-0553 

Strecker. 

Carbon  dioxide,  CO2    . 

-28-+7 

0.1843 

Regnault. 

4-1  1 

1.2995 

Lummer  and 

«                          4(                        t< 

15-100 

0.2025 

M 

Pringsheim. 

«                         «                        <« 

11-214 

0.2169 

« 

"       monoxide,  CO  . 

23-99 

0.2425 

Wiedemann. 

0 

1.403 

Wullner. 

«              «             <« 

26-198 

0.2426 

" 

IOO 

T-395 

" 

"       disulphide,  CS2 

86-190 

0.1596 

Regnault. 

3-67 

1.205 

Beyme. 

Chlorine 
u 

I3-2O2 
16-343 

0.1241 
0.1125 

« 
Strecker. 

20-340 

0 

1-323 
:-336 

Strecker. 
Martini. 

Chloroform,  CHClg      '. 

27-IlS 

0.1441 

Wiedemann. 

22-78 

1.  102 

Beyme. 

«                 «* 

28-189 

0.1489 

<« 

99.8 

1.150 

Stevens. 

Ether,  C4H10O      . 

69-224 

0.4797 

Regnault. 

3-46 

1.025 

Beyme. 

««            « 

27-189 

0.4618 

Wiedemann. 

42-45 

1.029 

Miiller. 

«            i« 

25-111 

0.4280 

« 

I2-2O 

1.024 

Low. 

Hydrochloric  acid^  Hci 

13-100 

0.1940 

Strecker. 

2O 

1.389 

Strecker. 

«              «        «< 

22-214 

0.1867 

Regnault. 

IOO 

1.400 

M 

Hydrogen 

—28-  +9 

3.3996 

«. 

4-16 

1.4080 

Lummer  and 

"     . 

12-198 

3.4090 

" 

Pringsheim. 

M 

21-100 

3.4100 

Wiedemann. 

"     '  sulphide,  H2S 

2O-2O6 

0.2451 

Regnault. 

10-40 

1.276 

Muller. 

Methane,  CH4      . 

18-208 

0.5929 

«' 

11-30 

1.316 

<« 

Nitrogen 

O-2OO 

0.2438 

«i 

_ 

1.41 

Cazin. 

" 

20-440 

0.2419 

Holborn  and 

u 

20-630 

0.2464 

Austin. 

« 

20-800 

0.2497 

«< 

Nitric  oxide,  'NO*. 

13-172 

0.2317 

Regnault. 

Nitrogen  tetroxide,  NO2 

27-67 

1.625 

Berthelot  and 

- 

I-3I 

Natanson. 

<i              «           K 

27-150 

1.115 

Olger. 

«              «           <« 

27-280 

0.65 

" 

Nitrous  oxide,  N2O 

16-207 

0.2262 

Regnault. 

o 

1.311 

Wullner. 

<«           «   •      u 

26-103 

0.2126 

Wiedemann. 

IOO 

1.272 

M 

«<           <«         « 

27-206 

0.2241 

M 

Oxygen. 

13-207 

0.2175 

Regnault. 

5-H 

1-3977 

Lummer  and 

M 

20-440 

0.2240 

Holborn  and 

Pringsheim. 

« 

20-630 

0.2300 

Austin. 

Sulphur  dioxide,  SO2    . 
Water  vapor,  H2O 

I6-2O2  . 
0 

0.1544 
04655 

Regnault. 
Thiesen. 

16-34 
78 

1.256 
1.274 

Muller. 
Beyme. 

«                  «                 (( 

100 

0.421 

" 

94 

i-33 

Jaeger. 

U                  ««                 <« 

180 

0.51 

<« 

SMITHSONIAN  TABLES. 


244 


TABLES  266-269. 
THERMOMETERS. 

TABLE  266.  —  Gas  and  Mercury  Thermometers. 


If  /H,  ty,  4)02,  '16,  *59»  *r>  are  temperatures  measured  with  the  hydrogen,  nitrogen,  carbonic  acid, 
i6m,  59UI,  and  "  verre  dur  "  (Tonnelot),  respectively,  then 

/a  _/T  =  IQ^  [—0.61859  +  0.0047351.*—  O.OOOOH577./2]* 
fc  —  /T  =  (l™tf)'  [—  0.55541  +  0.0048240.*—  0.000024807  ./*]* 
[-0.33386  +  0.0039910^-0.000016678.^]* 

[—0.67039  +  0.0047351.  /  —  o.ooooi  1  577./2]t 


fe  —  to  = 

*  Chappuis  ;  Trav.  et  Me"m.  du  Bur.  internal,  des  Poids  et  Mes.  6,  1 
t  Thiesen,  Scheel,  Sell;  Wiss.  Abh.  d.  Phys.  Techn.  Reichanstalt,  2,  1895;  Scheel;  Wied.  Ann.  58,  1896;  D.  Mech. 
Ztg.  1897. 

TABLE  267.   tH-t16   (Hydrogen  -16ra). 


0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0° 

.000° 

-.007° 

-OI3° 

—  .019° 

-.025° 

—.031° 

—.036° 

-.042° 

—.047° 

-.051° 

IO 

—.056 

—  .061 

-.065 

-.069 

—.073 

—.077 

—.080 

—.084 

-.087 

—.090 

20 

—•093 

—.096 

-.098 

—  .101 

—.103 

-.105 

—.107 

—  .109 

—  .no 

—.112 

30 

—•"3 

—.114 

—.115 

—  .Il6 

—.117 

—.118 

—  .119 

—.119 

—.119 

—  .120 

40 

—  .120 

—  .120 

—  .120 

—  .120 

—.119 

—.119 

—  .Il8 

—  .Il8 

—.117 

—.116 

5° 

—.116 

—  -115 

—.114 

—•"3 

—  .Ill 

—  .110 

—.109 

—.107 

—.106 

—  .104 

60 

—.103 

—  .101 

—.099 

—.097 

—.096 

—.094 

—.092 

—  .090 

-.087 

-.085 

B 

—.083 
—.058 

—.081 
—  .056 

—.078 
—•053 

—  .076 
—  .050 

—.074 
—.048 

—.071 
—.045 

-.069 
—  .042 

—.066 
—•039 

-.064 
—.036 

—.O6l 
—•033 

90 

—  -030 

—.027 

—.024 

—  .021 

—.018 

—.015 

—  .012 

—.009 

—  .006 

—.003 

100 

.000 

TABLE  268.   ta-tuo    (Hydrogen- 5  9111). 


0° 

i° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0° 

.000° 

-.0030 

—.006° 

-.009° 

—.011° 

—.014° 

—.016° 

—.018° 

—.020° 

—.022° 

IO 

20 
30 

—.024 

—•035 
—.038 

—.036 
—.037 

-.027 
.036 
—.037 

—.028 
—•037 
—.037 

—  .030 
—•037 
—•037 

—.031 

—037 
—.036 

—.032 
—.038 
—.036 

—•033 
—.038 

—•033 

—.034 

—.038 

—035 

—•035 
—.038 

—•034 

40 

—.034 

—•033 

—.032 

—.032 

—.031 

—  .030 

—  .029 

—.028 

—.028 

—.027 

50 

—  .026 

—.025 

—  .024 

—.023 

—  .022 

—  .O2I 

—  .O2O 

—  .019 

—.018 

—.017 

60 

—  .016 

—.015 

—.015 

—  .014 

—.013 

—  .012 

—  .Oil 

—  .OIO 

—  .009 

—.008 

70 

—.008 

—.007 

—.006 

—.005 

—.005 

—  .004 

—.003 

—.003 

—  .002 

—.001 

80 

—  .001 

—  .OOI 

.000 

.OOO 

+  .OO  I 

+  .OOI 

+  .OOI 

+  .OO  2 

+.002 

+  .002 

90 

+.002 

+.OO2 

+.OO  2 

+.002 

+  .002 

+.002 

+.001 

+  .OO  I 

+  .OOI 

.OOO 

100 

.OOO 

TABLE  269.    (Hydrogen  - 16"1),  (Hydrogen  -  591"). 


-5° 

—  10° 

-15° 

—20° 

-25° 

-30° 

-35° 

ta  —  t16 
tn  —  t69 

+0.04° 
+0.02° 

+0.08° 

+0.04° 

+O.I3° 

+0.07° 

+0.19° 

+0.10° 

+0.25° 

+0.14° 

+0.320 

+0.18° 

+0.40° 
+0.23° 

All  compiled  from  Landolt-Bbrnstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  270,  271. 
AIR  AND  MERCURY  THERMOMETERS. 

TABLE  270.    tAm-t16.    (Air-16111.) 


245 


•C. 

0° 

,o 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

0 

.000 

—  .006 

—  .012 

—.017 

—  .022 

—.027 

—.032 

—•037 

—  .041 

—•045 

10 

—.049 

—•053 

—.CW 

—.061 

—  .065 

—.068 

—.071 

—.074 

—.077 

—.080 

20 

-083 

—.086 

—.089 

—.091 

—.093 

-.095 

—.097 

—.099 

—  .IOI 

—  .102 

30 

—.103 

—  .104 

—.105 

—.I06 

—.107 

—.108 

—.109 

—  .110 

—  .110 

—  .IIO 

40 

—  .110 

—  .110 

—  .Ill 

—  .Ill 

—  .IIO 

—  .110 

—  .IIO 

—  .109 

—.109 

—.108 

5° 

—  .107 

—  .107 

—.106 

—.105 

—  .104 

—.103 

—  .IO2 

—  .101 

—  .100 

—  .098 

60 

-.096 

—  «°95 

—.093 

—.092 

—.090 

-.088 

—.086 

—.084 

—.082 

—  .080 

70 

—.078 

—.076 

—.074 

—.072 

—  .070 

-.067 

-.065 

—.062 

—.060 

—•057 

80 

—.054 

—.052 

—.049 

—.047 

—.044 

—  .041 

—.039 

—.036 

—034 

—031 

90 

—.028 

—.025 

—.023 

—  .020 

—.017 

—.014 

—  .Oil 

—.009 

—.006 

—.003 

100 

.000 

+.003 

+.006 

+.008 

+  .011 

+.014 

+.017 

+.019 

+.O22 

+.025 

110 

120 

+.028 

4-'°53 

+.030 
+•055 

+.033 
+.057 

+-°35 
+.060 

+.038 
+.062 

+.041 
+.064 

+.043 
+.066 

+.046 
+.068 

+.048 
+.070 

+.050 
+.072 

130 

+J*J 

+.074 

+.076 

+.078 

+.080 

+.081 

+.083 

+.084 

+.086 

+.087 

+.089 

140 

+.090 

+.091 

+.092 

+•093 

+.094 

+.095 

+.096 

+.096 

+.097 

+.097 

*5° 

+.098 

+.098 

+.098 

+  .099 

+.099 

+.099 

+.098 

+  .098 

+.098 

+.097 

160 

+.097 

+.096 

+.095 

+.094 

+.093 

+.092 

+.090 

+•089 

+  .088 

+.086 

170 

+.084 

-J-.082 

+.080 

+.078 

+.076 

+•073 

+.071 

+.068 

+.065 

+.062 

180 

+.059 

-K°55 

+•052 

+.048 

+.045 

+.041 

+•037 

+•033 

+.028 

+.023 

190 

+.019 

+.014 

+.009 

+.004 

—  .001 

—.007 

—.013 

—  .019 

—025 

—.031 

200 

—.038 

—  045 

—.051 

—.058 

—.066 

—•073 

—.080 

—.088 

—  .096 

-.103 

2IO 

—•113 

.122 

—.130 

—139 

—.148 

—  .158 

—.168 

-.177 

—.187 

—.198 

220 

—.208 

.219 

—.230 

—.252 

—  .264 

—.275 

—.287 

—.300 

—.312 

230 

—.325 

—  .338 

—  -35  ! 

—  .365 

—378 

—•392 

—.407 

—.421 

—.436 

—.450 

240 

—.466 

—  .481 

—•497 

—  -5X3 

—.529 

—•546 

-.562 

—579 

—597 

—.614 

250 

-.632 

.650 

—.668 

-.687 

-.706 

—•725 

—745 

—765 

—785 

—805 

260 

-.825 

—.846 

—.867 

-.889 

—.911 

—•933 

—955 

—978 

—  I.OOI 

—1.025 

270 

—  1.048 

—1.072 

—  1.096 

—  1.  121 

—  1.146 

—1.171 

-1.196 

—  1.222 

—1.248 

—1.274 

280 
290 

—  1.301 
—1.588 

—1.328 

—  1.618 

—I.356 
—1.649 

-!.68o 

—1.412 
—1.711 

—1.440 
—1.743 

—1.469 
-1.776 

-1.498 
—1.  808 

—1.528 
—1.841 

-1.558 
-1.874 

300 

—1.908 

TABLE  271.    tAiR-t59.    (Alr-69ni.) 


°c. 

0° 

lO 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

100 

.000 

.000 

.OOO 

.OOO 

.000 

.OOO 

.000 

.000 

.000 

.000 

1  10 

.000 

.000 

.000 

—  .001 

—  .001 

—  .OOI 

—  .001 

—  .001 

—  .002 

—  .002 

120 

—  .002 

—  .002 

—  .002 

—  .002 

—  .002 

—.003 

—.003 

—.003 

—  .004 

—.004 

130 

—.004 

—  .004 

—.005 

—.005 

—.006 

-.006 

—.006 

—.007 

—.007 

—.008 

140 

—.008 

—.008 

—.009 

—.009 

—  .OIO 

—  .010 

—  .Oil 

—  .Oil 

—  .OI2 

—  .OI2 

IS 

—.013 
—  .019 

—.013 

—  .020 

—.014 
—  .021 

—.015 
—  .021 

—  .Ol6 

—  .022 

—  .Ol6 
—.023 

—  .016 

—.024 

—.017 
—.025 

—.Ol8 
—  .026 

—  .019 

—.027 

170 

—.028 

—  .029 

—.030 

—.031 

—.032 

—•033 

—.034 

-.035 

—.037 

—.038 

1  80 
190 

—  -°39 

—  .0« 

—.040 
--053 

—.041 
-.055 

-.043 
—.056 

—.044 
—.057 

—.045 
—.059 

—  .046 

—.060 

—.048 
—.062 

—.049 
—  .064 

—.051 
-.066 

2OO 

—.067 

SMITHSONIAN  TABLES. 


246 


TABLES  272-274. 


GAS,   MERCURY,   ALCOHOL,   TOLUOL,   PETROLETHER,   PENTANE, 

THERMOMETERS. 

TABLE  272.  —  Is— tM  (Hydrogen-Mercury). 


Temper- 
ature, C. 

Thuringer 
Glass.* 

Verre  dur. 
Tonnelot.t 

Resistance 
Glass* 

English 
Crystal 
Glass* 

Choisy-le- 
Roi.* 

I22m.* 

Nitrogen 
Thermometer. 
Ta-Ts.t 

CO2  Ther- 
mometer. 
TH  —  Tooj-t 

0 

o 

0 

0 

o 

o 

o 

0 

o 

O 

.000 

.OOO 

.OOO 

.000 

.000 

.000 

.OOO 

.000 

10 
20 

—•075 

—.052 
-.085 

—.066 
—.108 

—.008 

—  .001 

—.007 
—.004 

—  .006 

—.006 
—  .010 

—.025 
—•043 

30 

—  .156 

—  .IO2 

—•131 

+.017 

+  .004 

—  .002 

—  .on 

—.054 

40 

—  .168 

—.107 

—.140 

+•037 

+  .014 

+  .OO  I 

—  .on 

—•059 

5° 

—.166 

—.103 

—•135 

+.057 

+.025 

+.004 

—  .009 

—•059 

60 

—.150 

—.090 

—.II9 

+.073 

+  •033 

+.008 

—.005 

—  -°53 

70 

—.124 

—.072 

—•095 

+.079 

+  .037 

+  .009 

—  .001 

—.044 

80 

—.088 

—  -050 

—.068 

+.070 

+  .032 

+  .007 

+.002 

—.031 

90 

—.047 

—  .026 

—.034 

+.046 

-J-.O22 

+  .006 

+.003 

—  .016 

100 

.OOO 

.OOO 

.OOO 

.000 

.000 

.OOO 

.000 

.000 

*  Schlosser,  Zt.  Instrkde.  21,  1901. 


t  Chappuis,  Trav.  et  mem.  du  Bur.  Intern,  des  Poids  et  Mes.  6, 


TABLE  273.  —Comparison  of  Air  and  High  Temperature  Mercury  Thermometers. 

Comparison  of  the  air  thermometer  with  the  high  temperature  mercury  thermometer,  filled  under 

pressure  and  made  of  59m  glass. 


Air. 

so™. 

Air. 

S9m. 

o 

o 

o 

0 

0 

0. 

375 

385-4 

100 

100. 

400 

412.3 

2OO 

200.4 

425 

440.7 

300 

304.1 

450 

469.1 

325 
350 

330.9 

358.1 

475 
500 

498.0 
527.8 

Mahlke,  Wied.  Ann.  1894. 


TABLE  274.  —  Comparison  of  Hydrogen  and  Other  Thermometers. 

Comparison  of  the  hydrogen  thermometer  with  the  toluol,  alcohol,  petrolether,  and  pentane  ther- 
mometers (verre  dur). 


Hydrogen. 

Toluol* 

Alcohol  I  * 

Alcohol  II.* 

Petrolether.  t 

Pentane.t 

o 

o 

0 

0 

0 

o 

0 

0.00 

o.oo 

0.00 

_ 

O.OO 

—  10 

—  20 

-8.54 

—  16.90 

-9.31 
—18.45 

—9-44 

—18.71 

— 

—9.03 
—17.87 

—3° 

—  25.10 

—27.44 

—27.84 

— 

—26.55 

—40 
—5° 

—33-15 
—41.08 

—36.30 

—45-05 

-36.84 
—45-74 

—  42.6 

—35-04 
—43-36 

—60 
—70 

—48.90 
-56.63 

-53.71 

—  62.31 

-54-55 
-63-31 

~ 

—5I-50 

~~^94o 

—  100 

_ 

—80.2 

—82.28 

—150 

_ 

_ 

_ 

—  113.0 

—116.87 

—  2OO 

*"" 

— 

~ 

—140.7 

—146.84 

*  Chappuis,  Arch.  sc.  phys.  (3)  18,  1892.  t  Holborn,  Ann.  d.  Phys.  (4)  6,  1901.  \  Rothe,  unpublished. 

All  compiled  from  Landolt-Bornstein-Meyerhoffer's  Physikalisch-chemische  Tabellen. 
SMITHSONIAN  TABLES. 


TABLES  275-277. 

TABLE  275.  —Platinum  Resistance  Thermometers. 


247 


Callendar  has  shown  that  if  we  define  the  platinum  temperature,  pt,  by  pt  =  ioo-{  (R —  R0) 
/(Rioo — RO)  }• ,  where  R  is  the  observed  resistance  at  t°  C.,  R0  that  at  O°,  RIOO  at  100°,  then  the  re- 
lation between  the  platinum  temperature  and  the  temperature  t  on  the  scale  of  the  gas  thermo- 
meter is  represented  by  t  —  pt  =  8  •{  t/ 100  —  I  ^  t/ioo  where  8  is  a  constant  for  any  given  sample 
of  platinum  and  about  1.50  for  pure  platinum  (impure  platinum  having  higher  values).  This  holds 
good  between  —  23°  and  450°  when  8  has  been  determined  by  the  boiling  point  of  sulphur  (445°.) 
See  Waidner  and  Burgess,  Bui.  Bureau  Standards,  6,  p.  149,  1909. 

TABLE  278.  —  Thermodynamic  Temperature  ol  the  Ice  Point,  and  Reduction  to  Thermodynamic  Scale. 
Mean  =  273. 10°  C.  (ice  point) 

For  a  discussion  of  the  various  values  and  for  the  corrections  of  the  various  gas  thermometers  to 
the  thermodynamic  scale  see  Buckingham,  Bull.  Bureau  Standards,  3,  p.  237,  1907. 

Scale  Corrections  for  Gas  Thermometers. 


Temp. 

Constant  pressure  =  76  cm. 

Constant  volume  ©0—273.10  C. 

He             H             N 

He           H            N 

—250° 

_ 

+0.02           —              — 

—  200 

+0.10        +0.26 

+0.01      +0.06 

—  100 
—   50 

+    .03        +0.03         +0.33 
+    .009      +0.004      +    -09 

.OOO  +   .014     +O.O7 
.OOO  +   .004     +  .02 

4-  25 

—   .OO2      —   .OO2      —   .013 

.000           .000     —   .006 

+    50 

—   .OO2      —   .003      —   .OI7 

.000           .000     —  .006 

+  75 

—   .002      —   .002      —   .012 

.OOO           .OOO     —  .004 

+  15° 

+    .005      +    .003      +    .04 

.OOO  +   .OOI      +    .OI 

+  200 

+45° 

+  1000 

+    .OI         +    .OI         +    .IO 
+    .07         +    .04        +    -SO 

+  .24      +  .01      +1.7 

.000   +    .002      +    .04 

o.oo    +  .01      +  .15 

—       +0.04         +   .70 

+1500 

-      +3-o 

See  Burgess,  The  Present  Status  of  the  Temperature  Scale,  Chemical  News,  107,  p.  169,  1913. 


TABLE  277.  —Standard  Points  for  the  Calibration  of  Thermometers. 


Substance. 

Point. 

Atmos- 
phere. 

Crucible. 

Temperatures. 

°C. 

Thermodynamic. 

Water 

boiling,  760  mm. 

air 

_ 

100.00 

100.00 

Napthalene 

«          «       « 

« 

— 

2  1  8.0 

218.0 

Benzophenone 

«         «       « 

_ 

— 

305.85- 

-O.I 

305-9 

Cadmium 

melting  or  solidify. 

air 

graphite 

320.8    - 

-O.2 

320.9 

Zinc 

«        «        « 

" 

« 

4I9O    = 

z  °-3 

419.4 

Sulphur 
Antimony 
Aluminum 

boiling,  760  mm. 
melting  or  solidify, 
solidification 

C02 

«< 

graphite 

44445  - 
629.8    - 
658.5    = 

-O.I 

=°'l 

-0.6 

444-55 
630.0 
658.7 

Silver 

melting  or  solidify. 

« 

tt 

960.0    - 

-0.7 

Gold 

«        «        « 

" 

« 

1062.4    - 

-0.8 

Copper 

u           ««          « 

H 

« 

1082.6    - 

1  0.8 

Li2SiO3 

melting 

air 

platinum 

I20I.O    - 

-  I.O 

Diopside,  pure 

" 

" 

« 

I39I.2     - 

^•5 

Nickel 

melting  or  solidify. 

HandN 

magnesia  and 

J452-3   = 

-2.O 

Mg.  aluminate 

Cobalt 

«        «        « 

<{ 

magnesia 

1489.8   - 

-2.0 

Palladium 

«        «        « 

air 

« 

1549.2   ., 

-2.0 

Anorthite,  pure 

melting 

it 

platinum 

1549-5   = 

-  2.O 

Platinum 

tt 

<( 

1752.     - 

z  5-* 

1755-     d 

•5-t 

*  Thermoelectric  extrapolation,    t  Optical  extrapolation. 

(Day  and  Sosman,  Journal  de  Physique,  1912.    Mesure  des  temperatures  e'leve'es.)    A  few  additional  points  are  :  H, 
boils  —  252.7°;  O,  boils  — 182.9°;  Hg.  freezes  —  37-7°;  Alumina  melts  2000° ;  Tungsten  melts  3000°. 

SMITHSONIAN  TABLES. 


248  TABLE  278. 

CORRECTION  FOR  TEMPERATURE  OF  MERCURY  IN  THERMOMETER 

STEM. 

The  Stem  Correction  is  proportional  to  «£(  T—  t) :  where  u  is  the  number  of  degrees  in  the 
exposed  stem ;  £  is  the  apparent  coefficient  of  expansion  of  mercury  in  the  glass ;  7'  is  the  measured 
temperature ;  and  t  is  the  mean  temperature  of  the  exposed  stem  determined  by  another  ther- 
mometer, exposed  some  10  cm.  from,  and  at  about  half  the  height  of,  the  exposed  stem  of  the  first. 

For  temperatures  up  to  ioo°C,  the  value  of  /8  is  for : 

Jena  glass  XVI111  or  Greiner  and  Friedrich  resistance  glass,  — ?—  or  0.000159; 


6300 


Jena  glass  59°,  ^ —  or  0.000164. 


At  100°  the  correction  is  in  round  numbers  0.01°  for  each  degree  of  the  exposed  stem ;  at  200° 
0.02° ;  and  for  higher  temperatures  proportionately  greater.  At  500°  it  may  amount  to  0.07°  for 
each  exposed  degree. 

Tables  278-280  are  taken  from  Rimbach,  Zeitschrift  fur  Instrumentenkunde,  10,  153,  1890,  and 
apply  to  thermometers  of  Jena  or  of  resistance  glass. 


TABLE  278.  — Stem  Correction  for  Thermometer  of  Jena  Glass  (0°-360°G.). 

Degree  length  0.9  to  i.i  mm;  /  =  the  observed  temperature;  /'=that  of  the  surrounding  air 
I  dm.  away ;  n  =  the  length  of  the  exposed  thread. 


CORRECTION  TO  BE  ADDED  TO  THE  READING  t. 

t  —  V 

70° 

80° 

90° 

100° 

120° 

140° 

160°  . 

180° 

200° 

220° 

10 

0.01 

0.0  1 

0.03 

0.04 

0.07 

O.IO 

0.13 

0.17 

0.19 

O.2I 

2O 

0.08 

O.I2 

0.14 

0.19 

0.25 

0.28 

0.32 

0.40 

0.49 

0-54 

30 

0.25 

0.28 

0.32 

0.36 

0.42 

0.48 

0-54 

0.66 

0.78 

0.87 

40 

0.30 

0-35 

0.41 

0.48 

O.6o 

0.67 

0.77 

0.92 

1.  08 

1.  2O 

1° 
60 

0.41 

0.52 

0.46 
0.60 

0.52 
0.68 

0.59 
0.79 

0.79 
0.99 

0.89 

I.  II 

0.98 
1.23 

.16 

.46 

1.38 
1.70 

1.87 

70 

0.63 

0.74 

0.85 

0.98 

1.  20 

1.32 

1-45 

.70 

1.99 

2.21 

80 

0.75 

0.87 

1.  01 

I.I  C 

1.38 

J-53 

1.70 

.98 

2.29 

2.54 

90 

0.87 

0.99 

1.13 

1.28 

1.62 

1.82 

1.94 

.25 

2.60 

2.89 

100 

0.98 

1.  12 

1.29 

1.47 

1.82 

2.03 

2.20 

2-55 

2.92 

3-24 

120 

- 

- 

1.88 

2.28 

2.49 

2.68 

3-59 

3-96 

I4O 

— 

— 

— 

— 

2-75 

2.97 

3.22 

3-75 

4.24 

4.69 

160 

- 

- 

- 

- 

3-35 

3.80 

4-35 

4-92 

5-45. 

180 

200 

_ 

** 

""* 

_ 

_ 

4.37 

4-99 
5.68 

5-63 
6-34 

6.22 

6.98 

22O 

I 

~ 

" 

" 

7-05 

7.82 

See  "  The  correction  for  Emergent  Stem  of  Mercurial  Thermometer."    Buckingham,  Bui.  Bur.  of  Standards, 
SMITHSONIAN  TABLES. 


TABLES  279,  280, 


249 


CORRECTION    FOR   TEMPERATURE   OF   MERCURY   IN   THERMOMETER 

STEM    (continued). 

TABLE  279.  -  Stem  Correction  for  Thermometer  of  Jena  Glass  (0°-360°  0). 

Degree  length  i  to  1.6  mm.;  /=the  observed  temperature;   t1—  that  of  the  surrounding  air 
one  dm.  away;  ;/  =  the  length  of  the  exposed  thread. 


CORRECTION  TO  BE  ADDED  TO  THERMOMETER  READING.* 

t-»        ' 

70° 

80° 

90° 

100° 

120° 

140° 

160° 

180° 

200° 

220° 

10° 

O.O2 

0.03 

0.05 

0.07 

O.I  I 

0.17 

O.2I 

0.27 

0-33 

0.38 

10° 

20 

O.I3 

0.15 

0.18 

O.22 

0.29 

0.38 

0.46 

0-53 

0.67 

20 

30 
40 

0.24 

°-35 

0.28 
0.41 

0.33 
0.48 

°-39 
0.56 

0.48 

0.68 

0-59 
0.82 

0.70 
0.94 

0.78 
1.04 

0.88 
1.16 

0.97 

3° 
40 

50 

0.47 

0.53 

0.62 

0.72 

0.88 

1.03 

I.I7 

I3I 

1.44 

i-59 

50 

60 

0.57 
0.69 

0.66 
0.79 

0.77 
0.92 

0.89 
i.  06 

1.09 
1.30 

1.25 
1.47 

1.42 
1.67 

1.58 

1.86 

1.74 
2.04 

1.90 
2.23 

60 
70 

80 

0.80 

0.91 

1.05 

1.  21 

1.52 

1.71 

1-94 

2.15 

2-33 

2-55 

80 

90 

0.91 

1.04 

1.19 

1.38 

i-73 

I.96 

2.20 

2.42 

2.64 

2.89 

90 

100 

i.  02 

1.18 

1.97 

2.18 

2-45 

2.70 

2.94 

3-23 

100 

no 

- 

— 

— 

I.78 

2.19 

2.43 

2.70 

2.98 

3.26 

3-57 

no 

120 

- 

— 

— 

I.98 

2-43 

2.69 

2.95 

3-26 

3-58 

3-92 

1  20 

130 

- 

_ 

_ 

_ 

2.68 

2-94 

3-20 

3.56 

3-89 

4.28 

130 

140 

- 

- 

- 

- 

2.92 

3.22 

3-47 

3.86 

4.22 

4.64 

140 

!£ 

- 

- 

- 

- 

- 

- 

3-74 
4.00 

4-15 
4.46 

4.90 

5.01 
5-39 

IS 

170 

180 

- 

- 

- 

- 

- 

- 

4.27 
4-54 

4.76 
5-07 

5-24 
5-59 

5-77 
6.15 

170 

180 

190 

200 

- 

: 

: 

- 

- 

- 

5-70 

5-95 
,6.30 

6.54 
6.94 

190 

200 

210 

- 

_ 

~ 

_ 

- 

- 

- 

- 

6.68 

7-35 

210 

220 

7.04 

7-75 

220 

*  See  Hovestadt's  "  Jena  Glass"  (translated  by  J.  D.  and  A.  Everett)  for  data  on  changes  of  thermometer  zeros. 


TABLE  280.  —  Stem  Correction  for  a  so-called  Normal  Thermometer  of  Jena  Glass  (0°-100°  0). 
Divided  into  tenth  degrees ;  degree  length  about  4  mm. 


CORRECTION  TO  BE  ADDED  TO  THE  READING  *. 

t  —  V 

30° 

35° 

40° 

45° 

60° 

55° 

60° 

66° 

70° 

75° 

80° 

85° 

IO 

0.04 

0.04 

0.05 

0.05 

0.05 

0.06 

O.o6 

0.07 

O.o8 

0.09 

O.IO 

O.IO 

20 

O.T2 

0.12 

0.13 

0.14 

0.15 

0.16 

0.17 

0.18 

0.19 

0.20 

0.22 

0.23 

30 

0.21 

0.22 

0.23 

0.24 

0.25 

0.25 

0.27 

0.29 

0.31 

°*33 

0.35 

0.37 

40 

£ 

0.28 
0.36 

o-4S 

0.29 
0.38 
0.48 

0.31 
0.40 
0.51 

0.42 
o-S3 

0-35 
0.44 

0.37 
0.46 
0.57 

O.6o 

0.41 
0.50 
0.63 

0-43 
0.53 
0.66 

o-45 
0.57 
0.69 

0.48 

0.61 
0-73 

0.65 

0.78 

£ 

•* 

_ 

— 

_ 

o.bb 

0.69 
0.76 

0.71 
0.8  1 

0-75 
0.87 

0.8  1 

0.87 

I.OO 

0.92 

1.  06 

90 

— 

— 

— 

— 

— 

— 

— 

0.92 

0.99 

i.  06 

1-13 

1.20 

IOO 

' 

\ 

jj 

~ 

" 

1.  10 

1.18 

1.26 

i-34 

SMITHSONIAN  TABLES. 


250  TABLES  281-282. 

TABLE  281.— Standard  Calibration  Curve  for  Pt— Pt.  Rh.  (10%  Rh.)  Thermo-Element 

Giving  the  temperature  for  every  100  microvolts.  For  use  in  conjunction  with  a  deviation  curve  determined  by  cali- 
bration of  the  particular  element  at  some  of  the  following  fixed  points: 


Water 
Napthalene 

boiling-£t. 

100.0 

217.95 

6431 
1585 

Tin 

melting-pt. 

231.9 

1706 

Benzophenone 
Cadmium 

boiling-pt. 
melting-pt. 

305.9 
320.9 

2365 
2503 

Zinc 

(i                  U 

419.4 

3430 

Sulphur 

boiling-pt. 

444-55 

3672 

Antimony 

melting-pt. 

630.0 

5530 

Aluminum 

"        << 

658.7 

5827 

Silver 
Gold 


melting-pt. 


Dfopside 
Nickel 

Palladium 
Platinum 


960.2 
1062.6 
1082.8 

I2OI. 

I3QI-5 

I4S2.6 

1549-5 
1755- 


Qiumv. 
10296 
IQ534 
11941 
14230 
14973 

16144 

18608 


E 

o 

IOOO. 

2OOO.            3OOO. 

4000. 

5000. 

6000. 

7000. 

8000. 

9000. 

E 

micro- 
volts. 

TEMPERATURES,    °C. 

micro- 
volts. 

o. 

o.o 

147-1 

265.4 

374-3 

478.1 

578.3 

675-3 

769.5 

861.1 

950.4 

o. 

IOO. 

17.8 

159-7 

276.6 

384-9 

488.3 

588.1 

684.8 

778-8 

870.1 

959-2    | 

IOO. 

200. 

34-5 

I72.I 

287.7 

395-4 

498.4 

597-9 

694-3 

788.0 

879.1 

968.0 

200. 

300. 

50.3 

184.3 

298.7 

405-9 

508.5 

607.7 

703.8 

797-2 

888.1 

976.7    i 

300. 

400. 

65-4 

196.3 

309-7 

416.3 

518.6 

617.4 

713-3 

806.4 

897.1 

985-4 

400. 

500. 

80.0 

208.  1 

320.6 

426.7 

528.6 

627.1 

722.7 

815-6 

906.1 

994-1 

500. 

600. 

94-1 

219.7 

331-5 

437-1 

538.6 

636.8 

732.1 

824.7 

915.0 

1002.8 

600. 

700. 

107.8 

231.2 

342.3 

447-4 

548.6 

646.5 

741-5 

833.8 

923-9 

1011.5 

700. 

800. 

121.  2 

242.7 

353-0 

457-7 

558.5 

656.1 

750.9 

842.9 

932.8 

I020.I 

800. 

000. 

134-3 

254-1 

363.7 

467-9 

568.4 

665.7 

760.2 

852.0 

941-6 

1028.7 

900. 

IOOO. 

I47.I 

265.4 

374-3 

478.1 

578.3 

675-3 

769-5 

861.1 

950.4 

1037.3 

IOOO. 

E 

IOOOO. 

I  IOOO. 

12000. 

13000. 

14000.    :    15000. 

16000. 

17000. 

iSooo. 

E 

micro- 
volts. 

TEMPERATURES,  °C. 

micro- 
volts. 

o. 

1037-3 

II22.2 

1205.9 

1289.3 

1372.4 

1454-8 

1537-5 

1620.9 

1704-3 

o. 

IOO. 

1045-9 

II3O.6 

1214.2 

1297.7 

1380.7 

1463-0 

1545-8 

1629.2 

1712.6 

IOO. 

200. 

1054-4 

II39-0 

1222.6 

1306.0 

1389-0 

1471-2 

I554-I 

1637.6 

1721.0 

200. 

300. 

1062.9 

II47.4 

1230.9 

I3I4.3 

1397-3 

1479-4 

1562.4 

1645.9 

1729-3   1 

300. 

400. 
500. 

1071.4 
1079-9 

II55-8 
1164.2 

1239-3 
1247.6 

1322.6 
1330-9 

1405-6 
1413-8 

1487.7 
1496.0 

1570.8 
I579-I 

I654-3 
1662.6 

1737.7 
1746.0 

400. 
500. 

600. 

1088.4 

II72.5 

1255-9 

1339-2 

1422,0 

I504-3 

1587.5 

1670.9 

1/54-3 

600. 

700. 

1096.9 

II80.9 

1264.3 

1347-5 

1430.2 

1512.6 

1595-8 

1679-3 

700. 

800. 
900. 

1105.4 
1113-8 

II89.2 
II97.6 

1272.6 
I28J.O 

1355-8 
1364-1 

1438.4 
1446.6 

1520.9 
1529-2 

1604.2 
1612.5 

1687.6 
1696.0 

800. 
900. 

IOOO. 

II22.2 

1205.9 

1289.3 

1372.4 

1454-8 

1537-5 

1620.9 

1704.3 

IOOO. 

TABLE  282.  — Standard  Calibration  Curve  lor  Copper  —  Constantan  Thermo-Eleinent. 

For  use  in  conjunction  with  a  deviation  curve  determined  by  the  calibration  of  the  particular  clement  at  some  of  the 
following  fixed  points: 

Water,  boiling-point,  100°,  4276  microvolts;  Napthalene,  boiling-point,  217.95,  10248  mv.;  Tin,  melting-point,  231.9, 
11009  mv.;  Benzophenone,  boiling-point,  305.9,  15203  mv.;  Cadmium,  melting-point,  320.9,  16083  mv. 


E. 

o 

IOOO. 

2OOO. 

30OO. 

4000. 

5000. 

6000. 

7000. 

8000. 

9000. 

E 

micro- 
volts. 

TEMPERATURES,  °C. 

micro- 
volts. 

o. 

o.oo 

25.27 

49.20 

72.08 

94-07 

II5-3I 

135-91 

155-95 

175-50 

194-62 

o. 

IOO. 

2.60 

27.72 

51.53 

74-31 

96.23 

117.40 

137-94 

157-92 

177-43 

196.51 

IOO. 

200. 

5-17 

30.15 

53.85 

76.54 

98.38 

119.48 

139.96 

159.89 

I79-36 

198.40 

200. 

300. 

7-73 

32.57 

56.16 

78.76 

100.52 

121.56 

141.98 

161.86 

181.28 

200.28 

300. 

400. 

10.28 

34.98 

58.46 

80.97 

102.66 

123.63 

143-99 

163.82 

183.20 

202.16 

400. 

500. 

12.81 

37.38 

60.76 

83-17 

104.79 

125.69 

146.00 

165.78 

185.11 

204.04 

500. 

600. 

15-33 

39.77 

63.04 

85.37 

106.91 

127-75 

148.00 

167-73 

187.02 

205.91 

600. 

700. 

17-83 

42.15 

65.31 

87.56 

109.02 

129.80 

150.00 

169.68 

188.93 

207.78 

700. 

800. 

20.32 

44.51 

67.58 

89.74 

III.  12 

131-84 

I5I-99 

171.62 

190.83 

209.64 

800. 

900. 

22.80 

46.86 

69.83 

91.91 

113.22 

133-88 

153-97 

173.56 

192.73 

211.50 

900. 

IOOO. 

25-27 

49.20 

72.08 

94-07 

115-31 

135-91 

155-95 

175-50 

194.62 

213-36 

IOOO. 

E 

IOOOO. 

I  IOOO. 

12000.   |   13000. 

I4OOO. 

15000.    16000.    17000. 

iSpoo. 

E 

volts. 

TEMPERATURES,  °C. 

micro- 
volts. 

o. 

213-36 

231.74 

249.82 

267.60 

285.13 

302.42 

3I9.49 

336.36 

353-09 

o. 

IOO. 

215.21 

233-56 

25I.6I 

269.36 

286.87 

304.14 

321.19 

338.04 

IOO. 

2OO. 

217.06 

235-38 

253-40 

271.12 

288.61 

305-85 

322.88 

339-72 

200. 

300. 

218.91 

237.20 

255-18 

272.88 

290.35 

307-56 

324-57 

341.40 

300. 

400. 

220.75 

239.01 

256.96 

274.64 

292.O8 

309.27 

326.26 

343-07 

400. 

500. 

222.59 

240.82 

258.74 

276.40 

293.81 

310.98 

327-95 

344-74 

500. 

000. 

224.43 

242.63 

260.52 

278.15 

295-54 

312.69 

329-64 

346.41 

600. 

700. 

226.26 

244.43 

262.29 

279-90 

297-26 

3I4-39 

331-32 

348.08 

700. 

800. 

228.09 

246.23 

264.06 

281.65 

298.98 

316.09 

333-00 

349-75 

800. 

900. 

229.92 

248.03 

265.83 

283.39 

300.70 

3I7.79 

334-68 

351-42 

900. 

IOOO. 

231-74 

249.82 

267.60 

285-13 

302.42 

3I9-49 

336.36 

353-09 

IOOO. 

Cf.  Day  and  Sosman,  Am.  Jour.  Sci.  29,  p.  93,  32,  p.  51;  ;  ibid.  R.  B.  Sosman,  30,  p.  i. 
SMITHSONIAN  TABLES. 


TABLES  283-285.  251 

RADIATION  CONSTANTS. 
TABLE  283.— Radiation  Formula  and  Constants  for  Perfect  Radiator. 

The  radiation  per  sq.  cm.  from  a  "  black  body  "  (exclusive  of  convection  losses)  at  the  temper' 
ature  T°  (absolute,  C)  to  one  at  /°  is  equal  to 

/=  ff  ( T^  —  /4)     (Stefan-Boltzmann)  ; 

where  <r=  1.374  X  io~ 12  gram-calories  per  second  per  sq.  centimeter. 
=8.26   X  io-"     "  "        "    minute  "      " 

=  5.75   X  io~12  watts  per  sq.  centimeter. 
The  distribution  of  this  energy  in  the  spectrum  is  represented  by  Planck's  formula : 


where  J\  is  the  intensity  of  the  energy  at  the  wave-length  A  (A  expressed  in  microns,  /x)  and  e  is 
the  base  of  the  Napierian  logarithms. 

Ci  =  9.226Xio-28  for/  in  ^-    -^-==3.86  X  io-22  for /in  ^-^ 

5CC '•  Cfll  •  CWl . 

6*2=  1.4450  for  A  in  cm. 
/max  =  3.ii  x  io+4  r6  for /in 


,-  =  1.30X10+6  T*  for/in^ 


sec.  cm*  cm? 

Amai  T=  0.2910  for  A  in  cm. 

h  =  Planck's  unit  =  elementary  "  Wirkungs  quantum  "  =  6.83  X  io~2T  ergs.  sec. 
k  =  constant  of  entropy  equation  =  1.42  X  io~ 16  ergs. /degrees. 

TABLE  284.— Radiation  in  Gram-Calories  per  24  Hours  per  sq.  cm.  from  a  Perfect  Radiator  at  t0  C  to 
an  absolutely  Cold  Space  (—273°  C). 

Computed  from  the  Stefan-Boltzmann  formula. 


t°C 

/ 

t°C 

/ 

t°C 

7 

*°C 

/ 

t°C 

/ 

tPC 

/ 

—273 

o 

—  I2O 

6S 

—  10 

57i 

+  12 

787 

+  34 

1059 

+56 

1400 

—  220 
—  2IO 

I 

2 

—  no 

—  100 

84 
107 

—8 
—6 

588 
606 

+  14 

+  16 

808 
831 

+36 
+  38 

1087 
JII5 

+60 

143° 
1470 

—  2OO 

3 

—90 

r34 

—4 

62  S 

+  18 

8SS 

+40 

"45 

+70 

1650 

—  IOX) 

5 

—80 

165 

—  2 

643 

+20 

879 

+42 

"74 

+80 

1850 

—  180 

9 

—70 

2OI 

O 

662 

+22 

903 

+44 

1204 

+90 

2070 

—  170 

—  160 

13 
19 

-60 

—5° 

245 
294 

+2 

+4 

682 
701 

+24 

+  26 

928 
9S3 

+46 
+48 

1234 
1265 

+ioo 
+200 

2310 

5960 

—150 
—  140 

9 

—40 
—30 

35° 
416 

+6 
+8 

722 
744 

+  28 
+  30 

979 
1005 

+  5o 
+52 

1298 
!33Q 

+  IOOO 
+  2OOO 

313X108 
318X10* 

—130 

50 

—  20  \ 

488 

+  10 

765 

+  32 

1032 

+  54 

1363 

+5000 

92iXio5 

TABLE  285.  —Values  of  JA  for  Various  Temperatures  Centigrade. 

Ekholm,  Met.  Z.  1902,  used  C\  =  8346  and  C%=  14349,  and  for  the  unit  of  time  the  day. 
For  10°,  the  values  for  J\  have  been  multiplied  by  10,  for  the  other  temperatures  by  100. 


A 

T=ioo°C 

30°  C 

15°  C 

o°C 

-30°  C 

—  80°  C 

\ 

100°  C 

30°  C 

15°  C 

o°C 

-30°  C 

—  80°  C 

M 

/* 

2 

3 

I 

So 

o 

4i 

o 
18 

0 

7 

O 
I 

o 
o 

18 
19 

5" 

443 

2961 
2626 

2281 

2175 
1954 

1491 
^63 

623 

594 

4 

469 

508 

272 

138 

27 

i 

20 

386 

2329 

2034 

1754 

1242 

561 

5 

1047 

1777 

1085 

628 

172 

8 

21 

337 

2068 

1816 

1574 

1129 

527 

6 

1526 

3464 

2296 

1454 

493 

39 

22 

295 

1840 

1622 

1413 

1026 

494 

7 

1768 

4954 

3481 

2353 

93  i 

105 

23 

259 

1639 

1448 

1270 

931 

460 

8 

1810 

5928 

4352 

3088 

1372 

203 

24 

228 

1462 

1298 

1141 

846 

428 

9 

1724 

6382 

4834 

3646 

173° 

316 

22 

202 

1307 

1165 

1028 

768 

398 

10 

J573 

6386 

4979 

378i 

1971 

426 

26 

179 

II7O 

1047 

926 

698 

369 

ii 

1398 

6127 

4833 

3798 

2098 

520 

28 

142 

947 

850 

757 

579 

3J7 

12 

1225 

5712 

4633 

3676 

2114 

592 

30 

114 

771 

696 

623 

482 

272 

'3 

1063 

5222 

4300 

3467 

2090 

640 

40 

44 

3" 

285 

259 

209 

H 

918 

4713 

3930 

3215 

2004 

666 

50 

20 

146 

J35 

124 

IO2 

15 

792 

4220 

3556 

2944 

1889 

673 

60 

10 

77 

72 

66 

55 

16 

683 

3759 

3198 

2674 

1760 

663 

80 

4 

27 

25 

24 

20 

14 

17 

590 

3340 

2862 

2417 

1626 

649 

IOO 

2 

12 

ii 

10 

9 

7 

SMITHSONIAN  TABLES. 


252 


TABLES  286,  287. 
COOLING  BY  RADIATION  AND  CONVECTION, 


TABLE  286.  -  At  Ordinary  Pressures. 

According  to  McFarlane*  the  rate  of  loss  of  heat  by  a  sphere 
placed  in  the  centre  of  a  spherical  enclosure  which  has  a 
blackened  surface,  and  is  kept  at  a  constant  temperature  of 
about  14°  C,  can  be  expressed  by  the  equations 

e  =  .000238  -f-  3.06  X  io-6/  —  2.6  X 


when  the  surface  of  the  sphere  is  blackened,  or 

e  =  .000168  -f-  1.98  X  io—  *t  —  1.7  X  io—  sfi, 

when  the  surface  is  that  of  polished  copper.  In  these  equa- 
tions, e  is  the  amount  of  heat  lost  in  c.  g.  s.  units,  that  is, 
the  quantity  of  heat,  small  calories,  radiated  per  second  per 
square  centimeter  of  surface  of  the  sphere,  per  degree  differ- 
ence of  temperature  t,  and  t  is  the  difference  of  temperature 
between  the  sphere  and  the  enclosure.  The  medium  through 
which  the  heat  passed  was  moist  air.  The  following  table 
gives  the  results. 


Differ- 
ence of 
tempera- 
ture 
t 

Value  of  e. 

Ratio. 

Polished  surface. 

Blackened  surface. 

5 

.000178 

.000252 

.707 

10 

.000186 

.O00266 

.699 

i5 

.000193 

.000279 

.692 

20 

.000201 

.000289 

.695 

25 

.000207 

.000298 

.694 

30 

.000212 

.000306 

.693 

35 

.000217 

.000313 

.693 

40 

.00022O 

.000319 

.693 

45 

.OO0223 

.000323 

.690 

5° 

.OO0225 

.000326 

.690 

55 

.OOO226 

.000328 

.690 

60 

.O00226 

.000328 

.690 

TABLE  287. -At  Different  Pressures. 

Experiments  made  by  J.  P.  Nicol  in  Tait's  Labo- 
ratory show  the  effect  of  pressure  of  the  en- 
closed air  on  the  rate  of  loss  of  heat.  In  this 
case  the  air  was  dry  and  the  enclosure  kept  at 
about  8°  C. 


Polished  surface. 

Blackened  surface. 

• 

et 

t 

et 

PRESSURE  76  CMS.  OF  MERCURY. 

63.8 

.00987 

6T.2 

.01746 

57-1 
44.8 

.00862 
.00736 
.00628 

50.2 
41.6 

34-4 

.01360 
.01078 
.00860 

40.5 

.00562 

27-3 

.00640 

34-2 
29.6 

.00438 
.00378 

20.5 

•00455 

23-3 

.00278 

- 

- 

18.6 

.00210 

~ 

PRESSURE  10.2  CMS.  OF  MERCURY. 

67.8 

.00492 

62.5 

.01298 

61.1 

55 

•00433 
.00383 

57-5 
53-2 

.01158 
.01048 

497 

.00340 

47-5 

.00898 

44.9 
40.8 

.00302 
.00268 

43-° 
28.5 

.00791 
.00490 

PRESSURE  r  CM.  OF  MERCURY. 

65 

.00388 

62.  S 

.01182 

60 

.00355 

57-5 

.01074 

50 

.00286 

54-2 

.01003 

40 

.00219 

41.7 

.00726 

30 

.00157 

37-5 

.00639 

23-5 

.00124 

34-o 

.00569 

- 

27-5 

.00446 

24.2 

.0039! 

SMITHSONIAN  TABLCS. 


*  "  Proc.  Roy.  Soc."  1872. 
t  "  Eroc.  Roy.  Soc."  Edinb.  1869. 
See  also  Compan,  AnnaL  de  cbi.  et  phys.  26,  p.  526. 


TABLES  288,  289.  253 

COOLING  BY  RADIATION  AND  CONVECTION. 

TABLE  288.  —  Cooling  of  Platinum  Wire  In  Copper  Envelope. 

Bottomley  gives  for  the  radiation  of  a  bright  platinum  wire  to  a  copper  envelope  when  the  space  between  is  at  the 
highest  vacuum  attainable  the  following  numbers :  — 

*  =  4o8°  C.,  ^  =  378.8  X  io-*,  temperature  of  enclosure  16°  C. 

*=5oS0C.,  «;=  726.1  Xio-4,          "  "          17°  C. 

It  was  found  at  this  degree  of  exhaustion  that  considerable  relative  change  of  the  vacuum  produced  very  small 
change  of  the  radiating  power.  The  curve  of  relation  between  degree  of  vacuum  and  radiation  becomes  asymp- 
totic for  high  exhaustions.  The  following  table  illustrates  the  variation  of  radiation  with  pressure  of  air  in 
enclosure. 


Temp,  of  enclosure  16°  C.,  ^  =  408°  C. 

Temp,  of  enclosure  17°  C.,  /  =  505°  C. 

Pressure  in  mm. 

et 

Pressure  in  mm. 

et 

740. 

8137.0  X  io-4 

0.094 

1688.0  X  io-4 

440. 

7971.0    " 

-053 

1255.0    « 

140. 

7875.0    ' 

•034 

II2O.O      ' 

42. 

759LO    ' 

.013 

920.4      " 

4. 

6036.0    « 

.0046 

831.4      " 

0.444 

2683.0    " 

.00052 

767.4      " 

.070 

•034 
.012 

1045.0    " 

727.3    « 
539-2    •' 

.00019 
Lowest  reached    1 
but  not  measured  ) 

746.4      ' 
726.1       " 

.OO5I 

436-4    ' 

.00007 

378.8    « 

TABLE  289.  —Effect  of  Pressure  on  Loss  of  Heat  at  Different  Temperatures. 

The  temperature  of  the  enclosure  was  about  15°  C.     The  numbers  give  the  total  radiation  in  therms  per  square  cen- 
timeter per  second. 


Pressure  in  mm. 

Temp,  of 

wire  in  C°. 

About 

10.0 

I.O 

0.25 

0.025 

o.i  M. 

100° 

0.14 

O.I  I 

0.05 

O.OI 

0.005 

2OO 

•31 

.24 

.11 

.02 

.0055 

300 

•50 

•38 

.18 

.04 

.0105 

4OO 

•75 

•53 

.25 

.07 

.025 

|00 

— 

.69 

•33 

•13 

•055 

600 

- 

•85 

•45 

•23 

.13 

7OO 

— 

— 

— 

•37 

.24 

800 

- 

- 

- 

.56 

.40 

900 

"f 

*"- 

"• 

** 

.6l 

NOTE.  —  An  interesting  example  (because  of  its  practical  importance  in  electric  light- 

ing) of  the  effect  of  difference  of  surface  condition  on  the  radiation  of  heat  is  given  on  the 

authority  of  Mr.  Evans  and  himself  in  Bottomley's  paper.     The  energy  required  to  keep 

up  a  certain  degree  of  incandescence  in  a  lamp  when  the  filament  is  dull  black  and  when 

it  is  "  flashed  "  with  coating  of  hard  bright  carbon,  was  found  to  be  as  follows  :  — 

Dull  black  filament,  57.9  watts. 

Bright  "           "        39.8  watts. 

SMITHSONIAN  TABLES. 


254 


TABLE  290. 
PROPERTIES   OF    STEAM, 

Metric  Measure. 


The  temperature  Centigrade  and  the  absolute  temperature  in  degrees  Centigrade,  together  with  other  data  for  steam 
or  water  vapor  stated  in  the  headings  of  the  columns,  are  here  given.  The  quantities  of  heat  are  in  therms  or  calo- 
ries according  as  the  gram  or  the  kilogram  is  taken  as  the  unit  of  mass. 


U 
H 

d 

•3 
1 

Pressure  in  mm. 
of  mercury. 

Pressure  in 
grams  per  sq. 
centimeter  =/>. 

Pressure  in 
atmospheres. 

Totalheatof  evap-  II 
oration  from  o°  at  1 
t°  —  H.  II 

Heat  of  liquid 

=*. 

Heat  of  evapora-  1 
tion  =  /f—  h. 

Outer  latent  or  ex-  I 
ternal-work  heat  1 
=  A».*  || 

11 
HE 

Inner  latent  or  in-  1 
ternal-work  heat 
—H—(h-\-Apv).\( 

Liters  per  gram, 
or  cubic  meters 
per  kilog.  =  v. 

Ratio  of  inner  la- 
tent heat  to  vol- 
ume of  steam.  t 

0° 

273 

4.60 

6.25 

0.006 

606.5 

o.oo 

606.5 

31.07 

575-4 

575-4 

210.66 

2.732 

5 

6-53 

8.88 

.009 

6o8.0 

5.00 

603.0 

31-47 

576.5 

571-5 

150.23 

3-805 

10 

283 

9.17 

12.47 

.012 

609.5 

10.00 

599-5 

31.89 

577-7 

108.51 

5.231 

15 

20 

288 
293 

12.70 
17-39 

17.27 
23.64 

.017 
.023 

Oil.  I 

612.6 

15.00 

2O.OI 

596-0 
592.6 

32.32 
32-75 

578.8 
579-8 

559-8 

79-35 

58.72 

7.104 
9-532 

25 

3° 

298 
303 

23-55 

32.02 
42.89 

0.031 
.042 

614.1 
615.6 

25.02 

30.03 

589.1 
585.6 

33-20 
33-66 

580.9 
582.0 

555-9 

43-96 
33-27 

12.64 
16.59 

35 

308 

41.83 

56.87 

.055 

617.2 

35.04 

582.1 

34.12 

583-1 

548^2 

25-44 

21-54 

40 

54-91 

74.65 

.072 

618.7 

40.05 

578.6 

34-59 

584.1 

544-1 

19.64 

27.70 

45 

3*8 

71-39 

97.06 

.094 

62O.2 

45.07 

575-1 

585.2 

540.1 

35.26 

5° 

323 

91.98 

125.0 

O.I2I 

621.7 

50.09 

57L7 

35-54 

586.2 

536.1 

12.049 

44-49 

g 

65 

328 
333 
338 

117.47 
148.79 
186.94 

159-7 
202.3 
254.2 

.246 

623.3 
624.8 
626.3 

60.13 
65.17 

568.2 
564.7 
561.1 

36.02 

36-51 
37.00 

587.2 
588.3 
589-3 

532.1 

528.1 
524.2 

9.561 

7.653 
6.171 

69.02 
84.94 

70 

343 

233.08 

316.9 

-306 

627.8 

70.20 

557-6 

3748 

590-4 

520.2 

5.014 

103.75 

75 

80 

348 

288.50 
354-62 

392.3 
482.1 

0.380 
.466 

629.4 
630.9 

75.24 
80.28 

554.1 
550.6 

37.96 
38-42 

59M 
592.5 

516.2 
512.2 

4.102 
3-379 

125.8 
ici.6 

85 
90 
95 

I 

433-00 
633.69 

588.7 
714.4 
861.7 

.570 
.691 
.834 

632.4 
633-9 
635'5 

85.33 
90.38 

95.44 

547-1 
543-6 
540.0 

38.88 

39-33 
39-76 

593-5 
594-6 
595-7 

508.2 
504-2 
500-3 

2.800 
2-334 
J-957 

181.5 
216.0 

255-7 

100 

373 

760.00 

1033- 

1.  000 

637.0 

100.5 

536.5 

40.20 

596.8 

496-3 

1.6496 

300.8 

105 

378 

906.41 

1232. 

•193 

638.5 

105.6 

533-o 

40.63 

597-9 

492-3 

I-3978 

352.2 

no 

383 

1075-4 

1462. 

.415 

640.0 

no.6 

5294 

41.05 

599-o 

488.4 

1.1903 

410.3 

"5 

388 

1269.4 

1726. 

.670 

641.6 

"5-7 

525-8 

41.46 

600.  i 

484.4 

1.0184 

475-6 

1  20 

393 

1491-3 

2027. 

.962 

643.1 

120.8 

522.3 

41.86 

601.2 

480.4 

0.8752 

549-0 

"5 

398 

1743.9 

2371. 

2.295 

644.6 

125.9 

518.7 

42.25 

602.4 

476.5 

0-7555 

630.7 

130 

403 

2030.3 

2760. 

2.671 

646.1 

131.0 

5I5*1 

42.63 

603-5 

472-5 

0.6548 

721.6 

140 

4oB 
413 

2353-7 
2717.6 

3200. 
3695- 

3-097 
3-576 

647.7 
649.2 

136.1 
141.2 

511.6 
508.0 

43.01 
43.38 

604.7 
605.8 

468.6 
464.6 

0.5698 
0.4977 

822.3 
933-5 

J45 

418 

3I25-6 

4249. 

4.113 

650.7 

146.3 

5044 

43-73 

607.0 

460.7 

04363 

1055-7 

150 

:55 

III 

3581-2 
4088.6 

4869. 
5589. 

4.712 
5-380 

652.2 
653-8 

I5L5 

500.8 
497-2 

44.09 
4443 

608.2 
609.3 

456.7 
452.8 

0-3839 
0.3388 

1190. 
1336- 

160 

433 

4651.6 

6324. 

6.120 

655.3 

161.7 

493-5 

4476 

610.5 

448.8 

0.3001 

1496. 

165 

438 

5274-5 

7171. 

6.940 

656.8 

166.9 

489.9 

45-09 

611.7 

444.8 

0.2665 

1669. 

170 

443 

5961-7 

8105. 

7.844 

658.3 

172.0 

486.3 

4540 

612.9 

440.9 

0.2375 

1856. 

XZ5 

448 

6717.4 

9I33- 

8.839 

659.9 

177.2 

482.7 

4571 

614.2 

436-9 

O.2I22 

2059. 

1  80 

185 

453 
458 

7546.4 
8453-2 

10260. 
11490. 

9.929 
11.123 

661.4 
662.9 

182.4 
187.6 

479.0 
475-3 

46.01 
46.30 

615.4 
616.6 

433-0 
429.0 

O.IOXDI 
0.1708 

2277. 
2512. 

190 

463 

9442.7 

12838. 

12.425 

664.4 

192.8 

471-7 

46.49 

617.9 

425.0 

0.1538 

2763. 

195 

468 

10520. 

14303- 

13.842 

666.0 

198.0 

468.0 

46.86 

619.1 

421.1 

0.1389 

3031- 

200 

473 

11689. 

15892. 

15.380 

667.5 

203.2 

464-3 

47.13 

620.4 

417.1 

0.1257 

33.8. 

*  Where  A  is  the  reciprocal  of  the  mechanical  equivalent  of  the  thermal  unit. 


_ff- 


=        internal-work  pressure 


Whefe  v  ^  taken  ^  lhres  the  Ufe  ig  ^yen  per  squflre 

v  mechanical  equivalent  of  heat 

decimetre,  and  where  v  is  taken  in  cubic  metres  the  pressure  is  given  per  square  metre,  —  the  mechanical  equivalent 
being  tliat  of  the  therm  and  the  kilogram-degree  or  calorie  respectively. 
SMITHSONIAN  TABLES. 


TABLE  291 . 
PROPERTIES  OF  STEAM. 

British  Measure. 


255 


The  quantities  given  in  the  different  columns  of  this  table  are  sufficiently  explained  by  the  headings.  The  abbrevia- 
tion B.  T.  U.  stands  for  British  thermal  units.  With  the  exception  of  column  3,  which  was  calculated  for  this 
table,  the  data  are  taken  from  a  table  given  by  Dwelshauvers-Dery  (Trans.  Am.  Sue.  Mech.  Eng.  vol.  xi.). 


Pressure 
in  pounds  per  1 
square  inch. 

Pressure 
in  pounds  per 
square  foot. 

5  JJ 

if 

Pi  rt 

A 

d« 

II 

Volume  per 
pound  in  cubic 
feet. 

Weight  per 
cubic  foot  in 
pounds. 

fa 
P.* 

^ 

K&« 

I| 

Sg,S 

1  g,*^ 
JSsSH 
•SJCSri 

External  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

| 

i  i?. 

2M^ 

*i!H 

H.c^M 

Total  heat  per  I 
pound  of  steam  1 
in  B.  T.  U. 

1 

144 

0.068 

IO2.O 

334-23 

0.0030 

70.1 

980.6 

62.34 

1043. 

1113.0 

2 

288 

.136 

126.3 

*73-23 

.0058 

94-4 

961.4 

64.62 

1026. 

II2O-4 

3 

432 

.204 

I4I.6 

117.98 

.0085 

109.9 

949-2 

66.58 

ion. 

1127.0 

4 

576 

.272 

I53-1 

89.80 

.0111 

121.4 

940.2 

67.06 

1007. 

II28.6 

S 

720 

•340 

162.3 

72.50 

.0137 

130.7 

932-8 

67.89 

IOOI. 

1131.4 

6 

864 

0.408 

170.1 

61.10 

0.0163 

138.6 

926.7 

68.58 

995-2 

"33-8 

7 

1008 

.476 

176.9 

53-°° 

.0189 

145-4 

921.3 

69.18 

990.5 

"35-9 

8 

1152 

•544 

182.9 

46.60 

.O2I4 

'S'-S 

916.5 

69.71 

986.2 

II37-7 

9 

1296 

.612 

188.3 

41.82 

.0239 

156.9 

912.2 

70.18 

982.4 

II39-4 

10 

1440 

.680 

193.2 

37.80 

.0264 

161.9 

908.3 

70.61 

979-o 

1140.9 

11 

1584 

0.748 

197.8 

34.61 

0.0289 

166.5 

904.8 

70.99 

975-8 

1142.3 

12 

1728 

.816 

2O2.O 

31.90 

.0314 

170.7 

901.5 

71-34 

972.8 

"43-5 

J3 

1872 

.884 

205.9 

29.58 

•0338 

J74-7 

898.4 

71.68 

970.0 

1144.7 

H 
15 

2Ol6 
2l6o 

•952 

1.020 

209.5 
213.0 

27-59 
25.87 

.0362 
•0387 

178.4 
181.9 

895-4 
892.7 

72.00 
72.29 

967.4 
965.0 

H45-9 
1146.9 

16 

2304 

1.  088 

216.3 

24-33 

0.04II 

185.2 

890.1 

72.57 

962.7 

1147.9 

17 

2448 

.156 

219.4 

22.98 

•0435 

188.4 

887.6 

72.82 

960.4 

1148.9 

18 

2592 

.224 

222.4 

21.78 

•0459 

191.4 

885.3 

73-07 

958.3 

1149.8 

19 

2736 

.292 

225.2 

20.70 

.0483 

'94-3 

883.1 

73-30 

956-3 

1  1  50.6 

20 

2880 

.360 

227.9 

19.72 

.0507 

197.0 

880.9 

73-53 

954-4 

1151.4 

21 

3024 

1.429 

23°-5 

18.84 

0.0531 

199.7 

878.8 

73-74 

952.6 

1152.2 

22 

3l68 

•497 

233-0 

18.03 

•0554 

2O2.2 

876.8 

73-94 

950.8 

"53-o 

23 

3312 

•565 

235-4 

17-3° 

.0578 

2047 

874.9 

74-13 

949.1 

"53-7 

24 

34  56 

•633 

237-7 

16.62 

.0602 

2O7.O 

873-I 

74-32 

947-4 

1154.4 

25 

3600 

.701 

240.0 

15-99 

.0625 

209.3 

871-3 

74.51 

945-8 

"55-i 

26 

27 

3744 
3888 

1.769 
•837 

242.2 
244-3 

15.42 
14.88 

0.0649 
.0672 

2II.5 

213-7 

869.6 
867.9 

74.69 
74.85 

944-3 
942.8 

1155.8 
1156.4 

28 

4032 

•9°5 

246.3 

14.38 

.0695 

215-7 

866.3 

75-01 

941-3 

ii57-i 

29 
30 

4176 
4320 

•973 
2.041 

248.3 
250.2 

I3-9I 
13.48 

.0619 
.0742 

217.8 
2197 

864.7 
863.2 

75-17 
75-33 

939-9 
938.5 

"57-7 
1158.3 

31 

4464 

2.109 

252.1 

13-07 

0.0765 

221.6 

861.7 

75-47 

937-2 

1  1  58.8 

32 

4608 

.177 

253-9 

12.68 

.0788 

223-5 

860.3 

75-6i 

935-9 

"59-4 

33 

4752 

•245 

255-7 

12.32 

.O8ll 

225-3 

858.9 

75-76 

934-6 

i  '59-9 

34 

4896 

•3!3 

257-5 

11.98 

.0835 

227.1 

857.5 

75-89 

933-4 

1160.5 

35 

5040 

.381 

259.2 

11.66 

.0858 

228.8 

856.1 

76.02 

932.1 

1161.0 

36 

5184 

2-449 

260.8 

11.36 

0.088  1 

230.5 

854.8 

76.16 

931.0 

1161.5 

37 

5328 

•5*7 

262.5 

11.07 

.0903 

232.2 

853.5 

76.28 

929.8 

1162.0 

38 

5472 

.585 

264.0 

10.79 

.0926 

233-8 

852-3 

76.40 

928.7 

1162.5 

39 

40 

5616 
5760 

•653 

.722 

265.6 
267.1 

10-53 
10.29 

.0949 
.0972 

235-4 
236.9 

851.0 
849-8 

76.52 
76.63 

927.6 
926.5 

1162.9 
1163.4 

41 

5904 

2.789 

268.6 

10.05 

0.0995 

238.5 

848.7 

76.75 

925-4 

1163.9 

42 

6048 

.857 

270.1 

9-83 

.1018 

239-9 

847-5 

76.86 

924.4 

1164.3 

43 

6192 

•925 

271.5 

9.61 

.IO4O 

241.4 

846.4 

76.97 

923-3 

1164.7 

44 

6336 

•993 

272.9 

9.41 

.1063 

242.9 

845.2 

77.07 

922.3 

1165.2 

45 

6480 

3-o6i 

274-3 

9.21 

.1086 

244-3 

844-1 

77.18 

921.3 

1165.6 

46 

6624 

3.129 

275.6 

9.02 

O.IIOS 

245.6 

843-1 

77.29 

920.4 

1  1  66.0 

47 

6768 

.197 

277.0 

8.84 

.1131 

247.0 

842.0 

77-39 

919.4 

1166.4 

48 

6912 

.265 

278.3 

8.67 

•TI53 

248.3 

841.0 

77-49 

918.5 

1166.8 

49 

7056 

•333 

279.6 

8.50 

.1176 

249.7 

840.0 

77-58 

9'7-5 

1167.2 

SMITHSONIAN  TABLES. 


256 


TABLE  291  (contittutd). 
PROPERTIES   OF   STEAM, 

British  measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

jj 

=4 

J 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot 
in  pounds. 

Heat  of  water 
per  pound  in 
B.  T.  U. 

Internal  latent  1 
heat  per  pound  I 
of  steam  in 
B.  T.  U. 

External  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

c 

Total  heat  per 
pound  of  steam 
in  B.  T.  U. 

50 

7200 

3.401 

280.8 

8-34 

0.1198 

251.0 

839.0 

77.67 

916.6 

1167.6 

51 

7344 

•469 

282.1 

8.19 

.1221 

252.2 

838.0 

77-76 

9T5-7 

II68.0 

52 

7488 

283-3 

8.04 

.1243 

253-5 

837.0 

77.85 

914.9 

1168.3 

53 

7632 

.605 

284.5 

7-9° 

.1266 

254-7 

836.0 

77-94 

914.0 

1168.7 

54 

7776 

.673 

285-7 

7.76 

.1288 

256.0 

835-I 

78.03 

1169.1 

55 

3-741 

286.9 

7-63 

O.I3IO 

257-1 

834.2 

78.12 

912.3 

1169.4 

56 

.810 

288.1 

7.50 

•J333 

258.3 

833.2 

78.21 

9IJ-5 

1169.8 

57 

.878 

289.2 

7.38 

•1355 

259-5 

832.3 

78.29 

910.6 

II70.I 

58 

8352 

.946 

290-3 

7.26 

•1377 

260.7 

83I-5 

78.37 

909.8 

1170.5 

59 

8496 

4.014 

291.4 

7.14 

.1400 

261.8 

830.6 

78.45 

909.0 

1170.8 

60 

8640 

4.082 

292.5 

7-03 

0.1422 

262.9 

829.7 

78.53 

908.2 

II7I.2 

61 

8784 

.150 

293.6 

6.92 

.1444 

264.0 

828.9 

78.61 

907-5 

1171.5 

62 
63 

8928 
9072 

.218 
.286 

294.7 
295-7 

6.82 
6.72 

.1466 
.1488 

265.1 
266.1 

828.0 
827.2 

78.68 
78.76 

906.7 
905-9 

II7I.8 
1172.1 

64 

9216 

•354 

296.7 

6.62 

.1511 

267.2 

826.4 

78.83 

905.2 

1172.4 

65 

9360 

4.422 

297.8 

6.52 

°-I533 

268.3 

825.6 

78.90 

904-5 

II72.8 

66 

9504 

•490 

298.8 

6-43 

269-3 

824.8 

78.97 

903-7 

1173.1 

67 

9648 

.558 

299.8 

6-34 

•1577 

270.4 

824.0 

79.04 

903.1 

"73-4 

68 

9792 

.626 

300.8 

6.25 

•'599 

271.4 

823.2 

79.11 

902.3 

II73-7 

69 

9936 

.694 

301.8 

6.17 

.1621 

272.4 

822.4 

79.18 

901.6 

1174.0 

70 

10080 

4.762 

302.7 

6.09 

0.1643 

273-4 

821.6 

79-25 

900.9 

II74-3 

71 

JO224 

•830 

303-7 

6.00 

.1665 

274-3 

820.9 

79-32 

1174.6 

72 

10368 

.898 

304.6 

5-93 

.1687 

275-3 

820.1 

79-39 

899.5 

1174.9 

73 

I05I2 

.966 

305-5 

5-8.5 

.1709 

276-3 

819.4 

79.46 

898.8 

"75-1 

74 

10656 

5-034 

306.5 

5.78 

•I731 

277.2 

818.7 

79-53 

898.1 

"75-4 

75 

I0800 

5.102 

307-4 

5-70 

0.1753 

278.2 

817.9 

79-59 

897-5 

H75-7 

76 

10944 

.170 

308.3 

5-63 

•1775 

279.1 

817.2 

79-65 

896.9 

1176.0 

77 

II088 

•238 

309.2 

5-57 

.1797 

280.0 

816.5 

79.71 

896.2 

1176.2 

78 

II232 

-306 

310.1 

5-50 

.1818 

280.9 

815.8 

79-77 

895.6 

1176.5 

79 

II376 

•374 

310.9 

5-43 

.1840 

281.8 

815.1 

79-83 

895-0 

1176.8 

80 

II520 

5-442 

311.8 

5-37 

0.1862 

282.7 

814.4 

79.89 

894-3 

1177.0 

81 

11664 

.510 

3I2-7 

5-31 

.1884 

283.6 

813.8 

79-95 

893-7 

"77-3 

82 
83 

Il8o8 
II952 

.646 

3I3-5 
3r4-4 

5-25 

.1906 
.1928 

284.5 

813.0 
812.4 

80.01 
80.07 

893.1 
892.5 

1177.6 

1177.8 

84 

I2096 

.714 

3I5-2 

5-J3 

.1949 

286.2 

811.7 

80.13 

891.9 

1178.0 

85 

I224O 

5.782 

316.0 

5-°7 

0.1971 

287.0 

8II.I 

80.19 

891.3 

1178.3 

86 

87 
88 

11384 
I2|28 
12672 

.850 
.918 
.986 

316.8 
3184 

5.02 
4.96 
4.91 

•'993 
.2015 
.2036 

287.9 
288.7 
289.5 

810.4 
809.8 
809.2 

80.25 
80.30 
80.35 

890.7 

1178.6 
1178.9 
1179.0 

89 

I28l6 

6.054 

319.2 

4.86 

.2058 

290.4 

808.5 

80.40 

888.9 

IJ79-3 

90 

12960 

6.122 

320.0 

4.81 

0.2080 

291.2 

807.9 

80.45 

888.4 

"79-5 

91 

13104 

.190 

320.8 

4.76 

.2102 

292.0 

807-3 

80.50 

887.8 

1179.8 

92 

13248 

.258 

321.6 

4.71 

.2123 

292.8 

806.7 

80.56 

887.2 

1180.0 

93 
94 

13536 

.327 
•396 

322.4 
323-1 

4.66 
4.62 

.2145 
.2166 

293.6 
294-3 

806.  1 
805-5 

80.6  1 
80.66 

886.7 
886.1 

1180.3 
1180.5 

95 

13680 

6.463 

323-9 

4-57 

0.2188 

295.1 

804.9 

80.71 

885.6 

1180.7 

96 

13824 

•531 

324.6 

4.53 

.2209 

295-9 

804-3 

80.76 

885.0 

1180.9 

97 

13968 

-599 

3254 

4.48 

.2231 

296.7 

803.7 

80.8  1 

884.5 

1181.2 

98 

I4II2 

.667 

326.1 

4-44 

.2252 

2974 

803.1 

80.86 

884.0 

1181.4 

99 

14256 

•735 

326.8 

4.40 

.2274 

298.2 

802.5 

80.91 

883.4 

1181.6 

SMITHSONIAN  TABLES. 


TABLE   291  (continued). 

PROPERTIES  OF  STEAM. 

British  Measure. 


257 


Pressure  in 
pounds  per 
square  inch. 

Pressuie  in 
pounds  per 
square  foot. 

Pressure  in 
atmospheres. 

Temp,  in 
degrees  Fahr. 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
per  pound  in 
B.  T.U.  II 

11 
4S§,S 

IsJ* 

fc^lJH 

JS.c'Sm 

External  latent  1 
heat  per  pound  1 
of  steam  in 
B.  T.  U.  | 

Total  latent 
heat  per  pound  1 
of  steam  in 
B.  T.  U. 

Total  heat  per 
pound  of  steam  1 
in  B.  T.  U. 

100 

14400 

6.803 

327.6 

4-356 

0.2295 

298.9 

802.0 

80.95 

882.9 

1181.8 

IOI 

.871 

328.3 

.316 

.2317 

299-7 

801.4 

Sl.OO 

882.4 

II82.I 

102 

14688 

•939 

329.0 

.276 

•2338 

300.4 

800.8 

81.05 

881.9 

1182.3 

103 

14832 

7.007 

329-7 

•237 

.2360 

30I.I 

800.3 

Sl.IO 

881.4 

1182.5 

I04 

14976 

•075 

330-4 

.199 

.2381 

301.9 

799-7 

81.14 

880.8 

1182.7 

105 

I5I20 

7-143 

331-1 

4.161 

0.2403 

302.6 

799-2 

81.18 

880.3 

1182.9 

106 

15264 

.211 

331-8 

.125 

.2424 

303-3 

798.6 

81.23 

879.8 

1183.1 

107 

15408 

.279 

332.5 

.088 

.2446 

304.0 

798.1 

81.27 

879-3 

Il83.4 

108 
109 

'5552 
15696 

•347 
415 

333-2 
333-8 

.018 

.2467 
.2489 

304-7 
3054 

797-5 
797.0 

81.31 
81.36 

878.8 
878.3 

1183.6 
1183.8 

110 

15840 

7-483 

334-5 

3-984 

0.2510 

306.1 

796.5 

81.41 

877.9 

1184.0 

in 

15984 

•551 

335-2 

•95° 

•2531 

306.8 

795-9 

81.45 

8774 

1184.2 

112 

16128 

.619 

335-8 

.917 

•2553 

307.5 

7954 

81.50 

876.9 

1184.4 

113 

16272 

.687 

336-5 

.885 

•2574 

308.2 

794-9 

81.54 

876.4 

1184.6 

114 

16416 

•755 

337-2 

.853 

•2596 

308.8 

794-4 

8158 

875.9 

1184.8 

115 

16560 

7.823 

337-8 

3.821 

0.2617 

309-5 

793-8 

81.62 

875.5 

1185.0 

116 

16704 

.891 

338.5 

.790 

.2638 

3IO.2 

793-3 

81.66 

875.0 

1185.2 

117 

16848 

•959 

339-i 

.760 

.2660 

310.8 

792.8 

81.70 

874-5 

1185.4 

1x8 

16992 

8.027 

339-7 

•73° 

.2681 

3II-5 

792.3 

81.74 

874-1 

1185.6 

119 

17136 

•095 

3404 

.700 

.2702 

3I2.I 

791.8 

81.78 

873.6 

1185.7 

120 

17280 

8.163 

341.0 

3.671 

0.2724 

312.8 

79L3 

81.82 

873.2 

1185.9 

121 
122 

17424 
17568 

.231 
•299 

341.6 
342.2 

•643 
.615 

•2745 
.2766 

3134 

790.8 
79°-3 

81.86 
81.90 

872.7 
872.2 

II86.I 
Il86.3 

123 

17712 

-367 

342.8 

.587 

.2787 

3J4-7 

789.9 

81.94 

871.8 

1186.5 

124 

17856 

435 

343-5 

.560 

.2809 

3I5-3 

789.4 

81.98 

871.4 

1186.7 

125 

18000 

8-503 

344-1 

3-534 

0.2830 

316.0 

788.9 

82.02 

870.9 

1186.9 

126 

18144 

•571 

344-7 

•5°7 

.2851 

316.6 

788.4 

82.06 

870.5 

1187.1 

127 

18288 

•639 

345-3 

.481 

.2872 

317.2 

787.9 

82.09 

870.0 

1187.2 

128 
129 

18432 
18576 

.708 
.776 

345-9 
346.5 

456 
431 

•2893 
.2915 

3I7-8 
318.4 

787-5 
787.0 

82.13 
82.17 

869.6 
869.2 

1187.4 
1187.6 

130 

18720 

8.844 

347-J 

3-406 

0.2936 

319.0 

786.5 

82.21 

868.7 

1187.8 

132 

!9oo8 

.912 
.980 

347-6 
348.2 

.382 
•358 

•2957 
.2978 

3I9-7 
320.3 

786.1 
785-6 

82.25 
82.28 

868.3 
867.9 

II88.0 
II88.I 

133 
134 

19152 
19296 

9.048 
.116 

348.8 
349-4 

•334 
.310 

.2999 
.3021 

320.9 
321-5 

785.1 
784.7 

82.32 
82.35 

867.5 
867.0 

1188.3 
1188.5 

135 

19440 

9.184 

349-9 

3.287 

0.3042 

322.1 

784.2 

82.38 

866.6 

1188.7 

136 

19584 

.252 

350-5 

.265 

•3063 

322.6 

783-8 

82.42 

866.2 

II88.8 

137 

19728 

•320 

351-1 

442 

.3084 

323-2 

783-3 

82.45 

865.8 

1189.0 

138 

19872 

.388 

35r-6 

.220 

•3105 

782.9 

82.49 

865.4 

1189.2 

139 

20016 

•456 

352-2 

.199 

.3126 

324-4 

782.4 

82.52 

865.0 

1189.4 

140 

20160 

9.524 

352-8 

3-177 

0-3147 

325-0 

782.0 

82.56 

864.6 

1189.5 

141 
142 

20304 
20448 

.592 

353-3 
353-9 

.156 
•135 

.3168 
.3190 

325-5 
326.1 

781.6 
781.1 

82.59 
82.63 

864.2 
863.8 

1189.7 
1189.9 

20592 

.728 

354-4 

•IJ5 

.3211 

326.7 

780.7 

82.66 

863.4 

II90.0 

144 

20736 

•796 

355-o 

.094 

•3232 

327.2 

780.3 

82.69 

863.0 

II90.2 

145 

20880 

9.864 

355-5 

3-074 

0-3253 

327.8 

779-8 

82.72 

862.6 

1190.4 

146 

21024 

•932 

356.o 

•054 

•3274 

328.4 

779-4 

82.75 

862.2 

1190.5 

$ 

21168 
21312 

IO.OOO 

.068 

356.6 
357-1 

•035 
.016 

•3295 

328.9 

779-0 
778.6 

82.79 
82.82 

861.8 
861.4 

1190.7 
1190.9 

149 

21456 

.136 

357-6 

•997 

•3337 

330-0 

778.1 

82.86 

861.0 

II9I.O 

SMITHSONIAN  TABLES. 


258 


TABLE    291    (continued). 

PROPERTIES  OF  STEAM, 

British  Measure. 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

•sj 

£4  rt 

ii 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
per  pound  in 

Internal  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

External  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

Total  heat  per 
pound  of  steam  I 
in  B.  T.  U. 

150 

2I6OO 

10.204 

358.2 

2.978 

0.3358 

330-6 

777-7 

82.89 

860.6 

II9I.2 

151 

21744 

.272 

3587 

.960 

•3379 

33I-I 

777-3 

82.92 

860.2 

1191.3 

J52 

21888 

•340 

359-2 

.941 

.3400 

33  !  -6 

776.9 

82.95 

859-9 

1191.5 

I53 

22032 

.408 

359-7 

•923 

•3421 

332.2 

776.5 

82.98 

859-5 

1191.7 

154 

22176 

•476 

360.2 

.906 

.3442 

332-7 

776.1 

83.01 

859.1 

1191.8 

155 

22320 

10-544 

360.7 

2.888 

0.3462 

333-2 

775-7 

83.04 

858.7 

II92.0 

156 

22464 

.612 

361-3 

.871 

.3483 

333-8 

775-3 

83-07 

858.3 

II92.I 

157 
158 

22608 
22752 
22896 

.680 
.748 
.8l6 

361.8 

llli 

-854 
.837 
.820 

•35°4 
•3525 
•3546 

334-3 
334-8 
335-3 

774-9 
774-5 
774-1 

83.10 

83-I3 
83-16 

858.0 
857.6 

1192.3 
1192.4 
1192.6 

160 

161 

23040 
23184 

10.884 
.952 

363.8 

2.803 
.787 

0.3567 

335-9 
336.4 

773-7 
773-3 

83.19 
83.22 

856.9 
856.5 

1192.7 
1192.9 

162 
163 

23328 
23472 

II.O2O 
.088 

364*8 

.771 
•755 

•3630 

336-9 
337-4 

772.9 
772-5 

83.25 
83.28 

856.1 
855.8 

1193.0 
1193.2 

164 

23616 

•IS7 

365-3 

•739 

•3650 

337-9 

772.1 

83-3I 

855.4 

H93.3 

165 

23760 

11.225 

365.7 

2.724 

0.3671 

338.4 

771.7 

83-34 

855-1 

ir93-5 

1  66 

23904 

•293 

366.2 

.708 

•3692 

338.9 

77L3 

83-37 

8547 

1193.6 

167 

24048 

.361 

366.7 

•693 

•3713 

339-4 

771.0 

83.39 

854.3 

1193.8 

1  68 

24192 

.429 

367-2 

.678 

•3734 

339-9 

770.6 

854.0 

"93-9 

169 

24336 

•497 

367-7 

.663 

•3754 

340-4 

770.2 

8345 

853-6 

1194.1 

170 

24480 

"•565 

368.2 

2.649 

0-3775 

340-9 

769.8 

83.48 

853-3 

1194.2 

171 

24624 

•633 

368.6 

•634 

.3796 

341-4 

769.4 

83.51 

852.9 

1194.4 

172 

24768 

.701 

369.1 

.620 

.3817 

34L9 

769.1 

83-54 

852.6 

"94-5 

24912 

•769 

369.6 

.606 

•3838 

342.4 

768.7 

83.56 

852.2 

1194.7 

174 

25056 

•837 

370.0 

•592 

•3858 

342-9 

768.3 

83-59 

851.9 

1194.8 

175 

25200 

11.905 

370.5 

2.578 

0.3879 

343-4 

767.9 

83.62 

851.6 

1194.9 

176 

25344 

•973 

371.0 

•564 

.3900 

343-9 

767-6 

83.64 

851.2 

1195.1 

177 

25488 

12.041 

371.4 

•55° 

.3921 

344-3 

767.2 

83.67 

850.9 

1195.2 

178 

25632 

.109 

371-9 

•537 

•3942 

344-8 

766.8 

83.70 

850.5 

"95-4 

179 

25776 

.177 

372.4 

524 

.3962 

345-3 

766.5 

83-73 

850.2 

"95-5 

180 

25920 

12.245 

372.8 

2.510 

0-3983 

345-8 

766.1 

83-75 

849.9 

1195.6 

181 

26064 

.313 

373-3 

•497 

.4004 

346.3 

765-8 

8377 

849-5 

1195.8 

182 
183 

26208 
26352 

.381 
•449 

373-7 
374-2 

•485 
.472 

.4025 
.4046 

346.7 
347-2 

7654 
765.0 

83.80 
83.83 

849.2 
848.9 

"95-9 
1196.1 

184 

26496 

•S'7 

374-6 

•459 

.4066 

347-7 

764-7 

83.86 

848-5 

1196.2 

185 

186 

26640 
26784 
26928 

12.585 

•653 
.721 

375-1 
375-5 
376.o 

2.447 

.434 
.422 

0.4087 
.4108 
.4129 

348.1 
348.6 

349-1 

764.3 
764.0 

763-6 

83.88 
83.90 
83-92 

848.2 
847.9 
847.5 

1196.3 

"96-5 
1196.6 

188 
189 

27072 
27216 

.789 
.857 

376.4 
376.8 

.410 
•398 

.4150 
.4170 

349-5 
350.0 

763-3 
762.9 

83-95 
83-97 

847.2 
846.9 

1196.7 
1196.9 

190 

27360 

12.925 

377-3 

2.386 

0.4191 

350.4 

762.6 

83-99 

846.6 

1197.0 

191 

27504 

•993 

377-7 

•374 

.4212 

350.9 

762.2 

84.02 

846-3 

1197.1 

192 

27648 

13.061 

378.2 

•362 

•4233 

351.3 

761.9 

84.04 

845-9 

1197.3 

193 

27792 

.129 

378.6 

•351 

•4254 

351-8 

761.6 

84.06 

845-6 

1197.4 

194 

27936 

.197 

379-0 

•339 

•4275 

352-2 

761.2 

84.08 

845-3 

U97.5 

195 

28080 

13-265 

379-4 

2-328 

0.4296 

352-7 

760.9 

84.10 

845-0 

1197.7 

196 

28224 

•333 

379-9 

•3T7 

.4316 

353-1 

760.5 

84.13 

844.7 

1197.8 

197 

28368 

.401 

380.3 

.306 

•4337 

353-6 

760.2 

84.16 

844-4 

1197.9 

198 

28512 

.469 

380.7 

•4358 

354-0 

759-9 

84.19 

844.0 

1198.1 

199 

28656 

•537 

381.1 

.2894 

•4379 

354-4 

759.5 

84.21 

843-7 

1198.2 

SMITHSONIAN  TABLES. 


TABLE    291    (continued). 

PROPERTIES  OF  STEAM. 

British  Measure. 


259 


Pressure  in 
pounds  per 
square  inch. 

Pressure  in 
pounds  per 
square  foot. 

.5  § 

<U  J3 
II 

Temp,  in 
degrees  Fahr. 

Volume  per 
pound  in 
cubic  feet. 

Weight  per 
cubic  foot  in 
pounds. 

Heat  of  water 
per  pound  in 

frf.  u. 

Internal  latent 
heat  per  pound 
of  steam  in 
B.  T.  U.  | 

External  latent 
heat  per  pound 
of  steam  in 
B.  T.  U. 

'c  o  c 
Jfe|C> 

!|l* 

h.e'oM 

Total  heat  per 
pound  of  steam 
in  B.  T.  U. 

200 

201 

28800 
28944 

13605 
I3-673 

381.6 
382.0 

2.273 
.262 

0.4399 
.4420 

354-9 

355-3 

759-2 
758.9 

84-23 
84.26 

843-4 
843-1 

"98.3 
1198.4 

2O2 
203 
204 

29088 
29232 
29376 

13742 
I3.8lO 
I3-878 

382.4 
382.8 
383.2 

.252 
.241 
.231 

.4441 
.4461 
.4482 

355-8 
356.2 
356.6 

758.5 
758.2 

757-9 

84.28 
84-30 
84-33 

842.8 
842.5 
842.2 

1198.6 
1198.7 
1198.8 

205 

29C20 

13.946 

383-7 

2.221 

0.4503 

357-1 

757-5 

84.35 

841.9 

1199.0 

206 

29664 

I4.OI4 

384.1 

.211 

4523 

357-5 

757-2 

84-37 

841.6 

II99.I 

207 

29808 

14.082 

384.5 

.2OI 

•4544 

357-9 

756-9 

8440 

841.3 

II99.2 

208 
209 

29952 
30096 

14.150 
I4.2I8 

384.9 
385-3 

:!§! 

•4564 
.4585 

358-3 
358.8 

756.6 
756.2 

84.42 
84.44 

841.0 
840.7 

11  99-3 
1199.4 

210 

211 
212 

30240 

30384 
30528 

14.386 

14-454 
14.522 

385-7 
386.1 

386.  s 

2.171 
.162 
.152 

0.4605 
.4626 
.4646 

359-2 
359-6 
360.0 

755-9 
755-6 
755-3 

84.46 
84.48 
84.51 

840.4 
840.1 
839-8 

II99.6 
1199.7 
II99.8 

213 

214 

30672 
30816 

14.590 
14.658 

386.9 
387.3 

.143 
.134 

.4666 
.4687 

360.4 
360.9 

755-o 
754-7 

84-53 
84-55 

839-5 
839.2 

1199.9 
1  200.  1 

215 

216 

30960 
31104 

14.726 
14.794 

387-7 
388.1 

2.124 

0.4707 
.4727 

361-3 
361.7 

754-3 
754-o 

84.57 
84.60 

ifl 

1200.2 
1200-3 

217 

31248 

14.862 

388.  s 

.106 

.4748 

362.1 

753-7 

84.62 

838.3 

I2OO.4 

218 

3r392 

14.930 

388.9 

.097 

362.5 

753-4 

84.64 

838.0 

I2OO.5 

219 

31536 

14.998 

389-3 

.088 

.4788 

362.9 

753-1 

84.66 

837.7 

1200.7 

SMITHSONIAN  TABLES. 


260 


TABLE  292. 


RATIO  OF  THE  ELECTROSTATIC  TO  THE  ELECTROMAGNETIC  UNIT  OF 

ELECTRICITY  =  F. 


Date. 

V 
Cm.  per  sec. 

Mean. 

Determined  by 

Reference. 

1856 

3-nXio10 

R.  Kohlrausch  and 
W.  Weber. 

Pogg.  Ann.  99  ;  1856. 

1868 

2.75-2.92  X  io10 

2.84 

Maxwell. 

Phil.  Trans.  ;  1868. 

1869 

2.71-2.88 

2.8l 

Thomson  and  King. 

B.  A.  Report  ;  1869. 

1874 

2.86-3.00 

2.90 

McKichan. 

Phil.  Mag.  47  ;  1874. 

1879 
1879 
1879 

2.950-3.018 

2.981 
2.96 
2.967 

Rowland. 
Ayrton  and  Perry. 
Hockin. 

Phil.  Mag.  28  ;  1889. 
Phil.  Mag.  7  ;   1879. 
B.  A.  Report  ;  1879. 

1880 

_ 

2.955 

Shida. 

Phil.  Mag.  io  ;  1880. 

1881 

2.98-3.00 

2.99 

Stoletow. 

Jour,  de  Phys.  ;  1881. 

1882 

2.87 

Exner. 

Wien.  Ber.  ;  1882. 

1883 

_ 

2.963 

J.  J.  Thomson. 

Phil.  Trans.  ;  1883. 

1884 

3.001-3.029 

3.019 

Klemencic. 

Wien.  Ber.  83,  89,  93  ;  1881-6. 

« 

3.016-3.031 

1886 

3-OIS 

Colley. 

Wied.  Ann.  28  ;  1886. 

1886-8 

2.999-3.009 

<l 

3.003-3.008 

3.009 

Himstedt. 

Wied.  Ann.  29,  33,  35  ;  1887-8. 

(« 

3.005-3.015 

1888 

2.92 

Thomson,    Ayrton 

and  Perry. 

Electr.  Rev.  23;  1888-9. 

1889 

2.995-3.010 

3-OOO 

Rosa. 

Phil.  Mag.  28  ;  1889. 

1890 

2.996 

J.  J.  Thomson  and 

Searle. 

Phil.  Trans.  ;  1890. 

1891 

- 

3.009 

Pellat. 

Jour,  de  Phys.  io  ;  1891. 

1892 

2.990-2.995 

2.991 

Abraham. 

Ann.  Chim.  et  Phys.  27;  1829. 

1896 

3.001 

Hurmuzescu. 

Ann.  Chim.  et  Phys.  io;  1897. 

1898 

- 

2-9973 

Perot  and  Fabry. 

Ann.  Chim.  et  Phys.  13  ;  1898. 

1898 

— 

3.026 

Webster. 

Phys.  Rev.  6  ;  1898. 

1899 

— 

3.009 

Lodge    and    Glaze- 

brook. 

Cam.  Phil.  Soc.  18;  1899. 

1904-7 

2.99706-2.99741 

2.9971 

Rosa  and  Dorsey. 

Bull.  Bur.  Standards  3  ;  1907. 

The  last  of  the  above  determinations  is  the  result  of  an  extended  series  of  measurements  upon 
various  forms  of  condensers,  and  is  believed  to  be  correct  within  I  /ioo  per  cent.  This,  however, 
assumes  that  the  International  Ohm  is  io9  c.g.s.  units.  The  value  of  V\&  therefore  subject  to 
one-half  the  error  of  the  International  Ohm. 


SMITHSONIAN  TABLES. 


TABLE  293.  26 1 

ABSOLUTE   MEASUREMENTS  OF   CURRENTS   AND   OF  THE    ELECTRO- 
MOTIVE   FORCE   OF   STANDARD   CELLS. 


Electromotive 

Electrochemical  Equiv- 

! 

Force*  of 

alent  of  Silver. 

8 

Date. 

Observer. 

Method. 

Clark 
Cell  at 

Weston 
Cell  at 
o  r* 

Filter 
Paper 

Volta- 

Porous 
Cup 
Volta- 

No- 
Septum 
Volta- 

1 

15°  C. 

2OU  C. 

meter. 

meter. 

meter. 

M 

Volts. 

Volts. 

Mg. 

Mg. 

Mg. 

1872 

Clark 

(  Electrodynamometer 
(  Sine  Galvanometer 

1-4573 
1.4562 

- 

- 

- 

:} 

I 

1873 

F.  Kohlrausch 

Tangent  Galvanometer 

- 

1.1363 

- 

2 

1882 

Mascart 

Current  Balance 

_ 

_ 

_ 

1.1156 

3 

1884 

F.  and  W.  Kohlrausch 

Tangent  Galvanometer 

_ 

_ 

_ 

_ 

1.1183 

4 

1884 

Rayleigh  and  Sedgwick 

Current  Balance 

1-435 

- 

i.  "794 

- 

5 

1886 

Gray 

Sine  Galvanometer 

_ 

_ 

1.1183 

6 

1887 

Koepsel 

Electromag.  Balance 

_ 

_ 

1.11740 

_ 

7  i 

1890 

Potier  and  Pellat 

Electrodynamometer 

_ 

_ 

_ 

1.1192 

8 

1896 

Kahle  t 

Electrodynamometer 

I-4325 

1.0183 

- 

- 

1.1183 

9 

1898 

Patterson  and  Guthe 

Electrodynamometer 

_ 

1.1192 

— 

— 

10 

1899 

Carhart  and  Guthe 

Electrodynamometer 

1-4333 

_ 

•  _ 

_ 

_ 

n 

1902 

Callendar  and  King 

Electrodynamometer 

1-4334 

_ 

_ 

_ 

_ 

12 

1903 

Pellat  and  Leduc 

Electrodynamometer 

_ 

1.1195 

- 

_ 

13 

1904 

Van  Dijk  and  Kunst 

Tangent  Galvanometer 

- 

- 

1.11823 

- 

- 

14 

1905 

Guthe 

Electrodynamometer 

1.43296 

1.01853 

— 

I-  "773 

— 

15 

1906 

Van  Dijk 

Revision  of  1904  work 

_ 

— 

1.1180 

_ 

16 

1907 

Ayrton,  Mather  and  Smith 

Current  Balance 

1-4323 

1.01819 

_ 

_ 

_ 

17 

1907 

Smith,  Mather  and  Lowry 

With  the  above 

1.11827 

_ 

_ 

18 

1908 

Janet,  Laporte  and  Jouaust  t 

Current  Balance 

_ 

1.01836 

_ 

_ 

19 

1908 

Janet,  Laporte  and  de  la  Gorce 

With  the  above 

_ 

1.11821 

- 

- 

20] 

1908 

Guillet  t 

Current  Balance 

_ 

1.01812 

— 

— 

_ 

21 

1908 

Pellat  I 

Electrodynamometer 

_ 

1.01831 

_ 

_ 

_ 

22 

1910 
1911 

Haga  and  Boerema 
Rosa,  Dorsey  and  Miller 

Tangent  Galvanometer 
Current  Balance 

- 

1.01825 
1.01822 

- 

- 

: 

23 
24 

1911 

Rosa,  Vinal  and  McDaniel 

With  the  above 

_ 

_ 

_ 

1.11804 

1.11804 

25 

1913 

Haga  and  Boerema 

Tangent  Galvanometer 

- 

— 

~ 

i.  11802 

26 

I  Proc.  Roy.  Soc.  May  3oth,  1872  (Values  in  B.  A.  volts     14  Ann.  d.  Phys.  vol.  14,  p.  569,  1904. 

at  15.5  C.).                                                                     IS  Bull.  B.  S.  vol.  2,  p.  33,  1906. 

2  Pogg.  Ann.  vol.  149,  p.  170  (anode  wrapped  in  cloth).    16  Ann.  d.  Phys.  vol.  19,  p.  249,  1906. 

3  J.  de  Phys.  vol.  i,  p.  109,  vol.  3,  p.  283.                          17  Phil.  Trans.  A,  vol,  207,  p.  463,  1008. 
4  Wied.  Ann.  vol.  27,  p.  i,  1886.                                         18  Phil.  Trans.  A,  vol.  207,  p.  545,  1908. 

5  Phil.  Trans.  A,  vol.  175,  p.  411,  1884.                              19  Bull.  Int.  Soc.  Electr.  vol.  8,  p.  459,  1008.  C.  R.  vol. 

6  Phil.  Mag.  vol.  22,  p.  389,  1886.                                                i 
7  Ann.  d.  Phys.  vol.  31,  p.  250,  1887.                                  20  Bu 

3,  p.  718,  ion. 
.  Int.  Soc.  Electr.  vol.  8,  p.  523,  1908. 

8  J.  de  Phys.  vol.  9,  p.  381,  1890.                                        21  Bull.  Int.  Soc.  Electr.  vol.  8,  p.  535,  1908. 
9  Zs  f  Instr.  vol.  17,  p.  97,  143-4,  vol.  18,  p.  276.              22  Bull.  Int.  Soc.  Electr.  vol.  8,  p.  573,  1008. 

10  Phys.  Rev.  vol.  7,  P-  257-   (Added  Ag20).                         23  Proc.  Ak.  Wiss.  Amster.  vol.  13,  p.  587. 

ii  Phys.  Rev.  vol.  9,  p.  288,  1899.                                        24  Bull.  Bureau  Standards,  vol.  8,  p.  269,  1912. 

12  Phil.  Trans.  A,  vol.  199,  p.  81,  1902.                                25  Bull.  Bulletin  Standards,  vol.  8,  p.  367,  1912. 
13  C.  R.  vol.  136,  p.  1649.   (Muslin  and  filter  paper  both  26  Arch.  Neer.  Sci.  IIIA,  vol.  3,  P-  324,  1913. 

used.) 

*  The  values  given  in  these  columns  are  not  strictly  absolute  volts  since  they  were  in  most  cases  determined  in  terms 
of  an  absolute  ampere  and  an  international  ohm.  Hence  they  may  be  called  "semi-absolute."  No  absolute  determina- 
tions of  the  ohm  have  been  made  in  recent  times,  but  some  are  in  progress. 

t  Other  values  usually  given  as  Kahle's  results  and  officially  used  by  the  Reichsanstalt  are  voltameter  determinations. 
To  include  them  here  would  necessitate  including  many  others  similarly  made.  The  value  1.1183  includes  5  filter  paper 
determinations  out  of  26  observations. 

t  These  values  have  been  corrected  for  the  difference  between  the  French  ohm  at  this  time  and  that  in  use  elsewhere. 
(C.  R.  vol.  153,  P- 7i8.) 


Measurements  prior  to  Van  Dijk  (1906)  and  the  subsequent  filter  paper  voltameter  determinations  are  now  only  of 
historical  interest,  but  the  large  amount  of  work  done  in  recent  years  makes  these  early  determinations  of  especial  inter- 
est. The  errors  due  to  the  use  of  filter  paper  and  other  impurities  (acid,  alkali,  colloidal  matter,  etc.)  in  the  voltameter 
electrolyte  make  it  impossible  to  apply  corrections.  The  values  for  the  cell  are  not  readily  comparable  owing  to  varia- 
tions in  the  voltage  of  the  cell  itself  and  the  unit  of  resistance.  See  Dora,  Wiss.  Abhl.  der  Phys.  Tech.  Reich.,  vol.  II,  p. 
257.  Since  1911  the  voltage  adopted  for  the  Weston  Normal  Cell  at  20°  C.  is  1.0183  international  volts  in  all  the  leading 
countries.  The  international  volt  is  to  be  distinguished  from  the  absolute  volt  since  it  is  based  on  the  definition  of  the 
mercury  ohm  and  the  silver  voltameter,  taking  the  electrochemical  equivalent  of  silver  to  be  1.11800  mg  per  coulomb. 
The  difference  between  the  international  volt  and  the  absolute  volt  is  negligible  for  practical  purposes.  The  tempera- 
ture coefficient  of  the  Weston  Normal  Cell  (saturated  type)  is  given  in  Table  294.  The  new  value  of  the  Weston  cell  was 
adopted  in  the  United  States  on  January  i,  1911. 

SMITHSONIAN  TABLES. 


262  TABLE  294. 

COMPOSITION  AND  ELECTROMOTIVE  FORCE  OF  VOLTAIC  CELLS. 

The  electromotive  forces  given  in  this  table  approximately  represent  what  may  be  expected  from  a  cell  in  good  work- 
ing order,  but  with  the  exception  of  the  standard  cells  all  of  them  are  subject  to  considerable  variation. 


(a)  DOUBLE  FLUID  CELLS. 

Name  of 
cell. 

Negative  pole. 

Solution. 

Positive 
pole. 

Solution. 

** 

ail 

w.S 

Bunsen  .    . 

Amalgamated  zinc 

(  i  part  H2SO4  to  1 
(     12  parts  H2O  .  J 

Carbon 

Fuming  H2NOa 

1.94 

« 

«                « 

« 

«« 

HNO3,  density  1.38 

1.86 

Chr  ornate  . 

«                <t 

f  i2partsK2Cr2O7l 
to  25  parts  of  1 
|     H2SO4  and  100  [ 
[    parts  H2O  .     .  J 

«< 

(  i   part  H2SO4  to  ) 
(      12  parts  H2O     .  ) 

2.00 

« 

<(                « 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O  .  j 

«( 

(  12  parts  K2Cr2O7  ( 
1    to  100  parts  H2O  J 

2.03 

Daniell*   . 

«                « 

(  i  part  H2SO4  to  ) 
I     4  parts  H2O    .  J 

Copper 

(  Saturated  solution  ) 
\  ofCuS04+sH2Oi 

1.06 

« 

«                « 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O  .  ( 

« 

« 

1.09 

u 

«                «< 

(  5%    solution    of  { 
\    ZnS04  +  6H20( 

u 

«« 

i.  08 

« 

«                « 

(  i  part  NaCl   to  ) 
I     4  parts  H2O   .  j 

<« 

<« 

1.05 

Grove   .    . 

«                « 

(  i  part  H2SO4  to  ) 
I      12  parts  H2O  .  J 

Platinum 

Fuming  HNO3  .    . 

i-93 

« 

«                <« 

Solution  of  ZnSO4 

« 

HNO8,  density  1.33 

1.66 

a 

<«                «< 

(  H2SO4  solution,  ) 
(      density  1.136  .  ) 

«{ 

Concentrated  HNO3 

i-93 

a 

«                « 

(  H2SO4  solution,  ) 
(      density  1.136  .  f 

« 

HNO8,  density  1.33 

1.79 

« 

<c                   « 

(  H2SO4  solution,  ) 
(      density  1.06    .  ) 

• 

« 

1.71 

it 

«                   « 

(  H2SO4  solution,  ) 
(      density  1.14    .  ) 

« 

HNOs,  density  1.19 

1.66 

M 

«                  <« 

(  H2SO4  solution,  ) 
(      density  1.06     .  ) 

<« 

«<           «            «« 

1.61 

M 

((                       <( 

NaCl  solution  .    . 

M 

"       density  1.33 

1.88 

Marie  Davy 

({                  « 

(  i  part  H2SO4  to  ) 
(      12  parts  H2O    ) 

Carbon 

(  Paste  of  protosul-  ) 
<    phate  of  mercury  > 
(    and  water  .    .     .  ) 

1.50 

Partz     .    . 

(«                      « 

Solution  of  MgSO4 

<« 

Solution  of  K2Cr2O7 

2.06 

*  The  Minotto  or  Sawdust,  the  Meidinger,  the  Callaud,  and  the  Lockwood  cells  are  modifications  of  the  Daniell, 
and  hence  have  about  the  same  electromotive  force. 

SMITHSONIAN  TABLES. 


TABLE  294  (continued).  26$ 

COMPOSITION  AND  ELECTROMOTIVE  FORCE  OF  VOLTAIC  CELLS. 


Name  of  cell. 

Negative 
pole. 

Solution. 

Positive  pole. 

E.  M.  F. 
in  volts. 

(to)  SINGLE  FLUID  CELLS. 

Leclanche    .    .    . 

Chaperon    .     .    . 
Edison-Lelande    . 
Chloride  of  silver 
Law    

Amal.zinc 

«        « 

«        « 

Zinc    .    . 
« 

<« 

Amal.zinc 
«i        « 

«        « 

Zinc  .     . 

Solution  of  sal-ammo-  ) 
niac                 .         .  J 

f  Carbon.  Depolari- 
1  zer  :    manganese 
1  peroxide     with 
[powdered  carbon 
I  Copper.  Depolar- 

j  izer  :  CuO  .    .     . 
«« 

(  Silver.    Depolari-  1 
|  zer  :  silver  chl'ride  f 
Carbon  .... 

« 

« 
« 

Cadmium    .    .    . 
Copper  .... 

I.46 

0.98 
0.70 
1.02 

i-37 
i-3 

1.08 

2.OI 

0-34 
0.98 

(  Solution  of  caustic       ) 
1     potash    .                  .  ( 

I  23  %  solution   of  sal-  ) 
{      ammoniac  .     .     .     .  J 
15%          " 
f  ipt.ZnO,ipt.NH4Cl,' 
J   3  Pts-  plaster  of  paris, 
1    2  pts.  ZnCl2,and  water 
[  to  make  a  paste    .    . 
Solution   of  chromate 
of  potash    .... 
12  parts  K2Cr2O7  + 
25  parts  H2SO4  -f- 
100  parts  H2O    .    . 
i  part  H2SO4  +           \ 
12  parts  H2O  -f-        >• 
i  part  CaSO4      .    .  ) 
H2O               .... 

Dry  cell  (Gassner) 
Poggendorff     .    . 

M 

J.  Regnault  .    .    . 
Volta  couple    .    . 

(c)  STANDARD  CELLS. 

Weston  normal    . 
Clark  standard    . 

(Cadmi'm) 
(  am'lgamj 

(     Zinc     i 
j  am'lgamj 

(  Saturated  solution  of  ) 
i               CdS04              \ 

(  Saturated  solution  of  ) 
\              ZnSO*              J 

Mercury. 
Depolarizer:  paste 
of    Hg2SO4    and 
CdSO4    .    .    .    . 
Mercury. 
Depolarizer:  paste 
'  of  Hg2SO4     and 
ZnSO4    .... 

1.0183* 

at  20°  C 

1434* 
at  is°C 

(d)  SECONDARY  CELLS. 

Lead  accumulator 

Regnier  (i)  .    .    . 

•«       (2).    .    . 
Main  

Lead  .    . 

Copper    . 

Amal.  zinc 
Amal.  zinc 

Iron    .    . 

H2SO4  solution  of        } 
density  i.i      .    .    .  J 

CuSO4+H2SO4  .    . 

ZnSO4  solution  .    .     . 
H2SO4  density  ab't  i.i 

KOH  20  %  solution   . 

PbO2  . 

2.2f 

(  1.68  to 
^0.85,  av- 
(  erage  1.3. 
2.36 
2.50 
(  i.i,  mean 
]    of  full 
(  discharge. 

M 

"    inH2SO4     . 
<« 

Edison    .... 

A  nickel  oxide    . 

-  *  E.  M.  F.  hitherto  used  at  Bureau  of  Standards.  See  p.  851.  The  temperature  formula  is  Et  =  £20—0.0000406 
(t— 20)  — 0.00000095  (t— 20)2  +  0.00000001  (t— 20)8.  tThe  value  given  is  that  adopted  by  the  Chicago  International 
Electrical  Congress  in  1893.  The  temperature  formula  is  Et  =  E^  —  o.ooi  19  (t— 15)  —  0.000007  (t— 15)*. 

t  F.  Streintz  gives  the  following  value  of  the  temperature  variation  —  at  different  stages  of  charge : 

dt 

E.  M.  F.          1.9223      1.9828      2.0031      2.0084  2.0105      2.0779     2.2070 

dE/dtXio8            140          228          335          285  255           130           73 

Dolezalek  gives  the  following  relation  between  E.  M.  F.  and  acid  concentration : 
Per  cent  HoSO*  64.5  52.2  35.3  21.4  5.2 
E.M.F.,  o°C  2.37  2.25  2.10  2.00  1.89 

SMITHSONIAN  TABLES. 


264 


TABLE  295. 


CONTACT   DIFFERENCE   OF 

Solids  with  Liquids  and 
Temperature  of  substances 


<J 

, 

a 

Platinum. 

c 

i 

N 

Distilled  water 

(.01 

)  to 

<     IU 

.269 

to 

.148 

T7I 

(  .2857 
/     to   > 

(  —.105 

/                     -f|-| 

(-17 

.100 

.1/1 

11 

(  -345) 

.177 

<              LU 

Alum  solution  :  saturated 
at  16°  5  C 

—.127 

-653 

—•139 

.246 

—.225 

-536 

Copper  sulphate  solution  : 

sp.  gr.  1.087  at  i6°.6  C. 

~ 

.103 

~ 

~ 

^ 

—  ' 

"" 

Copper  sulphate  solution  :  1 
saturated  at  15°  C.   .     .    J 

- 

.070 

- 

- 

- 

- 

- 

Sea  salt  solution:  sp.  gr. 
1.18  at  20°.5  C.     .     .     . 

- 

—475 

~.605 

- 

—.856 

—•334 

-565 

Sal-ammoniac      solution  :  1 
saturated  at  150.5  c-     •    ) 

- 

-396 

-.652 

-.189 

•059 

-.364 

-.637 

Zinc  sulphate  solution  :  sp.  1 
gr.  1.125  at  i6°.9  C.  .    .    ) 

- 

- 

- 

- 

- 

- 

-.238 

Zinc    sulphate    solution  : 

saturated  at  I5°.3  C.     . 

— 

~ 

~ 

— 

— 

— 

—430 

One  part  distilled  water  + 

3   parts    saturated    zinc 
sulphate  solution  .     .     . 

— 

— 

— 

- 

- 

- 

—444 

Strong    sulphuric    acid    in 
distilled  water  : 

i  to  20  by  weight     .     .    . 

- 

. 

_ 

_ 

_ 

. 

—•344 

i  to  10  by  volume    .     .    . 

(  about  i 

I  —  -035  J 

i  to  5  by  weight  .... 

- 

- 

- 

- 

- 

- 

.01 

5  to  i  by  weight  .... 

to 

- 

- 

—  .120 

- 

—•25 

- 

Concentrated  sulphuric  acid 

•55 
to 

1.113 

(     -72 
}     t0 

to     > 

Concentrated  nitric  acid 

.85 

(  1.252 

1.6   ) 
.672 

Mercurous  sulphate  paste  . 

_ 

_ 

_ 

_ 

_ 

_ 

Distilled  water  containing  £ 
trace  of  sulphuric  acid      ) 

- 

- 

- 

- 

- 

- 

—.241 

*  Everett's  "  Units  and  Physical  Constants:  "  Table  of 


SMITHSONIAN  TABLES. 


TABLE  295  (continued). 


265 


POTENTIAL    IN    VOLTS. 

Liauids  with  Liquids  in  Air.* 
during  experiment  about  16°  C. 


U 

| 

Id 

H 

1 

|i 

in 

Ik 

IS 

l°« 

•81 

i 

1 

I 

. 

1 

Jrt 

fl 

11 

t!a 

JU 

"c 

&  . 

. 

•3 

,52 

<n  o3 

fcSS 

1& 

a& 

bo 

II 

1 

I 

to  • 

5 

|| 

~  2 

1* 

P 

If 

| 
C/3 

Distilled  water  

.100 

.231 

_ 

_ 

_ 

—•043 

_. 

.164 

- 

_ 

Alum  solution  :  saturated 

at  i6°.5  C    .     .         .     . 

— 

—.014 

~ 

— 

~ 

— 

~ 

— 

"• 

~ 

Copper  sulphate  solution  : 
sp.  gr.  1.087  at  i6°.6  C. 

- 

- 

- 

- 

- 

- 

.090 

- 

- 

- 

Copper  sulphate  solution  : 
saturated  at  15°  C.   .     . 

- 

- 

- 

—•043 

- 

- 

- 

•095 

.102 

- 

Sea  salt  solution  :  sp.  gr. 

1.18  at  20°-5  C.     .     .     . 

—  -435 

Sal-ammoniac      solution:) 
saturated  at  15°.  5  C.     .    J 

- 

—•348 

- 

- 

- 

- 

- 

- 

- 

- 

Zinc    sulphate    solution  :  ) 

sp.  gr.  1.125  at  I6°-9  C.    j 

Zinc    sulphate     solution  :  / 
saturated  at  i5°-3  C.     .    j 

—.284 

- 

- 

—  .200 

- 

—.095 

- 

- 

- 

- 

One  part  distilled  water  -f-  ) 

3    parts    saturated    zinc  > 

— 

— 

— 

— 

— 

—  .102 

— 

— 

— 

— 

sulphate  solution      .     .    ) 

Strong    sulphuric    acid    in 

distilled  water  : 

i  to  20  by  weight     .     .     . 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

i  to  10  by  volume    .     .    . 

-.358 

- 

- 

- 

- 

- 

- 

- 

- 

- 

i  to  5  by  weight  .... 

.429 

- 

- 

- 

- 

- 

- 

- 

- 

- 

5  to  i  by  weight  .... 

- 

—  .016 

- 

- 

- 

- 

- 

- 

- 

- 

Concentrated  sulphuric  acid 

.848 

- 

- 

1.298 

1.456 

1.269 

- 

1.699 

- 

- 

Concentrated  nitric  acid 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

_ 

Mercurous  sulphate  paste  . 
Distilled  water  containing  ) 
trace  of  sulphuric  acid  .    ) 

- 

- 

•475 

- 

- 

- 

- 

- 

.078 

Ayrton  and  Perry's  results,  prepared  by  Ayrton. 
SMITHSONIAN  TABLES. 


266  TABLE  296. 

CONTACT  DIFFERENCE  OF  POTENTIAL  IN  VOLTS. 

Solids  with  Solids  In  Air.* 

The  following  results  are  the  "  Volta  differences  of  potential,"  as  measured  by  an  electrometer. 
They  represent  the  difference  of  the  potentials  of  the  air  near  each  of  two  metals  placed  in  con- 
tact. This  should  not  be  confused  with  the  junction  electromotive  force  at  the  junction  of  two 
metals  in  metallic  contact,  which  has  a  definite  value,  proportional  to  the  coefficient  of  Peltier 
effect.  The  Volta  difference  of  potential  has  been  found  to  vary  with  the  condition  of  the  me- 
tallic surfaces  and  with  the  nature  of  the  surrounding  gas.  No  great  reliance,  therefore,  can  be 
placed  on  the  tabulated  values. 

The  temperature  of  the  substances  during  the  experiment  was  about  18°  C. 


Zinc 

Carbon. 

Copper. 

Iron. 

Lead. 

Platinum. 

Tin. 

Zinc. 

amal- 

Brass. 

gam. 

Carbon  .     .     . 

0 

•370 

485 

.858 

•"3 

•795 

1.096! 

I.2o8f 

4Mt 

Copper  .    .     . 

—•370 

0 

.146 

•542 

-238 

456 

•750 

.894 

.087 

Iron  .... 

-.485t 

—.146 

0 

401  1 

-.369 

•3'3t 

.6oot 

•744t 

—  .064 

Lead      .    .    . 

—.858 

—.542 

—401 

O 

—.771 

—.099 

.210 

•357t 

—472 

Platinum    .     . 

—ii3t 

.238 

.369 

.771 

0 

.690 

.981 

I.I2St 

.287 

Tin    .... 

—  795t 

-458 

—.313 

.099 

-.690 

0 

.281 

463 

—•372 

Zinc  .... 

—1.096! 

—•750 

—  .600 

-.216 

-.981 

.281 

0 

.144 

—.679 

"    amalgam 

—  i.2o8t 

-.894 

—•744 

—  357t 

—  I.I25t 

—463 

—.144 

0 

—.822 

Brass     .    .    . 

—414 

-.087 

.064 

.472 

-.287 

•372 

.679 

.822 

0 

The  numbers  not  marked  were  obtained  by  direct  experiment,  those  marked  with  a  dag- 

ger by  calculation,  on  the  assumption  that  in  a  compound  circuit  of  metals,  all  at  the  same 

temperature,  there  is  no  electromotive  force. 

The  numbers  in  the  same  vertical  column  are  the  differences  of  potential  in  volts  between 

the  substance  named  at  the  top  of  the  column  and  the  substance  named  on  the  same  line  in 

the  first  column,  when  the  two  substances  are  in  contact. 

The  metals  used  were  those  ordinarily  obtained  in  commerce. 

*  Everett's  "  Units  and  Physical  Constants.' 
pared  by  Ayrton. 

SMITHSONIAN  TABLES. 


The  table  is  from  Ayrton  and  Perry's  experiments,  and  was  pre- 


TABLE  297. 


267 


DIFFERENCE    OF    POTENTIAL    BETWEEN    METALS    IN    SOLUTIONS    OF 

SALTS. 

The  following  numbers  are  given  by  G.  Magnanini*  for  the  difference  of  potential  in  hundredths  of  a  volt  between 
zinc  in  a  normal  solution  of  sulphuric  acid  and  the  metals  named  at  the  head  of  the  different  columns  when  placed 
in  the  solution  named  in  the  first  column.  The  solutions  were  contained  in  a  U-tube,  and  the  sign  of  the  differ- 
ence of  potential  is  such  that  the  current  will  flow  from  the  more  positive  to  the  less  positive  through  the  ex- 
ternal circuit. 


Strength  of  the  solution  in 
gram  molecules  per 
liter. 

Ziuc.t 

Cadmium,  t 

Lead. 

Tin. 

Copper. 

Silver. 

No.  of 
molecules. 

Salt. 

Difference  of  potential  in  cemivolts. 

I.O 

H2SO4 
NaOH 

O.O 
—32.1 

36.6 
19-5 

35J 

51-3 
0.2 

100.7 
8o.2 

I2I-3 

95-8 

I.O 

KOH 

—42-5 

15-5 

32.0 

—  1.2 

77.0 

104.0 

°*5 

Na2SO4 

1.4 

35-6 

50.8 

5X4 

101.3 

120.9 

I.O 

Na2S2O8 

—5-9 

24.1 

45-3 

457 

38-8 

64.8 

I.O 

KN08 

ii.8j 

31.9 

42.6 

3,., 

8l.2 

1057 

I.O 

NaNO8 

"•5 

32-3 

51.0 

40.9 

957 

114.8 

0.5 

K2CrO4 

23-9i 

42.8 

41.2 

40.9 

94.6 

I  a  i.o 

O.c 

K2Cr2O7 

72.8 

61.1 

78.4 

68.1 

123.6 

132.4 

0.5 

K2S04 

1.8 

347 

51-0 

40.9 

957 

114.8 

0.5 

(NH4)2S04 

—0-5 

37-i 

53-2 

57-6J 

101.5 

1257 

0.25 

0.167 

K4FeC6N6 
K6Fe2(CN)2 

—6.1 

4I.O§ 

Sf.a 

41.2 
130.9 

-t 

110.7 

87.8 
124.9 

I.O 

KCNS 

—  1.2 

32-5 

52.8 

527 

52.5 

72.5 

I.O 

NaNO8 

4-5 

35-2 

50.2 

49.0 

103.6 

104.6? 

0.5 

SrNO8 

14.8 

38.3 

50.6 

48.7 

103.0 

"9-3 

0.125 

I.O 

Ba(N08)2 
KNO8 

39-3 
35-6 

47-5 

52.8 
49.9 

109.6 
104.8 

121.5 
115.0 

0.2 

KClOfl 

15-10* 

39-9 

53-8 

577 

IO5-3 

120.9 

0.167 

KBrOs 

13-20* 

40.7 

50-9 

111.3 

120.8 

I.O 

NH4C1 

2.9 

324 

51.3 

50-9 

81.2 

101.7 

I.O 

KF 

2.8 

22.5 

4I.I 

50.8 

61.3 

61.5 

I.O 

NaCl 



51.2 

5°-3 

80.9 

101.3 

I.O 

KBr 

2-3 

3J7 

47.2 

73-6 

82.4 

I.O 

KC1 

32-1 

51.6 

52-6 

81.6 

107.6 

o-5 

NaaSO8 

—8.2 

28.7 

41.0 

31.0 

68.7 

103.7 

-II 

NaOBr 

18.4 

41.6 

73.1 

70.6* 

89.9 

997 

1.0 

C4H606 
C4H606 

5-5 
4.1 

397 
41-3 

6l-3 
61.6 

544§ 
57-6 

104.6 
110.9 

123.4 
1257 

o-5 

C4H4KNaO6 

—7.9 

51-5 

42-47 

100.8 

119.7 

*  "  Rend,  della  R.  Ace.  di  Roma,"  1890. 

t  Amalgamated. 

t  Not  constant. 

§  After  some  time. 

It  A  quantity  of  bromine  was  used  corresponding  to  NaOH  =  i. 


SMITHSONIAN  TABLES. 


268  TABLE  298. 

THERMOELECTRIC  POWER. 

The  thermoelectric  power  of  a  circuit  of  two  metals  is  the  electromotive  force  produced  by  one 
degree  C.  difference  of  temperature  between  the  junctions.  The  thermoelectric  power  varies  with 
the  temperature,  thus  :  thermoelectric  power  =  Q  =  dE  /dt  =  A  +  Bt,  where  A  is  the  thermoelec- 
tric power  at  o°  C.,  B  is  a  constant,  and  /  is  the  mean  temperature  of  the  junctions.  The  neutral 
point  is  the  temperature  at  which  dE  /dt  =  o,  and  its  value  is  —  A  /B.  When  a  current  is  caused 
to  flow  in  a  circuit  of  two  metals  originally  at  a  uniform  temperature,  heat  is  liberated  at  one  of 
the  junctions  and  absorbed  at  the  other.  The  rate  of  production  or  liberation  of  heat  at  each 
junction,  or  Peltier  effect,  is  given  in  calories  per  second,  by  multiplying  the  current  by  the  co- 
efficient of  the  Peltier  effect.  This  coefficient  in  calories  per  coulomb  =  QT/J,  in  which  Q  is  in 
volts,  Tis  the  absolute  temperature  of  the  junction,  and  ^  =  4.19.  Heat  is  also  liberated  or  ab- 
sorbed in  each  of  the  metals  as  the  current  flows  through  portions  of  varying  temperature.  The 
rate  of  production  or  liberation  of  heat  in  each  metal,  or  the  Thomson  effect,  is  given  in  calories 
per  second  by  multiplying  the  current  by  the  coefficient  of  the  Thomson  effect.  This  coefficient, 
in  calories  per  coulomb,  =  BT6/J,  in  which  B  is  in  volts  per  degree  C.,  7*is  the  mean  absolute 
temperature  of  the  junctions,  and  6  is  the  difference  of  temperature  of  the  junctions.  (BT)  is  Sir 
W.  Thomson's  "  Specific  Heat  of  electricity."  The  algebraic  signs  are  so  chosen  in  the  following 
table  that  when  A  is  positive,  the  current  flows  in  the  metal  considered  from  the  cold  junction  to 
the  hot.  When  B  is  positive,  Q  increases  (algebraically)  with  the  temperature.  The  values  of 
At  B>  and  thermoelectric  power,  in  the  following  table  are  with  respect  to  lead  as  the  other  metal 
of  the  thermoelectric  circuit.  The  thermoelectric  power  of  a  couple  composed  of  two  metals,  i 
and  2,  is  given  by  subtracting  the  value  for  2  from  that  for  i  ;  when  this  difference  is  positive,  the 
current  flows  from  the  cold  junction  to  the  hot  in  i.  In  the  following  table,  A  is  given  in  micro- 
volts, B  in  microvolts  per  degree  C.,  and  the  neutral  point  in  degrees  C. 

The  table  has  been  compiled  from  the  results  of  Becquerel,  Matthiessen  and  Tait ;  in  reducing 
the  results,  the  electromotive  force  of  the  Grove  and  Daniell  cells  has  been  taken  as  1.95  and 
1.07  volts.  The  value  for  constantin  was  reduced  from  results  given  in  Landolt-Bornstein's 
tables.  The  thermoelectric  powers  of  antimony  and  bismuth  alloys  are  given  by  Becquerel  in  the 
reference  given  below. 


Substance. 

A 
Microvolts. 

B 
Microvolts. 

Thermoelectric  power 
at  mean  temp,  of 
junctions  (microvolts). 

Neutral 
point 
A. 
B 

Author- 
ity. 

20°  C. 

50°  C. 

Aluminum  

0.76 
11.94 

-2.63 

—1-34 

—2.80 
—I7-I5 

—  2.22 

21.8 
83.57 

3-°4 

—  0.0039 
0.0506 

—0.0424 
—0.0094 
—  O.OIOI 

0.0482 

0.0000 

0.0094 

0.0506 

—0.2384 

0.0506 

0.68 

—6.0 

—22.6 

—26.4 
—17.0 
12.95 

13-56 
97.0 
89.0 

65.0 

45.0 
—3.48 

22. 

—1.52 
0.10 

-3-8 

—  1.2 

-3-° 
—  16.2 

—17-5 

0.00 

—2.03 
0.413 

22.8 

0.56 

14.47 
12.7 

39-9 

—4-75 
—2.45 

+I~?& 

—3-30 
—14.74 

—  I2.IO 
—9.10 

o.oo 
—1-75 

3-30 

I5-50 
24-33 

195 
-2~36 

-^62 
—143 

[-277] 
356 

236 
[-431] 

T 

M 

« 

B 
T 
B 

M 

« 

« 
« 
«{ 

B 
T 
B 
M 

T 
M 

« 

T 
«i 

M 
B 

M 

T 
M 
B 

T 
« 
« 

Antimony,  comm'l  pressed  wire 
"           axial  

equatorial    .... 
"           ordinary      .... 

(4 

Arsenic  . 

Bismuth,  comm'l  pressed  wire  . 
pure            "          "     . 
"         crystal,  axial  .... 
"        equatorial  .     . 
"         commercial   .... 
Cadmium    .         

Cobalt    

Constantin  

Copper   

"       commercial      .... 
"       galvanoplastic  .... 
Gold  ....... 

« 

Iron    

"    pianoforte  wire      .... 
"    commercial  .              . 

««            « 

Lead  

«« 

Nickel     

"      (-18°  to  175°)  .    .    .    . 
(25o°-3oo°)    

"       (above  340°)  

SMITHSONIAN  TABLES. 


TABLES  298  («»tf««w/)-299.-  THERMOELECTRIC  POWER.  269 

TABLE  298.  —  Thermoelectric  Power  (continued). 


Substance. 

A 
Microvolts. 

B 

Microvolts. 

Thermoelectric  power 
at  mean  temp  of 
junctions  (microvolts). 

Neutral 
point 
A 
~  B 

Author- 
ity. 

20°  C. 

50°  C. 

6.18 

-257 
o.oo 

—7.90 
-5-90 
-6.15 

—  2.12 
—  11.27 

0-43 
—2.32 

0-0355 

0.0074 
0.0109 

—0.0062 
0.0133 

—  0.0055 

—0.0147 
0.0325 

—0.0055 
—  0.0238 

6.9 

—29.9 
—  0.9 
—2.42 
8.82 

—8.03 

-5-63 
—6.26 
—807. 
—2.41 

—3-00 

—  10.62 
—502. 

—  500. 
—  160. 

—O.I 

0-33 

—2.79 

—3-7 

7.96 
6.9 

—  2.20 

MS 

—0.94 
2.14 

—8.21 

-5-23 
—  6.42 

—2.86 

—2.18 
—9-65 

—429-3 

-0-33 

0.16 
—3-51 

—174 

347 

—55 

[-1274] 
444 
[-1118] 

—144 
347 

78 
-98 

T 
B 

M 

« 

T 
u 

B 

H 

T 

M 
T 
M 
B 
T 
M 
B 
H 

H 

« 

M 
T 

u 

M 

Phosphorus  (red)    
Platinum    . 

"          (hardened)    .... 
(malleable)    .... 

another  specimen  .     . 
Platinum-iridium  alloys  : 
85%Pt+i5%Ir    .... 
90%Pt+io%Ir    .... 
95%rt+5%Ir   .... 
Selenium    ...          ... 

Silver     

"      (pure  hard)    
"      wire  

Steel      

Tellurium  

« 

"               o      

a 

« 

Zinc  

"    pure  pressed    

B     Ed.  Becquerel,  "  Ann.  de  Chim.  et  de  Phys."  [4]  vol.  8. 
M    Matthiesen,  "  Pogg.  Ann."  vol.  103,  reduced  by  Fleming  Jenkin. 
T    Tait,  "Trans.  R.  S.  E."  vol.  27,  reduced  by  Mascart. 
B     Haken,  Ann.  der  Phys.  32,  p.  291,  1910.  (Electrical  conductivity  of  Te/J  =  0.04,  Tea  1.7 
e.  m.  units.) 

TABLE  299.  -  Thermoelectric  Power  of  Alloys. 

The  thermoelectric  powers  of  a  number  of  alloys  are  given  in  this  table,  the  authority  being  Ed.  Becquerel.  They  are 
relative  to  lead,  and  for  a  mean  temperature  of  50°  C.  In  reducing  the  results  from  copper  as,a  reference  metal, 
the  thermoelectric  power  of  lead  to  copper  was  taken  as —  1.9. 


Substance. 

II 

•si 

Thermoelec  1 
trie  power  in  1 
microvolts.  1 

Substance. 

.>.£ 

rt  c 

13  § 

W  o* 

Thermoelec-  1 
trie  power  in  I 
microvolts.  1 

Substance. 

Relative 

quantity. 

Thermoelec-  1 
trie  power  in  1 
microvolts.  1 

Antimony 
Cadmium 

806) 
696  f 

227 

Antimony 
Zinc 

2  ) 
I  > 

43 

Bismuth 
Antimony 

t! 

-5T.4 

Antimony 
Cadmium 
Zinc 

2  > 

146 

Tin 

Antimony 
Cadmium 

12) 

10  > 

35 

Bismuth 
Antimony 

?! 

-63-2 

Antimony 
Cadmium 
Bismuth 
Antimony 
Zinc 

806) 
696  [ 
121  ) 
806) 

137 
95 

Zinc 

Antimony 
Tellurium 

Antimony 
Bismuth 

3$ 
1} 

10.2 

8.8 

Bismuth 
Antimony 

Bismuth 
Antimony 

Bismuth 

2) 

—68.2 
—66.9 

Antimony 
Zinc 
Bismuth 
Antimony 

806) 
406  [ 
121  ) 

4] 

8.1 

Antimony 
Iron 

Antimony 

H 

2.5 
1.4 

Tin 

Bismuth 
Selenium 

if 

60 
—24-5 

Cadmium 
Lead 

1 

76 

Magnesium 
Antimony 

»i 

—0.4 

Bismuth 
Zinc 

'*} 

—  31-! 

i  J 

Lead 

1  1 

Bismuth 

12  ) 

Antimony 
Cadmium 

4l 

Bismuth 

-43-8 

Arsenic 

if 

—  46.0 

Zinc 
Tin 

f'f 

46 

Bismuth 
Antimony 

«} 

—33-4 

Bismuth 
Bismuth  sulphide 

!} 

68.1 

270 


TABLES  300,301. 
TABLE  300.—  Thermoelectric  Power  against  Platinum. 


One  junction  is  supposed  to  be  at  o°C;  +  indicates  that  the  current  flows  from  the  o°  junction 
into  the  platinum.     The  rhodium  and  iridium  were  rolled,  the  other  metals  drawn.* 


Tempera- 
ture, °  C. 

Au. 

Ag. 

90%Pt+ 
io%Pd. 

1C 

9 

%pt+ 
D%pd. 

Pd. 

90%Pt+ 
io%Rh. 

9<>%Pt+ 
io%Ru. 

Ir. 

Rh. 

-I85 

—0.15 

—  0.16 

—  O.I  I 

+0.24 

+0.77 

_ 

-0-53 

—0.28 

—0.24 

—80 

—0.31 

—0.30 

—  0.09 

+0.15 

+0-39 

— 

—0-39 

—0.32 

—  0.31 

+  IOO 

+0.74 

+0.72 

+0.26 

—0.19 

—0.56 

— 

+0.73 

+0.65 

+0.65 

+  200 

+  1.8 

+1-7 

+0.62 

—0.31 

—  1.20 

— 

+1.6 

+  1-5 

+1-5 

+300 

+3-o 

+3-o 

+  1.0 

—0.37 

—  2.0 

+2-3 

+  2.6 

+  2-5 

+  2.6 

+400 
+  500 
+  600 
+700 

+4-5 
+6.1 

+7.9 
+9-9 

4-4-5 

+6.2 
+8.2 

+10.6 

+1.5 
+1.9 

+2.4 

+2.9 

—0.35 

—o.i  8 

+0.12 

--0.61 

—2.8 
-3-8 
-4-9 

—6-3 

±3'2 
+4.1 

+5-i 

+  6.2 

+3-6 
+4-6 
+5-7 
+6.9 

+3-6 
+4-8 
+6.1 
+7-6 

+3-7 
+5-1 
+6.5 
+8.1 

+800 

+  12.0 

+13.2 

+3.4 

-1.2 

—7-9 

+7.2 

+8.0 

+9.1         +9.9 

+900 
+  1000 

+  14-3 
+  16.8 

+16.0 

+3.8 

+4.3 

-2.1 

-3-i 

-9.6 
—".5 

+8.3 
+9-5 

+9.2 
+  10.4 

+  10.8 

+  12.6 

+  11.7 
+  13-7 

+  1100 

— 

— 

+4-8 

-4.2 

—  J3-5 

+  10.6 

+  11.6 

+  14-5 

+  15.8 

+(1300) 

_ 

— 

+I3-1 

+  14.2 

+  18.6 

+20.4 

+(1500) 

* 

^ 

" 

" 

"~ 

+  15.6 

+  16.9 

+23-1 

+25.6 

Holborn  and  Day. 


TABLE  301.— Thermal  E.  M.  F  of  Pure  Platinum  Against  Platinum-Rhodium  Alloys,  In  Millivolts  * 


10  p.  ct. 

1 

I  p.  Ct. 

5  P.  ct. 

Low. 

High. 

Stan- 
dard. 

15  p.  ct. 

20  p.  Ct. 

30  p.  ct.t 

40  p.  ct.t 

xoop.ct.J 

100° 

O.2I 

0.55 

O.6"? 

0.64 

0.64 

6 

o  65 

°5 

2OO 

0.42 

i.iB 

1.41 

1-41 

1.43 

1.50 

I.CI 

3oo 

0.63 

1.85 

2.28 

2.32 

2.32 

2.41 



2.34 

2.45 

2-57 

400 

0.84 

2-53 

3.21 

3-26 

3-25 

345 

3-50 

3.50 

3.64 

3-76 

|oo 
6oo 
700 

1.05 
1.25 
1.45 

3.22 
3-92 
4.62 

4.17 

5.16 
6.19 

4.23 
5-24 
6.28 

4-23 
6^7 

4-55 
5-71 
6.94 

4.6O 

5.83 
7.l8 

7-49 

4-93 
7.80 

5.08 

6-55 
8.14 

800 

1.65 

5-33 

7.25 

7.35 

7-33 

8.23 

8.60 

9.01 

9-37 

9.87 

900 

1.85 

6.05 

8-35 

8.46 

8.43 

9-57 

10.09 

10.67 

11.09 

11.74 

IOOO 

2.05 

6.79 

9-47 

9.60 

9-57 

10.96 

11.65 

12.42 

12.94 

13-74 

1  100 

2.25 

7-53 

10.64 

10.77 

10.74 

12.40 

13.29 

H-33 

14.99 

15.87 

I2OO 

2-45 

8.29 

11.82 

11.97 

"•93 

13-87 

14.96 

16.39 

17.13 

18.10 

1300 
1400 

2.65 
2.86 

9.06 
9.82 

13.02 

14.22 

I3.l8 
14-39 

14-34 

15-38 
16.98 

16.65 
18.39 

18.51 
20.67 

21-73 

20.46 

I5OO 

3.06 

10  ^6 

15.43 

15.61 

ic.cc 

18.41 

2O.  I  5 

I6OO 

3.26 

11.31 

16.63 

16.82 

*  j-jj 
16.75 

10.94 

2I.9O 

1700 

3-46 

12.05 

17.83 

18.03 

17.95 

21.47 

1755 

3.56 

12.44 

18.49 

18.70 

18.61 

22.11 

24.55 

*  Carnegie  Institution,  Pub.  157,  1911. 
J  Holborn  and  Day,  mean  value,  1899. 

SMITHSONIAN  TABLES. 


t  Holborn  and  Wien,  1892. 


TABLES  302-304. 


TABLE  302.  -  Peltier  Effect. 


271 


The  coefficient  of  Peltier  effect  may  be  calculated  from  the  constants  A  and  B  of  Table  298, 
as  there  shown.  Experimental  results,  expressed  in  slightly  different  units,  are  here  given.  The 
figures  are  for  the  heat  production  at  a  junction  of  copper  and  the  metal  named,  in  calories  per 
ampere-hour.  The  current  flowing  from  copper  to  the  metal  named,  a  positive  sign  indicates 
a  warming  of  the  junction.  The  temperature  not  being  stated  by  either  author,  and  Le  Roux  not 
giving  the  algebraic  signs,  these  results  are  not  of  great  value. 


Calories  per  ampere-hour. 

44 

.0 

in 

^6 

C/3 

3 

<tn 

3 

» 

d 

2 

£ 

bb 

d 

Jahn*     .     . 

- 

- 

- 

~ 

—.62 

- 

-3.6: 

4-36 

0.32 

-4. 

-.58 

Le  Rouxf  . 

13.02 

4-8 

19.1 

25.8 

0.46 

2.47 

2-5 

- 

- 

- 

•39 

#  "Wied.  Ann.  "vol.  34,  p.  767. 

t  "  Ann.  de  Chim.  et  de  Phys."  (4)  vol. 

J  Becquerel's  antimony  is  806  parts  Sb  4 


10,  p.  201. 

Becquerel's  antimony  is  806  parts  Sb  +  406  parts  Zn  4-  121  parts  Bi. 
§  Becquerel's  bismuth  is  10  parts  Bi  + 1  part  Sb. 


TABLE  303. -Peltier  Effect,  Fe-Constantan,  Ni-Ou,  0-560°  0. 


Temperature. 

0° 

20° 

.30° 

240° 

320° 

560° 

Fe-Constantan  .     .     . 

3.1 

3-6 

4-5 

6.2 

8.2 

I2.5 

{in  Gram.  Cal  "X-io8 

Ni-Cu       .... 

I.Q2 

2  I  c 

2  4.C 

206 

I  QI 

2.l8 

per  coulomb 

*•«>« 

TABLE  304. -Peltier  Electromotive  Force  in  Millivolts. 


Metal 
against 
Copper. 

£ 

£ 

s 

4 

ti 

< 

c 

< 

i 

a 

CO 

j 

< 

•t 

m 

t 

£ 

s 

Le  Roux 

-5.64 

—2-93 

—•53 

—•45 

- 

- 

- 

- 

- 

- 

- 

- 

+22.3 

Jahn  .    .    . 

- 

-3.68 

—.72 

—.68 

-.48 

- 

- 

- 

- 

+•37 

- 

+5-07 

- 

Edlund  .     . 

- 

-2.96 

—.16 

—  .or 

+.03 

+.33 

+.50 

+.56 

+.70 

+  1.02 

+2-I7 

- 

+17.7 

Caswell  .    . 

- 

- 

- 

- 

+.03 

- 

- 

- 

+.70 

+.8S 

- 

+6.0 

+  16.1 

Le  Roux,  1867;  Jahn,  1888;  Edlund,  1870-71 ;  Caswell,  Phys.  Rev.  33,  p.  381,  1911. 
SMITHSONIAN  TABLES. 


272  TABLE  305. 

VARIOUS  DETERMINATIONS  OF  THE  VALUE  OF  THE  OHM. 


Date. 

Observer, 

Method. 

Value  of 
B.  A.  unit  in 
ohms. 

Value  of  Sie- 
mens unit, 
B.  A.  unit. 

Value  of 
ohm  in  cms. 
of  Hg. 

1882 
1883 

Lord  Rayleigh 
Lord  Rayleigh 

Rotating  coil 
Lorenz  method 

0.98651 
.98677 

0.95412 
.95412 

106.24 

106.21 

1884 
1887 
1887 

Mascart   . 
Rowland  . 

Kohlrausch 

Induced  current 
Mean  of  several  methods 
Damping  of  magnets 

.98611 
.98644 
.98660 

•95374 
•95349 
•95338 

106.33 
106.32 
106.32 

1882  { 
I888J 

Glazebrook 

Induced  currents    . 

.98665 

•95352 

106.29 

1890 

Wuilleumeier  . 

Mean  effect  of  induced 

1890 

Duncan  and  Wilkes 

currents 
Lorenz  method 

.98686 
.98634 

•95355 
•95341 

106.31 
106.34 

1891 

Jones 

Lorenz  method 

_   *f* 

106.31 

1894 

Jones 

Lorenz  method 

_ 

_ 

1  06.  H 

1895 

Himstedt 

Mean  effect  of  induced 

+J*J 

current 

_ 

_ 

106.28 

1897 
1899 

Ayrton  and  Jones    . 
Guillet     . 

Lorenz  method 
Mean  effect  of  induced  cur 

(-98634) 

rent,  using 

- 

106.27 

a  calibrated  i  coo-ohm  c 

3il      .      .      . 

- 

106.20 

Means        . 

0.98651 

0.95366 

106.288 

1883 

1884 

Wild        .  •      . 
Wiedemann     . 

Damping  of  magnet 
Earth  inductor 

- 

- 

106.03 
106.19 

1884 

H.  F.  Weber  . 

Induced  current 

_ 

_ 

l°S-37 

1884 

H.  F.  Weber  . 

Rotating  coil  . 

_ 

— 

>       x- 

106.16 

1884 

Roiti 

Mean  effect  of  induced  current,  using 

1885 

Himstedt 

German  silver  coils  certified  by  makers 
Mean  effect  of  induced  current,  using 

- 

105.89 

1885 

Lorenz     .        . 

Gennan  silver  coils  certifie 
Lorenz  method 

i  by  makers 

- 

105.98 
105.93 

1889 

Dorn 

Damping  of  magnet 

_ 

_ 

106.24 

1911 

Nat.  Phys.  Lab. 

2  phase   .... 

106.27 

The  legal  value  of  the  ohm  is  the  resistance  of  a  column  of  mercury  of  uniform  cross-section, 
weighing  14.4521  gms.,  and  having  a  length  of  106.30  cms.  This  is  known  as  the  international 
ohm.  Mercury  ohms  conforming  to  these  specifications  have  been  prepared  in  recent  years  at 
the  Physikalisch-Technische  Reichsanstalt,  the  National  Physical  Laboratory,  and  the  Bureau  of 
Standards.  The  wire  standards  of  resistance  at  the  above-named  laboratories  agree  in  value  to 
within  two  parts  in  100000.  Hence  there  is  a  very  close  agreement  in  the  values  of  precision 
resistances  calibrated  at  these  laboratories. 


SMITHSONIAN  TABLES. 


TABLE  306. 


273 


SPECIFIC  RESISTANCE  OF  METALLIC  WIRES, 


This  table  is  modified  from  the  table  compiled  by  Jenkin  (1862)  from  Matthiessen's  results  by  taking  the  resistance  of 
silver,  gold,  and  copper  from  the  observed  metre  gramme  value  and  assuming  the  densities  found  by  Matthiessen, 
namely,  10.468,  19.265,  and  8.95. 


rt  u 

a 

« 

a 

rt 

-  ,<-> 

•si 

"3*2 

*°  M    . 

"5 

"8 

o  no 

«""  8 

0  e°a 

u§. 

^§1 

U£ 

"oM! 

"r  5 

su  « 

°ol| 

ill 

O    •"'*•• 

o  <o  bo 

•4-»     *^     U 

°o|s 

•4-»      .,     rt 

°ol& 

S:* 

Substance. 

rt  g  w 

rt  t! 

8  £-s 

5H 

P'l 

«  1  g 

»ll 

«)«.*• 

I  «.s 

3§S 

c  o>  ,i 
rt  c  S 

»  °s 

in 

ts  °^ 

t?  o.S 

Hi 

*2* 
§5^ 

•«  «  " 

21  1 

'ga« 

^'^§ 

111 

Il-i 

in 

518 

Silver  annealed  . 

1.460  X  icr6 

0.01859 

.1523 

8.781 

.2184 

0.377 

"      hard  drawn 

1.585       « 

0.02019 

.1659 

9.538 

.2379 

- 

Copper  annealed 

1.584       " 

0.02017 

.1421 

9.529 

.2037 

0.388 

"     hard  drawn    . 

I.6I9       " 

0.02062 

.1449 

9.741 

.2078 

- 

Gold  annealed    . 

2.088       " 

0.02659 

.4025 

12.56 

.5771 

0.365 

"    hard  drawn 

2.125       " 

0.02706 

.4094 

12.78 

.5870 

- 

Aluminium  annealed  . 

2.906       " 

0.03699 

.0747 

17.48 

.1071 

- 

Zinc  pressed 

5.613        « 

0.07146 

.4012 

33.76 

.5753 

0.365 

Platinum  annealed 

9-035        " 

0.1150 

1.934 

54.35 

2.772 

- 

Iron 

9.693        « 

0.1234 

.7551 

58.31 

1.083 

- 

Nickel 

12.43       " 

0.1583 

1.057 

74-78 

1.515 

- 

Tin  pressed 

13.18       " 

0.1678 

.9608 

79.29 

1-377 

0.365 

Lead      "             ... 

19.14       « 

0.2437 

2.227 

115.1 

3-I93 

0.387 

Antimony  pressed 

3542       " 

0.4510 

2.379 

213.1 

3.410 

0.389 

Bismuth         " 

130.9        " 

1.667 

12.86 

787.5 

18.43 

0.354 

Mercury         " 

94.07       " 

1.198 

12.79 

565.9 

18.34 

0.072 

Platinum-silver,  2  parts  Ag,  ) 

24-33       " 

0.3098 

2.919 

146.4 

4.186 

0.031 

i  part  Pt,  by  weight        .  ) 

German  silver     . 

20.89       " 

0.2660 

1.825 

125-7 

2.617 

0.044 

Gold-silver,  2  parts  Au,     ) 

10.84       " 

0.1380 

1.646 

65.21 

2-359 

0.065 

i  part  Ag,  by  weight      .  ) 

SMITHSONIAN  TABLES. 


274 


TABLE  3O7. 
SPECIFIC    RESISTANCE    OF    METALS, 


The  resistance  is  here  given  as  the  resistance  in  microhms  per  cm.  cube  when  the  specific  re- 
sistance of  mercury  at  o°  is  taken  as  94.1  microhms. 


Substance. 

State. 

Temperature,  °C. 

Resistance. 

Authority. 

Aluminum       .     . 

C    D. 

—189. 

0.64 

Niccolai,  1907. 

V 

*-^y* 

—  100. 
0. 

VX.VSf 

'•53 
2.62 

44                 (i 

« 

« 

+  IOO. 

3.86 

«           « 

« 

" 

400. 

8.0 

«                          1C 

« 

20. 

2.828 

See  p.  284. 

Antimony  .     .    . 

—  190. 

10.5 

Eucken,  Gelhoff  . 

« 

0. 

38.6 

Mean. 

« 

liquid 

+860. 

120. 

de  la  Rive. 

Arsenic  .... 

o. 

35- 

Matthiessen. 

Bismuth      .     .    . 

18. 

119.0 

Jager,  Diesselhorst. 

H 

100. 

160.2 

«<            « 

Cadmium    .    .    . 

drawn 

—1  60. 

2.72 

Lees,  1908. 

" 

•< 

1  8. 

7-54 

Jager,  Diesselhorst. 

* 

" 

100. 

9.82 

«             « 

" 

liquid 

318. 

34-  * 

Mean. 

Caesium  .... 

-187. 

5-25 

Guntz,  Broniewski. 

" 

o. 

19. 

Mean. 

Calcium      . 

99.5  pure 

20. 

10.5 

Moissan,  Chavanne 

Chromium  .     .     . 

O. 

2.6 

Shukow. 

Cobalt    .... 
Copper  .... 

99.8  pure 
annealed 

20. 
20. 

9-7 

1.724 

Reichardt,  1901. 
See  p.  284. 

M 

hard-drawn 

2O. 

1.77 

«                   44 

" 

electrolytic 

—206. 

.144 

Dewar,    Fleming, 

It 

" 

+  205. 

2.92 

Dickson. 

" 

pure 

4OO. 

4.10 

Niccolai,  1907. 

Gallium  .... 

0. 

53- 

Guntz,  Broniewski. 

Gold  

99.9  pure 

j9~ 

0.68 

D,  F,  D,  1898. 

N 

0. 

2.22 

Mean. 

M 

pure,  drawn 

1  8. 

2.42 

J,  D,  1900. 

Indium  .... 

99.9  pure 

I94-S 

0. 

3-77 
»-37 

D,  F,  D,  1898. 
Erhardt,  1881. 

Iridium  .... 

—  186. 

1.92 

Broniewski,  Hack- 

" 

o. 

6.10 

spill,  1911. 

" 

+  100. 

8'3    2 

it               (4 

pure,  soft 

—  -.  -    * 

D,  F,  D,  1898. 

o. 

s 

U        II          41              14 

" 

"        " 

+98.5 

17.8 

It        <4          41               li 

" 

«        ii 

196.1 

21.5 

l(        <«          14               44 

" 

«t 

400. 

43-3 

Niccolai,  1907. 

—  steel       .    .    . 

cast 

ord. 

19.1 

Kohlrausch. 

M 

M 

yel.  ht. 

104. 

" 

" 

" 

wh.  ht. 

114. 

14 

" 

piano-wire 

0. 

Strouhal,  Barus,'83- 

" 

temp,  glass,  hard 

o. 

45-7 

it              ..       <* 

" 

"  yellow 

o. 

27. 

"             "       " 

" 

"      blue 

0. 

20.5 

II                              «               14 

«' 

"      soft 

0. 

15-9 

41                              II               II 

Lead      .... 

cold-pressed 

—187. 

6.02 

D,  F,  D,  1898. 

i<          44 

—  78. 

14.1 

II       U          14              II 

«          o 

0. 

20.4 

41      4<         41             II 

M 

«(                      Cl 

90.4 

28.0 

II      tl         14              II 

" 

«<            (I 

196.1 

36-9 

14       II         41              (1 

M 

318. 

94. 

Vincentini,  Omodei. 

Lithium.    .    .    . 

solid 

-187. 

-7*t 

1.34 

Guntz,  Broniewski. 

SMITHSONIAN  TABLES. 


TABLE  307  (continued). 
SPECIFIC  RESISTANCE  OF   METALS. 


275 


The  resistance  is  here  given  as  the  resistance  in  microhms  per  cm.  cube  when  the  specific 
resistance  of  mercury  ato°  C  is  taken  as  94.1  microhms. 


Substance. 

State. 

Temperature,  °C. 

Resistance. 

Authority. 

Lithium,  continued 

O. 

8.55 

Guntz,  Broniewski. 

"                 " 

99-3 

12.7 

«                          U 

Manganese  .     .     . 

liquid 

230. 

45-2 

Bernini,  1905. 
Shukow. 

Magnesium  .     .     . 

free  from  zn. 

—183. 

1.  00 

Dewar,  Fleming, 

"  . 

44                  44                 14 

—  78. 

2-97 

Dickson,  1898. 

" 

4(                 <4                 14 

o. 

4-35 

D,  F,  D,  1898. 

u 

(4                 44                 44 

98.5 

5-99 

44        Cl        4(             44 

tt 

pure 

400. 

11.9 

Niccolai,  1907. 

Mercury  .... 

solid 

-183.5 

6.97 

D,  F,  D,  1898. 

" 

—147.5 

10.57 

"            " 

(4 

" 

—  102.9 

15.04 

"            " 

—  50-3 

21.3 

44                         (4 

" 

44 

—  39-2 

25-5 

44                         4. 

" 

It 

-  36-1 

80.6 

44                         44 

M 

liquid 

o.o 

94.07 

<4                         44 

" 

H 

IO. 

94.92 

Strecker,  1885. 

M 

" 

20. 

95-74 

44                           4« 

II 

" 

5°. 

98.50 

Grimaldi,  1888. 

* 

" 

IOO. 

103.25 

Vincentini,Omodei, 

" 

" 

200. 

114.27 

1890. 

H 

44 

350. 

135.5 

" 

Nickel      .... 

pure 

-182.5 

1.44 

Fleming,  1900. 

" 

" 

-78.2 

4-3  r 

«4                         44 

u 

" 

0. 

6-93 

44                         44 

tt 

" 

94.9 

n.  i 

44                         44 

11 

400. 

60.2 

Niccolai,  1907. 

Osmium  .... 
Palladium     .     .    . 

very  pure 

20. 

9-5 

2.78 

Blau,  1905. 
Dewar,  Fleming,'96 

" 

44                 44 

—  78. 

7.17 

"            "         " 

M 

44                  44 

O. 

10.21 

44                         44                   44 

" 

U                 44 

98.5 

J3-79 

"                          .4                  44 

Platinum  .    .    .    . 

wire 

—  203.1 

2.44 

D,  F,  D. 

" 

* 

—  97.5 

6.87 

44       44         44 

" 

" 

o. 

10.96 

44       <4        44 

M 

" 

IOO. 

14.85 

44       44         44 

" 

400. 

26.0 

Niccolai,  1907. 

Rhodium      .     .    . 

—  186. 

0.70 

Broniewski,  Hack- 

" 

-78-3 

3-09 

spill,  1911. 

" 

0. 

4.69 

44                   44 

" 

IOO. 

6.60 

44                   44 

Rubidium     .    .    . 

solid 

—190. 

2-5 

Hackspill,  1910. 

" 

* 

0. 

ii.o 

44                               44 

H 

liquid 

40. 

19.6 

(4                               44 

Silver  

electrolytic 

—  183. 

O  "3QO 

D,  F,  D,  1898. 

—  78. 

1.  02  1 

44       44         44             44 

<• 

' 

o. 

1.468 

44       44        44             44 

" 

« 

98.15 

2.062 

44       U        .4            14 

M 

< 

192.1 

2.608 

44       44        44             44 

« 

< 

400. 

3-77 

Niccolai,  1907. 

It 

Silicium   .... 

999.8  pure 

18. 

1.629 

Jager,  Diesselhorst 

Strontium    .    .    . 

20. 

24'.8 

Matthiessen,  1857. 

Sodium    .... 

solid 

—178. 

0.80 

Guntz,  Broniewski, 

" 

" 

-78.3 

2.86 

1909. 

" 

" 

0. 

4.48 

(4 

SO- 

5-32 

SMITHSONIAN  TABLES. 


276  TABLES  307,308. 

SPECIFIC  RESISTANCE  OF  METALS. 

TABLE  307  (concluded). 

The  resistance  is  here  given  as  the  resistance  in  microhms  per  cm.  cube  when  the  specific 
sistance  of  mercury  at  o°  C.  is  taken  as  04.1  microhms. 


resistance  of  mercury  at 


Substance. 

State. 

Temperature, 

Resistance. 

Authority. 

Tantalum 

Pure 

14.6 

Pirani 

Tellurium  
Thallium    .        .        •                 . 

Pure 

19.6° 
—  181 

21.5 

4.08 

Matthiessen,  1852. 

—  78. 

n.8 

u 

<i 

<                      a                     «                « 

n 

it 

98.5 

24.7 

<                      «                     «<                « 

Tin 

—  18* 

D   F   D  1898 

—  78. 

8.8 

i, 

«      «« 

i< 

i<      « 

it 

176 

2-5  6 

«      « 

Trace  Fe 

-IE 

1.62 

«      « 

u       « 

—  78. 

11      « 

i 

u       u 

<i      « 

« 

«       « 

8  oo 

<(      «< 

« 

<t       u 

10.37 

«      <« 

i 

Liquid 

De  la  Rive   1863 

TABLE  308.  — Temperature  Resistance  Coefficients. 

If  R0  is  the  resistance  at  the  temperature  t0,  and  Rt  at  the  temperature  t,  then  Rt  may  over  small 
ranges  of  temperature  be  approximately  represented  by  the  formula  Rt  =  R0  ( i  +  at). 


Substance. 

Temperature. 

a. 

See 
at 
foot. 

Substance. 

Temperature. 

a. 

See 
at 
foot. 

Aluminum   .     . 

18-100°  C. 

0.0039 

I 

Nickel   .    .    . 

0-100°  C. 

0.0062 

3 

.     . 

to  =    25° 

.0034 

2 

"       ... 

t0=    25° 

0.0043 

2 

ii 

IOO 

.0040 

" 

"       ... 

IOO 

.0043 

(1 

Bismuth  .    .     . 

500 

O-IOO 

.0050 
.00458 

" 

it 

500 

1000 

.0030 
.0037 

M 

Cadmium     .     . 

O-IOO 

.0042 

_ 

Palladium  .    . 

O-IOO 

•°°3S 

3 

Copper    .    .    . 

see  p.  284-85 

.0040 

_ 

Platinum    .     . 

O-IOO 

.0037 

"         ... 

t0  =  100° 

.0038 

2 

Silver    .     .     . 

O-IOO 

.0040 

" 

"         ... 

400 

.0042 

" 

"         ... 

to=    25° 

.0030 

2 

ii 

1000 

.0062 

ii 

"         ... 

IOO 

.0036 

" 

Gold  .  !  !  ! 

"       annealed 

18-100 

t0  =  100° 

.00368 
.0025 

2 

u 
Tantalum  .     . 

500 

O-IOO 

.0044 
•°°33 

6 

ii             ii 

500 

•°°35 

" 

Tin    .... 

18-100 

.0046 

I 

ii             u 

1000 

.0049 

" 

Tungsten  .    . 

18-100 

.0045 

" 

Iron,  pure    .     . 

O-IOO 

.0062 

3 

. 

t0  =  500° 

.0057 

2 

ii        ii 

to=  25° 

.0052 

2 

" 

1000 

.0089 

" 

u        ii 

IOO 

.0068 

" 

Zinc  .... 

O-IOO 

.0040 

3 

ii        ii 

coo 

f\r  A  .7 

({ 

it        ii 

500 

1000 

.O147 
.OO5O 

ii 

Advance    .     . 

t0  =     12° 

+  .OOOO2O 

2 

—  steel    .     .    . 

glass,  h'd 

.OOl6 

4 

5° 

—  .000008 

11 

M 

blue 

•0033 

"            .    . 

IOO 

—  .OOOOO7 

" 

(i 

piano  wire 

.OO32 

" 

"            .    . 

200 

+  .OOOOO7 

" 

Lead   ..'.'. 
Magnesium  .     . 

18-100 

O-IOO 

.0043 
.0038 

3 

Constantin 

12 

25 

+  .000008 
+  .000002 

m 

. 

to=   25° 

.OO5O 

2 

" 

IOO 

—.000033 

II 

. 

IOO 

.OO45 

" 

" 

200 

—  .OOOO2O 

u 

"          .    . 

500 

.0036 

" 

« 

500 

+  .OOOO27 

II 

Mercury*     .     . 
Molybdenum    . 

0-15 
to=  25° 

.0100 

.00088 
.0033 

5 

2 

Manganin  .    . 

12 

25 
IOO 

+.000006 
.000000 

—  .000042 

II 
« 

•     • 

IOO 

.0034 

" 

"         .    . 

250 

—  .000052 

II 

500 

.0050 

** 

. 

475 

.000000 

*' 

• 

1000 

.0048 

•    • 

500 

—  .000110 

II 

i,  Jager,  Diesselhorst,  Wiss.  Abh.  D.,  Phys.  Tech.  Reich.  3,  p.  269,  1900  ;  2,  Somerville,  Phys. 
Rev.  31,  p.  261,  1910,  33,  p.  77,  1911;  3,  Dewar,  Fleming,  1893,  ^96  5  Strouhal,  Barus,  1883; 
5,  Glazebrook  Phil.  Mag.  20,  p.  343,  1885;    6,  Pirani. 

SMITHSONIAN  TABLES. 


Mercury,  R  =  R0  (i  +  .000891  +0000011*). 


TABLE  309.  277 

CONDUCTIVITY  OF  THREE-METAL  AND  MISCELLANEOUS  ALLOYS. 


Conductivity  in  mhos  or 


ohms  per  cm.  cube 


=Cj=C0  (i-at+tfl). 


C0 

T 

Metals  and  alloys. 

Composition  by  weight. 

io* 

aXio" 

£Xio9 

.e 

9 

Gold-copper-silver  .     .     . 
«        «            « 

58.3  Au  4-  26.5  Cu  +  1  5.2  Ag 
66.5  Au  4-  15.4  Cu  -j-  18.1  Ag 
7.4  Au  4-  78.3  Cu  4-  14.3  Ag 

7.58 

6.83 
28.06 

574 
529 
1830 

924 

93 

7280 

I 

I 
I 

Nickel-copper-zinc  .    .     . 

(  1  2.84  Ni  4-  30.59  Cu  4-       ) 
(  6.57  Zn  by  volume    .    .    .  J 

4.92 

444 

5' 

I 

Brass 

Various      

12.2—15.6 

1-2  X  IO3 

2 

"      hard  drawn     .     .    . 

70.2  Cu  4-  29.8  Zn   .     .    .     . 

12.16 

- 

3 

"      annealed    .... 

14-35 

— 

— 

3 

German  silver          .     . 

Various 

•3—  C 

2 

t  6o.i6Cu4-  25.37  Zn  4- 
<  14.03  Ni4-  -30  Fe  with  trace 

3-33 

360 

_ 

4 

(  of  cobalt  and  manganese  . 

Aluminum  bronze    .    .    . 

_ 

7-5-8-5 

5-7  X  io2 

- 

2 

Phosphor  bronze     .     .     . 

_ 

IO-2O 

- 

- 

2 

Silicium  bronze  .... 

_  '         _ 

41 

- 

- 

5 

Manganese-copper  .    .     . 

"?o  Mn  4~  7o  Cu  

1.  00 

40 

- 

4 

Nickel-manganese-copper 

3Ni+24Mn  +  73Cu    .    . 

2.10 

—30 

- 

4 

Nickelin     

(  18.46  Ni  +  61.63  Cu  4- 
)  19.67  Zn  -j-  0.24  Fe  4- 
(  o.i9Co4-o.i8Mn    .     .    . 
(25.  i  Ni-f  74.41  Cu  + 

3.01 

300 

- 

4 

Patent  nickel           . 

<  o  42  Fe  4"  023  Zn  4~ 

2  C\? 

ICO 

4 

(0.13  Mn  4-  trace  of  cobalt 

(  53.28  Cu  4-  25.31  Ni-f 
<  16.89  Zn  4~  446  Fe  4- 

I.  CO 

410 

4 

f  o  77  Mn 

Copper-manganese-iron    . 

91  Cu  4-  7-1  Mn  4~  1-9  Fe 
70.6  Cu  -j-  23.2  Mn  +  6.2  Fe 
69.7  Cu  -f  29.9  Ni  +  0.3  Fe    . 

4.98 
1.30 
2.60 

120 
22 
1  2O 

- 

6 
6 

7 

84  Cu  4-  1  2  Mn  4-  4  Ni  .     .     . 

2  3 

6 

2 

60  Cu  4~  40  Ni  . 

2  O4. 

8 

1  Matthiessen.         8  W.  Siemens.                          5  Van  der  Ven.         6  Feussner. 

2  Various.                *  Feussner  and  Lindeck.         tt  Blood.                     7  Jaeger-Diesselhorst. 

SMITHSONIAN  TABLES. 


TABLE  31 0. 
CONDUCTING  POWER  OF  ALLOYS. 

This  table  shows  the  conducting  power  of  alloys  and  the  variation  of  the  conducting  power  with  temperature.*  The 
values  of  C0  were  obtained  from  the  original  results  by  assuming  silver  =  - — g-  mhos.  The  conductivity  is  taken 
as  Ct=  C0  (i — at-\-l>&\  and  the  range  of  temperature  was  from  o°  to  100°  C. 

The  table  is  arranged   in  three  groups  to  show(i)  that  certain  metals  when  melted  together  produce  a  solution 
which  has  a  conductivity  equal  to  the  mean  of  the  conductivities  of  the  components,  (2)  the  behavior  of  those 
metals  alloyed  with  others,  and  (3)  the  behavior  of  the  other  metals  alloyed  together. 
It  is  pointed  out  that,  with  a  few  exceptions,  the  percentage  variation  between  o°  and  100°  can  be  calculated  from  the 

formula  /"  =  Pc  — ;  where/  is  the  observed  and  /'  the  calculated  conducting  power  of  the  mixture  at  100°  C., 
and  P.  is  the  calculated  mean  variation  of  the  metals  mixed. 


Weight  % 

Vo  lume  % 

c 

Variation  per  100°  C. 

Alloys. 

10* 

b  X  io9 

of  first  named. 

Observed. 

Calculated. 

GROUP  i. 

Sn6Pb    ... 

77  O4 

8396 

7  S7 

38QO 

8670 

30  18 

2Q.67 

Sn4Cd 

8^  41 

83  10 

o  18 

4080 

1  1870 

2889 

3O  O3 

SnZn     

78.06 

77.71 

3880 

3O.  I  2 

3O.l6 

PbSn     

64  1  3 

6  40 

378O 

8420 

2Q  41 

2Q.IO 

ZnCdj 

2/1  76 

26  06 

16  16 

378O 

8oOO 

2986 

7    , 

2Q  67 

SnCd4   

23.  co 

13.67 

J/0*-1 
38  SO 

Q4.IO 

2Q  08 

CdPb6  

7-37 

10.57 

5.78 

35°° 

7270 

27.74 

27.60 

GROUP  2. 

Lead-silver  (Pb20Ag)  . 
Lead-silver  (PbAg) 
Lead-silver  (PbAg2)    . 

95-05 
48.97 

32-44 

94.64 

46.90 
30.64 

5.60 
8.03 
13.80 

3630 
I960 
1990 

7900 
3100 
26OO 

28.24 
16.53 
I7-36 

19.96 

7-73 
10.42 

Tin-gold  (Sni2Au)  .     . 

77-94 

90.32 

5-20 

3080 

6640 

24.20 

14.83 

"     "     (SrifAu)    .    . 

59-54 

79-54 

3-03 

2920 

6300 

22.90 

5-95 

Tin-copper     .... 

92.24 
80.58 

93-57 
83.60 

7-59 
8.05 

3680 
3330 

8130 
6840 

28.71 
26.24 

19.76 
M-57 

"        "       t  .    .    .    . 

12.49 

14.91 

5.57 

547 

294 

5.l8 

3-99 

"      t.     .    .    . 
t  .    .    .     . 

10.30 
9.67 

12.35 
II.Ol 

7.64 

666 
691 

1185 
3°4 

5-48 
6.60 

4.46 

5.22 

"      t.     .     .    . 

4.96 

6.O2 

12.44 

995 

705 

9-25 

7-83 

MS 

1.41 

39-41 

2670 

5070 

21.74 

20-53 

91.30 
53-85 

96.52 

75-51 

7.81 
8.65 

3820 
3770 

8190 
8550 

30.00 
29.18 

23-31 
11.89 

Zinc-copper  t      .     .     . 

36.70 

42.06 

13-75 

1370 

1340 

12.40 

11.29 

"        "        t      .     .     . 

25.00 

29.45 

13-70 

1270 

1240 

11.49 

10.08 

"   -    t     .    .     . 

23.61 

13-44 

1880 

1800 

1  2.80 

12.30 

10.88 

29.61 

2040 

3030 

1741 

17.42 

t      .    .    . 

. 

5-03 

38.09 

2470 

4IOO 

20.61 

20.62 

NOTE.  —  Barus,  in  the  "  Am.  Jour,  of  Sci."  vol.  36,  has  pointed  out  that  the  temperature  variation  of  platinum 
alloys  containing  less  than  10%  of  the  other  metal  can  be  nearly  expressed  by  an  equation  y  —  ^—  m,  where  y  is  the 

temperature  coefficient  and  x  the  specific  resistance,  m  and  n  being  constants.     If  a  be  the  temperature  coefficient  at 
o°  C.  and  s  the  corresponding  specific  resistance,  s  (a  +  m)  =  n. 

For  platinum  alloys  Barus's  experiments  gave  m  —  —  .000194  and  »  =  .0378. 
For  steel  m  =  —  .000303  and  n  •=.  .0620. 
Matthiessen's  experiments  reduced  by  Barus  gave  for 

Gold  alloys  m  =  —  .000045,  n  —  .00721 
lf     m  =  —  . 


Silver 
Copper 


.000112,  n  =  .00538. 
nt  =  —  .000386,  «  =  .  00055. 


*  From  the  experiments  of  Matthiessen  and  Vogt,  "  Phil.  Trans.  R.  S."  v.  154. 
t  Hard-drawn. 


SMITHSONIAN  TABLES. 


TABLES   310  (continued)-^  \  . 
TABLE  310.  — Conducting  Power  o£  Alloys. 


279 


GROUP  3. 

Alloys. 

Weight  % 

Volume  % 

10* 

aXio« 

bX  io9 

Variation  per  100°  C. 

of  first  named. 

Observed. 

Calculated. 

Gold-copper  t     .    .    . 

99-23 

08.36 

35-42 

2650 

4650 

21.87 

23.22 

"       t     .    .     • 

90-55 

8l.66 

10.16 

749 

81 

7.41 

7-53 

Gold-silver  t       ... 

87-95 

79-86 

13.46 

1090 

793 

10.09 

9-65 

"        »      *       ... 

87.95 

79.86 

13.61 

1140 

1160 

IO.2I 

9-59 

"      t       .     .    . 
"        "      * 

64.80 
64.80 

52.08 
52.08 

9-48 

673 

721 

246 

495 

6.49 
6.71 

6.58 
6.42 

«      t       .    .    . 

3T-33 

19.86 

13.69 

885 

8.23 

8.62 

"        «      * 

19.86 

13-73 

908 

641 

8.44 

8.31 

Gold-copper  t     .    .    . 

T      •      •      • 

34.83 
1.52 

19.17 
0.71 

12.94 

53-02 

864 
3320 

570 
7300 

8.07 
25.90 

8.18 

25.86 

Platinum-silver  t     .     • 

33-33 

19.65 

4.22 

330 

208 

3.10 

3-21 

"      t     .     . 

9.81 

5-°5 

11.38 

774 

656 

7.08 

7-25 

"      t     .    • 

5-oo 

2.51 

19.96 

1240 

1150 

11.29 

11.88 

Palladium-silver  t   .     • 

25.00 

23.28 

5-38 

324 

154 

3-40 

4.21 

Copper-silver  t        •     • 

98.08 

98.35 

56.49 

3450 

7990 

26.50 

27.30 

"      t         .    . 

«    f      .   , 

94.40 
76.74 

95-17 
77.64 

51.93 
44.06 

3250 
3030 

6940 
6070 

25-57 
24.29 

25.41 
21.92 

"    t       .    . 

42.75 

46.67 

47.29 

2870 

5280 

22-75 

24.00 

«       «     + 

7.14 

8.25 

50.65 

2750 

4360 

23.17 

25-57 

«     t       .   '. 

i-53 

50.30 

4120 

8740 

26.51 

29.77 

Iron-gold  t     .         •    • 

13.59 

27-93 

i-73 

3490 

7010 

27.92 

14.70 

«       "    t     . 

9.80 

21.18 

1.26 

2970 

1220 

17.55 

1  1.  20 

"       "    t     . 

476 

10.96 

1.46 

487 

103 

3-84 

13.40 

Iron-copper  f      .    .    . 

0.40 

0.46 

24.51 

J550 

2090 

13-44 

14.03 

Phosphorus-copper  t  . 

2.50 

- 

4.62 

476 

i45 

- 

- 

"      t  • 

0-95 

— 

14.91 

1320 

1640 

~ 

~ 

Arsenic-copper  t     .    . 

5-40 

_ 

3-97 

516 

989 

- 

- 

"       t     .    . 

2.80 

— 

8.12 

736 

446 

— 

— 

«       t     .    • 

trace 

; 

38-52 

2640 

4830 

-- 

Annealed. 


t  Hard-drawn. 


TABLE  311.  —  Allowable  Carrying  Capacity  of  Rubber-covered  Copper  Wires. 

(For  inside  wiring  —  Nat.  Board  Fire  Underwriters'  Rules.) 


B  +  S  Gage 

18 

16 

14 

12 

10 

8 

6 

5 

4 

3 

2 

• 

0 

00 

0000 

Amperes 

3 

6 

12 

17 

24 

33 

46 

54 

65 

76 

90 

107 

I27 

>5° 

210 

500,000  circ.  mills,  390  amp.;  1,000,000  c.  m.,  650  amp.;  2,000,000  c.  m.,  1,050  amp.     For 

insulated  al.  wire,  capacity  =84%  of  cu.     Preece  gives  as  formula  for  fusion  of  bare  wires 

I  =  ad^,  where  d  =  diam.  in  inches,  a  for  cu.  is  10,244  5  al.,  7585  ;  pt.,  5172  ;  German  silver, 

5230;  platinoid,  4750  ;  Fe,  3148  ;  Pb.,  1379;  alloy  2  pts.  Pb.,  i  of  Sn.,  1318. 

SMITHSONIAN  TABLES. 


280 


TABLE  312. 


RESISTANCE    OF    METALS   AND 

The  electrical  resistance  of  some  pure  metals  and  of  some  alloys  have  been  determined  by  Dewar  and  Fleming  and 
increases  as  the  temperature  is  lowered.  The  resistance  seems  to  approach  zero  for  the  pure  metals,  but  not  for 
temperature  tried.  The  following  table  gives  the  results  of  Dewar  and  Fleming.* 

When  the  temperature  is  raised  above  o°  C.  the  coefficient  decreases  for  the  pure  metals,  as  is  shown  by  the  experi- 
experiments  to  be  approximately  true,  namely,  that  the  resistance  of  any  pure  metal  is  proportional  to  its  absolute 
is  greater  the  lower  the  temperature,  because  the  total  resistance  is  smaller.  This  rule,  however,  does  not  even 
zero  Centigrade,  as  is  shown  in  the  tables  of  resistance  of  alloys.  (Cf.  Table  262.) 


Temperature  — 

100° 

20° 

0° 

—  80° 

Metal  or  alloy. 

Specific  resistance  in  c.  g.  s.  units. 

Aluminium,  pure  hard-drawn  wire  . 

4745 

3505 

3161 

- 

Copper,  pure  electrolytic  and  annealed  . 

1920 
2665 
I39?ot 

19300 

10907 
2139 
13867 

35720 

1457 
208l 

9521 
13494 

8752 
1647 

10473 
34707 

1349 
1948 
8613 

12266 

8221 
1559 

9575 
34524 

1400 

7470 

6i33 
1138 
6681 

33664 

Nickel,  pure  (prepared  by  Mond's  process  ) 
from   compound  of  nickel  and  carbon  >  . 
monoxide)                                                    ) 

German  silver,  commercial  wire 

Palladium-silver,  20  Pd  +  80  Ag     .        . 

15410 

14984 

14961 

14482 

Phosphor-bronze,  commercial  wire 

9071 

8588 

8479 

8054 

Platinoid,  Martino's  platinoid  with  i  to  2%  ) 
tungsten                                                        j  ' 

44590 

43823 

43601 

43022 

Platinum-iridium,  80  Pt  +  20  Ir      .        .        . 

31848 

29902 

29374 

27504 

Platinum-rhodium,  90  Pt  -\-  10  Rh  .        . 

18417 

14586 

13755 

10778 

Platinum-silver,  66.7  Ag  -f-  33.3  Pt  . 

27404 

269IS 

26818 

26311 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                              j  • 

- 

4046X  io3 

4092  X  i  o3 

4i89Xio3 

Carbon,  from  Edison-Swan  incandescent) 
lamp                                                              j  • 

3834X10^ 

3908  Xio3 

3955X108 

4054  X  i  o3 

Carbon,  adamantine,  from  Woodhouse  and  \ 
Rawson  incandescent  lamp                        J  • 

6i68Xio3 

6300X10* 

6363X108 

6495X108 

"  Phil.  Mag."  vol.  34,  1892. 

t  This  is  given  by  Dewar  and  Fleming  as  13777  for  o60.4,  which  appears  from  the  other  measurements  too  high. 
SMITHSONIAN  TABLES. 


TABLE  312  (continued). 
ALLOYS   AT   LOW   TEMPERATURES. 


28l 


by  Cailletet  and  Bouty  at  very  low  temperatures.  The  results  show  that  the  coefficient  of  change  with  temperature 
the  alloys.  The  resistance  of  carbon  was  found  by  Dewar  and  Fleming  to  increase  continuously  to  the  lowest 

ments  or  Miiller,  Benoit,  and  others.  Probably  the  simplest  rule  is  that  suggested  by  Clausius,  and  shown  by  these 
temperature.  This  gives  the  actual  change  of  resistance  per  degree,  a  constant ;  and  hence  the  percentage  of  change 
approximately  hold  for  alloys,  some  of  which  have  a  negative  temperature  coefficient  at  temperatures  not  far  from 


Temperature  = 

—  100° 

—  182° 

-197° 

Mean  value  of 
temperature  co- 
efficient between 
—  100°  and 
+  100°  C.* 

Metal  or  alloy. 

Specific  resistance  in  c.  g.  s.  units. 

Aluminum,  pure  hard-drawn  wire    . 

1928 

894 

- 

.00446 

Copper,  pure  electrolytic  and  annealed  . 

757 

272 

178 

431 

Gold,  soft  wire         

1207 
4010 

6110 

5295 
962 
5671 

604 
1067 

1900 

2821 
472 
2553 

608 
2290 

375 
578 

538 

34i 
377 
428 

Nickel,  pure  (prepared  by  Mond's  process  ) 
from  compound  of  nickel  and  carbon  >  . 
monoxide)                                                    ) 

Tin,  pure  wire  ....... 

German  silver,  commercial  wire 

33280 

32512 

- 

035 

Palladium-silver,  20  Pd  -f  80  Ag    . 

14256 

13797 

- 

039 

Phosphor-bronze,  commercial  wire  . 

7883 

737i 

- 

070 

Platinoid,  Martino's  platinoid  with  I  to  2%  ) 
tungsten                                                       ) 

42385 

4M54 

- 

025 

Platinum-iridium,  80  Pt  +  20  Ir 

26712 

24440 

- 

087 

Platinum-rhodium,  90  Pt  +  10  Rh  . 

9834 

7134 

- 

312 

Platinum-silver,  66.7  Ag  +  33-3  Pt  . 

26108 

25537 

- 

024 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                           } 

4218X10* 

432iXio8 

- 

- 

Carbon,  from  Edison-Swan  incandescent  ) 
lamp                                                           J  ' 

4079XI08 

4i8oXio8 

- 

031 

Carbon,  adamantine,  from  Woodhouse  and  ) 
Rawson  incandescent  lamp                        )  ' 

6533XI08 

- 

- 

029 

*  This  is  a  in  the  equation  J?  =  /?„  (i  -j-  a/),  as  calculated  from  the  equation  a 
SMITHSONIAN  TABLES. 


-"100  —  R— 100 

300  J?0 


282  TABLES  313,314. 

TABLE  313.  —  Variation  of  Electrical  Resistance  of  Glass  and  Porcelain  with  Temperature. 

The  following  table  gives  the  values  of  a,  b,  and  c  in  the  equation 

log  R  —  a  -f  bt  +  ct2, 

where  R  is  the  specific  resistance  expressed  in  ohms,  that  is,  the  resistance  in  ohms  per  centimeter  of  a  rod  on« 
square  centimeter  in  cross  section.* 


No. 

Kind  of  glass. 

Density. 

a 

b 

c 

Range  of 
temp. 
Centigrade. 

I 
2 

3 
4 

Test-tube  glass          .... 
«      <«        « 

2.458 

I3.86 
14.24 

16.21 
I3-M 

—.044 
—•055 
—•043 
—-031 

.000065 
.OOOI 
.0000394 
—  .000021 

0°-250° 

37-I31 

60-174 
10-85 

Lime  glass  (Japanese  manufacture)  . 

2-55 

5 

«         «            tt                   ti 

2.499 

14.002 

—.025 

—  .00006 

'35-95 

6 

Soda-lime  glass  (French  flask) 

2-533 

14.58 

—.049 

.000075 

45-120 

7 

Potash-soda  lime  glass 

2.58 

16.34 

—.0425 

.0000364 

66-193 

8 

Arsenic  enamel  flint  glass 

3-07 

18.17 

—•055 

.000088 

"S-^S 

9 

Flint  glass  (Thomson's  electrometer 
jar)         -.        

3.172 

18.021 

—  .036 

—  .OOOOO9I 

i  00-200 

10 

Porcelain  (white  evaporating  dish)  . 

- 

15-65 

—.042 

.00005 

68-290 

COMPOSITION  OF  SOME  OF  THE  ABOVE  SPECIMENS  OF  GLASS. 

Number  of  specimen  = 

3 

4 

5 

7 

8 

9 

Sil 
Po 
So 
Le 

61.3 
22.9 
Lime,  etc. 
bydiff. 

57-2 

21.  1 

Lime,  etc. 
bydiff. 

70.05 
1.44 
14.32 

2.70 

75-65 
7.92 
6.92 

54-2 

10.5 
7.0 
23-9 

55.18 
13.28 

31.01 

tash    
da       

ad  oxide     .... 

Lime       

15.8 

16.7 

10-33 

8.48 

o-3 

o-3S 

Magnesia        .... 

- 

- 

- 

0.36 

0.2 

0.06 

Arsenic  oxide 

- 

- 

- 

- 

3-5 

- 

Alumina,  iron  oxide,  etc. 

- 

- 

i-45 

0.70 

0.4 

0.67 

*  T.  Gray,  "Phil.  Mag."  1880,  and  "  Proc.  Roy.  Soc."  i88a. 
TABLE  314.  —  Temperature  Resistance  Coefficients  of  Glass,  Porcelain  and  Quartz  dr/dt. 


Temperature. 

450° 

500° 

575° 

600° 

700° 

750° 

800° 

9000 

1000° 

Glass  .  .  . 
Porcelain  .  . 
Quartz.  .  . 

—32. 

—6. 

-^ 

—.8 
-9.8 

—0.17 

—2.8 

—  O.I 

—1.6 

—  10. 

—0.06 

-'7° 
—  6.40 

—0.30 
—2.60 

—  O.I  2 
—  1.00 

Somerville,  Physical  Review,  31,  p.  261,  1910. 


SMITHSONIAN  TABLES. 


TABLE  315. 
TABULAR   COMPARISON   OF  WIRE   GAGES. 


Gage 
No. 

American 
Wire  Gage 
(B.  &  S.) 

Mils. 

American 
Wire  Gage 
(B.  &  S.) 
mm. 

Steel  Wire 

Steel  Wire 
Gage* 
mm. 

Stubs'  Steel 
Wire  Gage 

Mils. 

(British) 
Standard 
Wire  Gage 

Mils. 

Birmingham 
Wire  Gage 
(Stubs') 
Mils. 

Gage 

No.    j 

7-0 

490.0 

12.4 

$00. 

7-0 

6-0 

461.5 

11.7 

464. 

6-0 

5-o 

430-5 

10.9 

432. 

S-o 

4-0 

460. 

11.7 

393-8 

IO.O 

400. 

454- 

4-o 

410. 

10.4 

362.5 

9-2 

372. 

425. 

3-o 

2-0 

365. 

9-3 

331-0 

8.4 

348. 

380. 

2-O 

O 

325- 

8.3 

306.5 

7-8 

324. 

340. 

0     1 

I 

289. 

7-3 

283.0 

7.2 

227. 

300. 

300. 

I 

2 

258. 

6.5 

262.5 

6.7 

219. 

276. 

284. 

2 

3 

229. 

5-8 

243-7 

6.2 

212. 

252. 

259. 

3 

4 

204. 

5-2 

225.3 

5-7 

207. 

232. 

238. 

4 

5 

182. 

4.6 

207.0 

5-3 

204. 

212. 

220. 

5 

6 

162. 

4.1 

192.0 

4-9 

2OI. 

192. 

203. 

6    ! 

7 

144. 

3-7 

177.0 

4-5 

199. 

I76. 

180. 

7 

8 

128. 

3-3 

162.0 

4.1 

197. 

160. 

I6S. 

8    i 

9 

114. 

2.91 

148.3 

3-77 

194- 

144- 

I48. 

0 

10 

102. 

2-59 

135-0 

3-43 

1  01. 

128. 

134- 

10 

ii 

01. 

2.30 

120.5 

3.06 

188. 

116. 

120. 

ii 

12 

81. 

2.05 

105.5 

2.68 

185. 

104. 

109. 

12 

13 

72. 

1.83 

9L5 

2.32 

182. 

92. 

95- 

13 

14 

64. 

1.63 

80.0 

2.03 

180. 

80. 

S3- 

14 

IS 
16 
17 

57- 
Si- 

45- 

1-45 
1.29 
I.I5 

72.0 
62.5 
54-0 

1.83 
1-59 
1-37 

178. 
175. 
172. 

11: 

56. 

1 

3 

17 

18 

40. 

1.02 

47-5 

1.21 

168. 

48. 

49- 

18 

jg 

36. 

0.91 

41.0 

1.04 

164. 

40. 

42. 

J-9 

2O 

32. 

.81 

34-8 

0.88 

161. 

36. 

35- 

20    i 

21 

28.5 

.72 

31-7 

.81 

157- 

32. 

32. 

21 

22 
23 

25-3 

22.6 

.62 

•57 

28.6 
25.8 

II 

155- 
153- 

28. 

24- 

28. 
25- 

22 
23 

24 

2O.  I 

•Si 

23.0 

.58 

151- 

22. 

22. 

24 

11 

17.9 
15-9 

•45 
.40 

20.4 
18.1 

•52 
.46 

148. 
146. 

2O. 

18. 

2O. 

18. 

3 

27 

14.2 

.36 

17-3 

•439 

143- 

16.4 

16. 

27 

28 

12.6 

.32 

16.2 

.411 

139. 

14.8 

14. 

28 

29 

ii-3 

.29 

15-0 

.381 

134- 

13.6 

13- 

29 

30 

IO.O 

•25 

14.0 

.356 

127. 

12.4 

12. 

30    I 

31 

8.9 

.227 

13-2 

•335 

1  20. 

n.6 

10. 

31 

32 

8.0 

.202 

12.8 

.325 

"5- 

10.8 

9- 

32 

33 

7  ! 

.180 

11.8 

.300 

112. 

IO.O 

8. 

33 

34 

6^3 

.I60 

10.4 

.264 

no. 

9.2 

7- 

34 

11 

5-6 
5-0 

•143 
.127 

9-5 
9.0 

.241 
.229 

108. 
106. 

?1 

5- 
4* 

II 

11 

4-5 
4.0 

.113 

.101 

8.5 
8.0 

.216 
.203 

103. 

IOI. 

6.8 
6.0 

11 

39 

3-5 

.000 

7-5 

.191 

99. 

5-2 

39    i 

40 

3-1 

.080 

7-0 

.178 

97- 

4.8 

40     1 

41 

6.6 

.168 

95- 

4-4 

41 

42 

6.2 

•157 

92. 

4.0 

42 

43 

6.0 

.152 

88. 

3-6 

43 

44 

5-8 

.147 

85- 

3.2 

44 

5-5 

.140 

81. 

2.8 

45 

46 

5-2 

.132 

79- 

2.4 

46 

47 

S-o 

.127 

77- 

2.O 

47 

48 

4.8 

.122 

75- 

1.6 

48 

49 
50 

4.6 
4.4 

.117 

.112 

11: 

1.2 

I.O 

49 
SO 

*  The  Steel  Wire  Gage  is  the  same  gage  which  has  been  known  by  the  various  names:  "  Washburn  and  Moen,"  "Roeb- 
ling  "  "American  Steel  and  Wire  Co.'s."  Its  abbreviation  should  be  written  "Stl.  W.  G.,"  to  distinguish  it  from 
"S.  W.  G.,"  the  usual  abbreviation  for  the  (British)  Standard  Wire  Gage. 

Taken  from  Circular  No.  31.  Copper  Wire  Tables,  U.S.  Bureau  of  Standards  which  contains  more  complete  tables. 

SMITHSONIAN  TABLES. 


284  TABLES  316-322. 

WIRE    TABLES. 

TABLE  316.—  Introduction.    Mass  and  Volume  Resistivity  of  Copper  and  Aluminum, 

The  following  wire  tables  are  abridged  from  those  prepared  by  the  Bureau  of  Standards  at  the 
request  and  with  the  cooperation  of  the  Standards  Committee  of  the  American  Institute  of  Elec- 
trical Engineers  (Circular  No.  31  of  the  Bureau  of  Standards).  The  standard  of  copper  resist- 
ance used  is  "The  International  Annealed  Copper  Standard"  as  adopted  Sept.  5,  1913,  by  the 
International  Electrotechnical  Commission  and  takes  the  Resistivity  at  20°  C.  of  an  annealed  copper 
wire  one  meter  long  weighing  one  gram  as  equal  to  o.  1 5328  ohm.  This  standard  corresponds  to 
a  conductivity  of  58.  X  io~5  cgs.  units,  and  a  density  of  8.89,  at  20°  C. 

In  the  various  units  of  mass  and  volume  resistivity  this  may  be  stated  as 


The  tern 
However 


0.15328  ohm  (meter,  gram)  at  20°  C. 
875.20    ohms  (mile,  pound)  at  20°  C. 
1.7241    microhm-cm,  at  20°  C. 
0.67879  microhm-inch  at  20°  C. 
10.371    ohms  (mil,  foot)  at  20°  C. 

mperature  coefficient  for  this  particular  resistivity  is  820  =  0.00393  or  80  =  0.00427. 
However,  the  temperature  coefficient  is  proportional  to  the  conductivity,  and  hence  the  change  of 
resistivity  per  degree  C.  is  a  constant,  0.000597  ohm  (meter,  gram).  The  "constant  mass"  tem- 
perature coefficient  of  any  sample  is 

0.000597  -f  0.000005 

Et      resistivity  in  ohms  (meter,  gram)  at  t°  C  ' 

The  density  is  8.89  grams  per  cubic  centimeter  at  20°  C.,  which  is  equivalent  to  0.3212  pounds 
per  cubic  inch. 

The  values  in  the  tables  are  for  annealed  copper  of  standard  resistivity.  The  user  of  the 
tables  must  apply  the  proper  correction  for  copper  of  other  resistivity.  Hard-drawn  copper 
may  be  taken  as  about  2.7  per  cent  higher  resistivity  than  annealed  copper. 

The  aluminum  tables  are  based  on  a  figure  for  the  conductivity  published  by  the  U.  S.  Bureau 
of  Standards,  which  is  the  result  of  many  thousands  of  determinations  by  the  Aluminum  Company 
of  America.  A  volume  resistivity  of  2.828  michrom-cm.,  and  a  density  of  2.70  may  be  con- 
sidered to  be  good  average  values  for  commercial  hard-drawn  aluminum.  These  values  give  : 

Mass  resistivity,  in  ohms  (meter,  gram)  at  20°  C 0.0764 

"          "     «      (mile,  pound)  at  20°  C 436. 

Mass  per  cent  conductivity 200.7% 

Volume  resistivity,  in  michrom-cm.  at  20°  C 2.828 

in  microhm-inch  at  20°  C 1.113 

Volume  per  cent  conductivity 61.0% 

Density,  in  grams  per  cubic  centimeter 2.70 

Density,  in  pounds  per  cubic  inch »    .    .  0,0975 

SMITHSONIAN  TABLES. 


TABLES  317,318.  285 

WIRE  TABLES. 

TABLE  317.— Temperature  Coefficients  of  Copper  for  Different  Initial  Temperatures  (Centigrade) 

and  Different  Conductivities. 


Ohms 
(meter,  gram) 
at  20°  C. 

Per  cent 
conductivity. 

Oo 

«I5 

020 

«25 

<*3o 

aso 

0.161  34 
.159  66 

95% 
96% 

0.004  03 
.004  08 

0.003  80 
.00385 

0-003  73 
.00377 

0.003  67 

.00370 

0.003  60 

.00364 

0.003  36 
•00339 

.15802 
•157  53 

97  %^ 
97-3% 

.00413 

.004  14 

.00389 
.003  90 

.003  8  1 
.00382 

.003  74 
•00375 

.003  67 
.00368 

.003  42 
.00343 

.156  40 

.15482 

98% 
99% 

.00417 

.004  22 

•00393 
.003  97 

.00385 
.00389 

.00378 
.003  82 

.003  71 
•00374 

•003  45 
.00348 

.153  28 

.151  76 

100% 
101% 

.00427 
.00431 

.00401 
.00405 

.003  93 

.00397 

.00385 
.003  89 

.00378 
.003  82 

.003  52 
•0035S 

NOTE.  —  The  fundamental  relation  between  resistance  and  temperature  is  the  following: 

—  tj), 


where  atl  is  the  "temperature  coefficient,"  and  tj  is  the  "initial  temperature"  or  "temperature  of  reference." 

The  values  of  a  in  the  above  table  exhibit  the  fact  that  the  temperature  coefficient  of  copper  is  proportional  to  the 
conductivity.  The  table  was  calculated  by  means  of  the  following  formula,  which  holds  for  any  per  cent  conductivity,  », 
within  commercial  ranges,  and  for  centigrade  temperatures,  (n  is  considered  to  be  expressed  decimally:  e.g.,  if  percent 
conductivity  —  99  per  cent,  n  =  0.99.) 


— 20) 


n  (0.00393) 
TABLE  318.— Reduction  of  Observations  to  Standard  Temperature.  (Copper.) 


Temper- 
ature C. 

Corrections  to  reduce  Resistivity  to  20°  C. 

Factors  to  reduce  Resistance  to  20°  C. 

Temper- 
ature C. 

Ohm  (meter, 
gram). 

Microhm- 
cm. 

Ohm  (mile, 
pound). 

Microhm  — 
inch. 

For  96  per 
cent  con- 
ductivity. 

For  98  per 
cent  con- 
ductivity. 

For  loo  per 
cent  con- 
ductivity. 

o 
5 
10 

+0.011  94 
+  .00896 
4  .005  97 

+0.1361 
-j-  .1021 
+  .0681 

4  68.20 
4  Si.iS 
+  ^4.10 

+0.053  58 
4  .040  18 
.026  79 

1.0816 
i.  0600 
1.0392 

1.0834 
1.0613 
1.0401 

i  -°8S3 
1.0626 
1.0409 

o 
5 
10 

n 

12 
13 

+  .00537 
4  .00478 
4  .004  18 

+  .0612 

4-  .0544 
+  .0476 

+  30.69 
+  27.28 
+  23.87 

'    .024  II 
4  .021  43 

4  -01875 

1-0352 
1.0311 
1.0271 

1-0359 
1.0318 
1.0277 

1.0367 
1.0325 
1.0283 

ii 

12 

13 

14 
IS 
16 

+  .003  58 
4  .002  99 
4  .002  39 

+  .0408 
+  -0340 
+  .0272 

4  20.46 
4  17-05 
4-  13-64 

4  .016  07 
4  .013  40 
4-  .010  72 

1.0232 
1.0192 
1.0153 

1.0237 
1.0196 
1.0156 

1.0242 

I.020O 
I.  Ol6o 

14 
IS 
16 

17 
18 
19 

4-  .001  79 
4  .001  19 
4  .00060 

4-  .0204 
+  .0136 
4  .0068 

+  10.23 
4-    6.82 
+    3-41 

4  .00804 
4  .005  36 
4  .002  68 

1.0114 
1.0076 
1.0038 

1.0117 
1.0078 
1.0039 

1.0119 
1.0079 
1.0039 

i 
17 
18 
19 

20 

21 
22 

o 
—  .000  60 
—  .001  19 

o 

-  .0068 

—  .0136 

0 

—    3-41 
-    6.82 

o 
—  .002  68 
—  .005  36 

I.OOOO 

0.9962 
.9925 

I.OOOO 

0.9962 
.9924 

I.OOOO 

0.9961 
.9922 

20 

21 
22 

23 

24 
25 

—  .001  79 
-  .00239 
-  .00299 

—  .0204 
—  .0272 
—  .0340 

—  10.23 
—  13-64 
-  17-05 

—  .00804 
—  .010  72 
-  .01340 

.9888 
.9851 
.9815 

.9886 
.9848 

.9811 

.9883 

.9845 
.9807 

23 
24 
25 

26 
27 
28 

-  .00358 
—  .004  18 
—  .004  78 

—  .0408 
-  .0476 
—  .0544 

—  20.46 
-  23.87 
—  27.28 

—  .016  07 
-  .01875 
-  .02143 

•9779 
•9743 
.9707 

•9774 
•9737 
.9701 

.9770 
.9732 
•9695 

26 

11 

29 

30 
35 

-  -00537 
-  .00597 
-  .00896 

-  .0612 
1  -  .0681 

.IO2I 

-  30.69 
—  34.10 
-  51-15 

—  .024  ii 
—  .026  79 
—  .040  1  8 

.9672 
.9636 
.9464 

.9665 
.9629 
•9454 

,9658 

.9622 
•9443 

29 
30 

35 

40 
45 
50 

—  .oil  94 
—  .01493 
—  .017  92 

—    .I36l 
—    .I7OI 
—    .2O42 

-  68.20 
-  85.25 
—  102.30 

-  -05358 
-  .06698 
-  .08037 

.9298 
.9138 
.8983 

.9285 
.9122 
.8964 

.9271 
.9105 
.8945 

40 
45 
So 

55 
60 
65 

—  .020  90 
-  .02389 
—  .02687 

—    .2382 
—    .2722 
—    .3062 

-119-35 
—  136.40 
-153-45 

-  .093  76 
—  .107  16 
—  .120  56 

•8833 
.8689 
•8549 

.8812 
.8665 
•8523 

.8791 
.8642 
.8497 

g 

65 

70 
75 

—  .02986 
-  .03285 

-    .3403 
—    -3743 

—  170.50 
-187.55 

-  -13395 
—  .147  34 

.8413 
.8281 

•8385 
.8252 

.8358 
.8223 

70 
75 

SMITHSONIAN  TABLES. 


286 


TABLE  319. 
WIRE  TABLE,  STANDARD  ANNEALED  COPPER. 

American  Wire  Gage  (B.&S.).    English  Units. 


ENGLISH. 


Gage 

N£ 

Diameter 
in  Mils, 
at  20°  C. 

Cross-Section  at  20°  C. 

Ohms  per  1000  Feet.* 

Circular  Mils. 

Square  Inches. 

o°C 
(  =  32°F) 

20°  C 

(r=68°F) 

50°  C 

(=122°  F) 

75°  C 
(  =  i67°F) 

oooo 

OOO 

oo 

460.0 
409.6 
364.8 

211  600. 
167  800. 

133  ioo. 

0.1662 
.1318 
.1045 

0.045  1  6 

•05695 
.071  81 

0.049  OI 
.061  80 

.077  93 

0.054  79 
.06909 

.087  12 

0.059  61 
.075  16 
.09478 

0 

I 

2 

3|4.9 
289.3 
257.6 

IO5  500. 
83690. 

66  370. 

.08289 

•065  73 

.052  13 

.09055 
.1142 
.1440 

.09827 
.1239 
•1563 

.1099 
.1385 
•1747 

•"95 
•1507 
.1900 

3 
4 
5 

229.4 
204.3 
181.9 

52  640. 
41  740. 
33100. 

.041  34 
.032  78 
.02600 

.1816 
.2289 
.2887 

.1970 
.2485 
.3133 

.2203 
.2778 
•3502 

.2396 
.3022 
.3810 

6 

I 

162.0 

144-3 
128.5 

26250. 

20  820. 
16510. 

.020  62 
•01635 

.012  97 

.3640 
4590 
.5788 

•3951 
.4982 
.6282 

.4416 
.5569 
.7023 

.4805 
.6059 
.7640 

9 

10 

ii 

1144 
IOI-9 
90.74 

13090. 

10  380. 

8234. 

.010  28 

.008155 

.006  467 

.7299 
.9203 
1.161 

.7921 
.9989 
1.260 

.8855 
I.II7 
1.408 

-9633 
1.215 
1-532 

12 
13 
14 

80.81 
71.96 
64.08 

6530. 
5178. 
4107. 

.005  129 
.004  067 

.003  225 

1.463 
1.845 
2.327 

1.588 

2.003 
2.525 

1-775 
2.239 
2.823 

I-93I 
2.436 
3.071 

II 

17 

57.07 
50.82 
45.26 

3237. 
2583. 
2048. 

.002  558 

.002  028 
.001  609 

2-934 
3.700 
4.666 

3.184 
4.016 
5.064 

3.560 
4.489 
5.660 

3-873 
4.884 
6.158 

18 

!9 

20 

40.30 

35-»9 
31.96 

1624. 

1288. 

1022. 

.001  276 

.001  012 

.000  802  3 

5.883 
7.418 
9-355 

6.385 
8.051 
10.15 

7-138 
9.001 

"•35 

7765 
9792 
12.35 

21 

22 
23 

28.45 

25-35 
22.57 

8IO.I 
642.4 
509-5 

.000  636  3 
.000  504  6 
.0004002 

11.80 
14-87 
18.76 

12.80 
16.14 
20.36 

14-31 
18.05 
22.76 

15-57 
19.63 
24.76 

24 

3 

20.  i  o 
17.90 
15-94 

404.0 
320.4 
254.1 

.0003173 

.000  251  7 
.0001996 

23-65 
29.82 
37.61 

25.67 

32.37 
40.81 

28.70 
36.18 
45-63 

31.22 
39.36 
49-64 

29 

14.20 
12.64 
11.26 

201-5 

159-8 
126.7 

.000  1  58  3 
.000  125  5 
.00009953 

47-42 
59.80 
75-40 

5M7 
64.90 
81.83 

57-53 
72-55 
91.48 

62.59 

78.93 
99-52 

3° 
31 
32 

10.03 
8.928 
7-95° 

100-5 
79.70 
63.21 

.000  078  94 
.000  062  60 
.000  049  64 

95.08 
119.9 
151.2 

103.2 
130.1 
164.1 

"5-4 

145-5 
183.4 

I25.S 

I5g.2 
199-5 

33 
34 
35 

7.080 
6-305 
5-6i5 

5°'J3 
39-75 
31-52 

.00003937 

.000  031  22 
.OOO  O24  76 

190.6 
240.4 
303-1 

206.9 
260.9 
329.0 

231-3 

291.7 
367.8 

251.6 

3*7.3 
400.1 

36 

i 

5.000 
4453 
3-965 

25.00 
19.83 

15-72 

.00001964 
.00001557 

.000012  35 

382.2 
482.0 
607.8 

414-8 
523.1 
659.6 

463-7 
584.8 

737-4 

®J 

802.2 

39 

40 

3-531 
3-145 

12.47 
9.888 

.000  009  793 
.000  007  766 

766.4 
966.5 

831.8 
1049. 

929.8 
"73- 

1012. 
1276. 

*  Resistance  at  the  stated  temperatures  of  a  wire  whose  length  is  1000  feet  at  20°  C. 
SMITHSONIAN  TABLES. 


ENGLISH. 


TABLE  319  (continued). 


287 


V/IRE  TABLE,  STANDARD  ANNEALED  COPPER  (continued). 
American  Wire  Gage  (B.  &  S.).    English  Units  (continued). 


Gage 

No. 

Diameter 
in  Mils. 
at  20°  C. 

Pounds 

per 
1000  Feet. 

Feet 

per 
Pound. 

Feet  per  Ohm.* 

o°  C 
(=32°  F) 

20°   C 

(=68°  F) 

50°  C 

(=122°  F) 

75°  C 
(=167°  F) 

0000 
000 

oo 

460.0 
409.6 
364.8 

640.5 

507.9 
402.8 

1.561 
1.968 
2.482 

22    140. 
17    560. 

13  93°- 

20  400. 

16  180. 

12    830. 

18  250. 
14  470. 
II  480. 

16  780. 
13  300. 
10  550. 

0 

I 

2 

324.9 

289.3 
257.6 

3I9-5 
253-3 
200.9 

3.130 
3-947 
4-977 

II   040. 
8758. 
6946. 

10  180. 
8070. 

6400. 

9103. 
7219. 

5725. 

.tt 

5262. 

3 
4 
5 

229.4 
204.3 
181.9 

159-3 
126.4 
IOO.2 

6.276 
7.914 
9.980 

5508. 
4368. 
3464. 

5075. 
4025. 
3192. 

4540. 
3600. 

2855. 

4173. 
3309. 

2025. 

6 

I 

162.0 

144-3 
128.5 

79.46 
63.02 
49.98 

12.58 
15-87 

20.01 

2747. 
2179. 
1728. 

2531. 

2007. 

1592. 

2264. 

1796. 
1424. 

2081. 

1651. 

1309. 

9 

10 

ii 

114.4 
IOI-9 
90.74 

39-63 
31-43 
^24.92 

25.23 
31.82 
40.12 

1370. 
I087. 
861.7 

1262. 

1001. 

794.0 

1129. 

895.6 

710.2 

1038. 
823.2 
652.8 

12 
13 
14 

80.8  1 
71.96 
64.08 

1977 
15.68 
12-43 

50.59 
63.80 
80.44 

683.3 
541-9 
429.8 

629.6 

499-3 
396.o 

563.2 
446.7 

354-2 

517-7 

410.6 

325-6 

II 

17 

57-07 
50.82 
45.26 

9.858 
7.8l8 
6.200 

IOI-4 
127.9 
l6l.3 

340.8 
270.3 
214.3 

314.0 
249.0 
197.5 

280.9 

222.8 
176.7 

258.2 
204.8 

162.4 

18 

19 

20 

40.30 

35.89 
31.96 

4.917 

3-899 
3.092 

2034 
256.5 
3234 

170.0 
134.8 
106.9 

156-6 
124.2 
98.50 

I4O.I 
III.  I 

88.ii 

128.8 

IO2.I 
80.99 

21 
22 
23 

28.46 

25.35 
22.57 

2.452 

1.945 
1.542 

407.8 
514.2 
648.4 

84.78 
67.23 
53-32 

78.11 
61.95 
49.13 

69.87 
55-41 
43-94 

64-23 
50.94 
40-39 

24 

25 
26 

2O.  I  O 
17.90 
15-94 

1.223 
0.9699 
.7692 

817.7 
1031. 
1300. 

42.28 
33.53 
26.59 

38.96 
30.90 
24.50 

34.85 
27.64 
21.92 

32.03 
25.40 
2O.I5 

1 

29 

14.20 
12.64 
11.26 

.6100 

•4837 
.3836 

1639. 
2067. 
2607. 

21.09 
16.72 
13.26 

19-43 
i5-4i 

12.22 

17-38 
I3-78 
10.93 

15.98 
12.67 
10.05 

3° 
3i 
32 

10.03 
8.928 
7«95° 

.3042 
.2413 
•1913 

3287. 

4145. 
5227. 

10.52 

8-341 
6.614 

9.691 

7-685 
6.095 

8.669 
6-875 
5-452 

7.968 
6.319 
5-OII 

33 
34 
35 

7.080 
6.305 
5-6I5 

•i5'7 
.1203 

.095  42 

6591. 
8310. 

10  480. 

5-245 
4.160 

3.299 

4-833 
3.833 
3.040 

4-323 
3-429 
2.719 

3-974 
3-152 
2.499 

36 
% 

5.OOO 
4453 
3.965 

.075  68 
.060  01 
•047  59 

13   210. 

16  660. 

21    OIO. 

2.616 

2-075 
1.645 

2.4II 
I.9I2 
1.516 

2.156 
1.710 
1.356 

1.982 

1-572 
1.247 

39 
40 

3-531 
3-145 

•037  74 
.029  93 

26   5OO. 

33  4io. 

i'305 
!-o35 

1.202 
0-9534 

1-075 
0.8529 

0.9886 
.7840 

•  Length  at  20°  C.  of  a  wire  whose  resistance  is  i  ohm  at  the  stated  temperatures. 
SMITHSONIAN  TABLES. 


288  TABLE  319  (continued).  ENGLISH, 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER  (continued). 

American  Wire  Gage  (B.  &  S.».    English  Units  (continued). 


Gage 
No. 

Diameter 
in  Mils 
at 

20°  C. 

Ohms  per  Pound. 

Pounds  per  Ohm.       i 

o°C. 
(  =  32°F.) 

20°  C. 

(  =  68°F.) 

50°  C. 

(=I22°F.) 

20°  C. 

(  =  68°F.) 

oooo 

000 

00 

460.0 
409.6 
364.8 

o.ooo  070  51 

.OOO  II2I 

.000  1783 

o.ooo  076  52 

.OOO  1217 

.000  1935 

o.ooo  085  54 
.000  1360 
.000  2163 

13  070. 
8219. 
5169. 

0 

I 

2 

324.9 
289.3 
257.6 

.000  2835 
.000  4507 
.000  7166 

.000  3076 
.000  4891 
.000  7778 

.000  3439 
.000  5468 
.0008695 

325I- 

2044. 
1286. 

3 
4 

5 

229.4 
204.3 
181.9 

.001  140 

.001  8l2 

.002  881 

.001  237 
.001  966 

.003  127 

.001  383 

.002   198 

•003  495 

808.6 
508.5 
3I9.8 

6 
8 

l62.O 

144-3 
128.5 

.004  581 
.007  284 
.on  58 

.004  972 
.007  905 

.012  57 

.005  558 
.008838 
.014  05 

2OI.I 
126.5 

79-55 

9 
10 
ii 

1144 
IOI.9 
90.74 

.018  42 
.029  28 
.046  56 

.01999 
.031  78 

-050  53 

.022  34 

•035  53 
.056  49 

50-03 
3M7 
19.79 

12 
13 
M 

80.81 
71.96 
64.08 

.074  04 
.1177 

.1872 

-080  35 
.1278 
.2032 

.08983 
.1428 
.2271 

12.45 

7.827 
4.922 

II 

17 

57-07 
50.82 
45.26 

.2976 

•4733 
•7525 

-3230 
•5136 
5i§7 

.3611 

.5742 
.9130 

3.096 
1.947 
1.224 

18 

*9 
20 

40.30 

35-89 
31.96 

1.197 
1.903 
3.025 

1.299 
2.065 
3-283 

1.452 
2.308 
3.670 

0.7700 

.4843 
.3046 

21 
22 
23 

28.46 
25-35 

22.57 

4.810 
7.649 
12.16 

P21 
8.301 

13.20 

5.836 
9.280 
14.76 

•*9*S 
.1205 

.075  76 

24 

25 
26 

20.10 
17.90 
15-94 

19-34 
30.75 
48.89 

20.99 
33-37 
53-06 

23.46 
37-31 
59-32 

.047  65 
.029  97 
.018  85 

27 
28 
29 

I4.2O 
12.64 
11.26 

77.74 

123.6 

196.6 

84-37 
134.2 

213-3 

94.32 
150.0 

238-5 

.011  85 
.007  454 
.004688 

30 
31 
32 

IO.O3 
8.928 
7.950 

312.5 

497-0 
790.2 

339-2 
539-3 
857-6 

379-2 
602.9 

958.7 

.002  948 
.001  854 
.001  166 

33 
34 

35 

7.080 
6.305 
5.615 

1256. 
1998. 
3177. 

1364. 
2168. 
3448. 

1524. 

2424. 
3854. 

•ooo  7333 
.000  4612 
.000  2901 

36 
% 

5.000 
4453 
3-965 

5051- 
8032. 

12  770. 

3482. 

8717. 
13860. 

6128. 
9744- 
15490. 

.000  1824 
.000  1  147 
.000072  15    1 

39 

40 

3-531 

3-!45 

20  310. 
32  290. 

22  040. 

35  040. 

24  640. 
39  170. 

.000  045  38 
.000  028  54 

SMITHSONIAN  TABLES. 


METRIC,  TABLE  320. 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER, 

American  Wire  Gage  (B.  &  S.)  Metric  Units. 


289 


Gage 

No. 

Diameter 
in  mm. 
at  20°  C. 

Cross  Section 
in  mm.2 
at  20°  C. 

Ohms  per   Kilometer.  * 

o°C. 

20°  C. 

50°  C. 

75°  C. 

oooo 

000 
00 

11.68 
10.40 
9.266 

107.2 
85-03 
6743 

0.1482 
.1868 
•2356 

o.i  608 
.2028 
•2557 

0.1798 
.2267 
.2858 

0.1956 
.2466 
.3110 

o 

I 

2 

8.252 
7.348 
6-544 

53-48 
42.41 

33.63 

.2971 
•3746 
.4724 

•3224 
.4066 
•5127 

.3604 
•4545 
•5731 

.3921 

4944 
•6235 

3 
4 

5 

5.827 
5.189 
4.621 

26.67 
21.15 
16.77 

•5956 

•75" 
.9471 

.6465 
.8152 
1.028 

.7227 

•9"3 
1.149 

.7862 
.9914 
1.250 

6 

I 

4-II5 

3-665 
3.264 

!3-30 
IO-55 
8.366 

1.194 
1.506 
1.899 

1.296 
1.634 
2.061 

1.449 
1.827 
2.304 

I-576 
1.988 
2.506 

9 

10 

ii 

2.906 
2.588 
2.305 

6.634 
5.261 
4.172 

2-395 
3.020 
3.807 

2-599 
3-277 
4.132 

2-905 
3-663 
4.619 

3.161 

3-985 
5-025 

12 
13 
14 

2.053 
1.828 
1.628 

3.309 
2.624 
2.081 

4.801 
6.054 
7.634 

5.211 

6.571 
8.285 

5.825 

7-345 
9.262 

6.337 
10.08 

11 

I? 

1.450 
1.291 
1.150 

1.650 
1.309 
1.038 

9.627 
12.14 
I5-3I 

10.45 

J3-i7 
16.61 

n.68 

14-73 
i8-57 

12.71 
16.02 

20.20 

18 

19 

20 

1.024 
0.9116 
.8ll8 

0.8231 
.6527 
•5176 

19.30 

24-34 
30.69 

20.95 
26.42 
33-31 

23.42 
29-53 
37-24 

25.48 
32.12 
40.51 

21 

22 
23 

.7230 
.6438 

•5733 

.4105 

•3255 
.2582 

38.70 
48.80 
61.54 

42.00 
52.96 
66.79 

46.95 
59-21 
74.66 

51.08 
64.41 
8l.22 

24 

% 

.5106 

•4547 
.4049 

.2047 
.1624 
.1288 

77.60 

97.85 
123.4 

84.21 
106.2 
133-9 

94.14 
118.7 
149.7 

IO2.4 
129.1 
162.9 

27 
28 
29 

.3606 
.3211 

.2859 

.1021 
.080  98 

.064   22 

155.6 
196.2 
247.4 

168.9 
212.9 
268.5 

1  88.8 
238.0 
300.1 

2054 
258.9 
326.5 

3° 
31 

32 

•2546 
.2268 
.2019 

-°5o  93 
.040  39 
.032  03 

3"-9 
393-4 
496.0 

338.6 
426.9 
538.3 

378.5 
477.2 
601.8 

4II.7 
519.2 
6547 

33 
34 
35 

.1798 
.1601 
.1426 

.025  40 

.020    14 

•015  97 

623.5 
788.7 
994-5 

678.8 
856.0 
1079. 

758.8 

956.9 
1207. 

825.5 
1041. 
I3I3. 

36 

9 

.1270 
.1131 
.1007 

.012  67 
.010  05 

.007  967 

1254. 
1581. 
1994. 

1361. 
1716. 
2164. 

1522. 
1919. 
2419. 

1655. 
2087. 
2632. 

39 

40 

.089  69 
.079  87 

.006  318 
.005  oio 

2514. 
3J7i. 

2729. 
344L 

3051- 
3847- 

33I9- 
4185. 

•Resistance  at  the  stated  temperatures  of  a  wire  whose  length  is  i  kilometer  at  20°  C. 
SMITHSONIAN  TABLES. 


2QO  TABLE  320  (continued). 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER  (continued}. 
American  Wire  Gage  (B.  &  S.)    Metric  Units  (continued). 


METRIC, 


Gage 

No. 

Diameter 
in  mm. 
at  20°  C. 

Kilograms 
per 
Kilometer. 

Meters 
per 
Gram. 

Meters  per  Ohm.* 

o°C. 

20°  C. 

50°  C. 

75°  C. 

0000 

ooo 
oo 

11.68 

10.40 
9.266 

953'2 

755-9 
599-5 

o.ooi  049 

.OOI  323 

.001  668 

6749. 

5352. 
4245. 

6219. 
4932. 
39II- 

5563. 
4412. 

3499. 

5"3- 
4055. 
3216. 

o 
I 

2 

8.252 
7.348 
6-544 

475-4 
377-o 
299.0 

.002  103 

.002  652 

.003  345 

2117. 

3102. 
2460. 

i95x« 

2774. 

2200. 
1745- 

2550. 
2022. 
I604. 

3 
4 

5 

5.827 
5.189 
4.621 

237.1 
1  88.0 
149.1 

.004  217 

.00-5  318 
.006  706 

1679. 

I33I. 
1056. 

1547- 
1227. 
972.9 

I384. 

1097. 
870.2 

1272. 
IOO9. 

799-9 

6 
8 

4-"5 
3-665 
3.264 

118.2 

93-78 

74-37 

.008  457 
.010  66 
•013  45 

664.0 
526.6 

771-5 
6n.8 

485.2 

690.1 

547-3 
434-0 

6344 
503-1 
399-0 

9 

10 

ii 

2.906 

2.588 
2-305 

58.98 
46.77 
37-09 

.016  96 

.021  38 
.026  96 

417.6 

tilt 

384.8 

305-1 
242.0 

344-2 
273.0 
216.5 

316.4 
250.9 
199.0 

12 
13 
H 

%$ 

1.628 

29.42 

23-33 
18.50 

.03400 
.042  87 
.054  06 

208.3 
165.2 
131.0 

191.9 

152.2 
120.7 

171.7 
136.1 
108.0 

157.8 
125.1 
99-24 

15 
10 
17 

1.450 
1.291 
1.150 

14.67 
11.63 
9.226 

.06816 

•085  95 
.1084 

103.9 
82.38 
65-33 

95.71 
75-90 
60.20 

85.62 
67.90 
53-85 

78.70 
62.41 
49-50 

18 

19 
20 

1.024 
0.9116 
.8118 

7-3I7 
5-803 
4.602 

•1367 

.1723 

•2173 

5I.8l 
41.09 
32.58 

47-74 
37-86 
30.02 

42.70 
33-86 
26.86 

39-25 

3I.J3 

24.69 

21 

22 
23 

.7230 
.6438 
•5733 

3-649 
2.894 
2.295 

.2740 
•3455 
4357 

25.84 
20.49 
16.25 

23.81 
18.88 
14.97 

21.30 
16.89 
13-39 

19.58 

15.53 
12.31 

24 
25 
26 

.5106 

•4547 
.4049 

1.820 
1-443 
I.I45 

•8736 

12.89 
IO.22 
8.105 

11.87 
9.417 
7.468 

10.62 
8.424 
6.680 

9.764 

7-743 
6.141 

27 
28 
29 

.3606 
.3211 
.2859 

0.9078 
.7199 
.5709 

1.  102 
1.389 

1-752 

6.428 

5-097 
4.042 

5.922 
4.697 
3.725 

5.298 
4.201 
3-332 

4.870 
3.862 
3-063 

30 
31 
32 

•%£ 

.2019 

4527 
•3590 
.2847 

2.209 
2.785 
3-512 

3.206 
2.542 
2.016 

2-954 

3$ 

2.642 

2-095 
1.662 

2.429 
1.926 
1.527 

33 
34 
35 

.1798 
.1601 
.1426 

.2258 
.1791 
.1420 

4.429 

5.584 
7.042 

1.  006 

i.is 

0.9265 

1.318 
1.045 
0.8288 

1.  211 

0.9606 
.7618 

36 

37 
38 

.1270 
.1131 
.1007 

.1126 
.089  31 
.070  83 

8.879 
1  1.  2O 
14.12 

0.7974 
.6324 
.5015 

•7347 
.5827 
.4621 

.6572 
.5212 
.4133 

.6041 
.4791 
•3799 

39 
40 

.08969 
.079  87 

.056  17 
.044  54 

17.80 
22.45 

•3977  . 
•3154 

.3664 
.2906 

.3278 
.2600 

.3013 
.2390 

*  Length  at  20°  C.  of  a  wire  whose  resistance  is  i  ohm  at  the  stated  temperatures. 
SMITHSONIAN  TABLES. 


METRIC.  TABLE  320  (continued). 

WIRE  TABLE,  STANDARD  ANNEALED  COPPER  (continued). 

American  Wire  Gage  (B.  &  S.).    Metric  Units  (continued). 


291 


Gage 

Diameter 

Ohms  per  Kilogram. 

Grams  per  Ohm. 

No. 

at  20°  C. 

o°C. 

20°  C. 

50°  C. 

20°  C. 

0000 

ooo 
oo 

11.68 
10.40 
9.266 

o.ooo  155  4 

.000  247  2 

.000  393  o 

o.ooo  168  7 

.000  268  2 

.000  426  5 

o.ooo  188  6 
.000  299  9 
.000  476  8 

5  928  ooo. 
3  728  ooo. 
2  344  ooo. 

o 
I 

2 

8.252 
7.348 
6-544 

.000  624  9 
.000  993  6 
.001  580 

.OOO  678  2 

.001  078 
.001  715 

.000  758  2 
.001  206 
.001  917 

i  474  ooo. 
927  300. 

583  200. 

3 
4 

5 

5.827 
5.189 
4.621 

.002  512 

.003  995 
.006  352 

.002  726 
•004  335 
.006  893 

.003  048 
.004  846 
.007  706 

366  800. 
230  700. 
145  ioo. 

6 

i 

4-ii5 
3.665 
3.264 

.010  10 

.016  06 
•025  53 

.010  96 

•017  43 
.027  71 

.012  25 

.019  48 
.03098 

91   230. 

57  380. 
36  080. 

9 
10 
ii 

2.906 
2.588 
2-305 

.04060 
.064  56 
.1026 

.044  06 
.070  07 
.1114 

.049  26 
•078  33 
.1245 

22  690. 
14  270. 
8976. 

12 

'3 
H 

2.053 
.828 
.628 

.1632 

•2595 
.4127 

.1771 

.2817 
•4479 

.1980 

•3  '49 

.5007 

56.45 

355°. 
2233. 

13 

17 

.450 
.291 
.150 

.6562 
1.043 
1.659 

.7122 
1.132 
1.801 

•796i 
1.266 
2.013 

1404. 
883.1 
5554 

18 
19 

20 

1.024 
0.9116 
.8118 

2.638 
4.194 
6.670 

2.863 
4.55J 
7.238 

3.201 
3.089 
8.092 

349-3 
219.7 
138.2 

21 

22 
23 

.7230 
.6438 
•5733 

10.60 
1  6.86 
26.81 

11.51 

18.30 
29.10 

12.87 
20.46 
32.53 

86.88 
54.64 
34.36 

24 

25 
26 

.5106 

•4547 
.4049 

42.63 
67.79 
107.8 

46.27 

73-57 
117.0 

51.73 
82.25 
130.8 

21.61 

13-59 
§.548 

27 
28 
29 

.3606 
.3211 
.2859 

171.4 
272.5 
433-3 

186.0 
295.8 
470-3 

207.9 
33°-6 

5257 

5'376 

3-38i 
2.126 

3° 
3i 
32 

.2546 
.2268 
.2019 

689.0 
1096. 
1742. 

747.8 
1189. 
1891. 

836.0 
1329. 
2114. 

1-337 
0.8410 
.5289 

33 
34 

35 

.1798 
.1601 
.1426 

2770. 
4404. 
7003. 

3006. 
4780. 
7601. 

336i. 

£344. 
8497. 

.3326 
.2092 
.1316 

36 
37 

38 

.1270 
.1131 
.1007 

11140. 
17710. 
28150. 

12090. 
19220. 
30560. 

I35JO. 
21480. 
34160. 

.082  74 
.052  04 
•032  73 

39 

40 

.08969 
.079  87 

44770. 
71180. 

48590. 
77260. 

543!0. 
86360. 

.020  58 
.012  94 

SMITHSONIAN  TABLES. 


292 


TABLE  321  .-ALUMINUM  WIRE  TABLE. 

Hard-Drawn  Aluminum  Wire  at  20°  C.  (or,  68°  P.). 
American  Wire  Gage  (B.  &  S.).    English  Units. 


ENGLISH. 


Gage 
No. 

Diameter 
in  Mils. 

Cross  Section. 

Ohms 
per 
looo  t  eet. 

Pounds 
per 
looo  Feet. 

Pounds 
per  Ohm. 

Feet 
per  Ohm. 

Circular 

Mils. 

Square 
Inches. 

0000 

460. 

212  OOO. 

0.166 

0.0804 

I95. 

2420. 

12  400. 

OOO 

410. 

1  68  ooo. 

.132 

.IOI 

154- 

1520. 

9860. 

OO 

365. 

133  ooo. 

.105 

.128 

122. 

957. 

7820. 

0 

325. 

1  06  ooo. 

.0829 

.161 

97-0 

602. 

6200. 

I 

289. 

83  700. 

.0657 

.203 

76.9 

379- 

4920. 

2 

258. 

66  400. 

•0521 

.256 

61.0 

238. 

3900. 

3 
4 

229. 
204. 

52  600. 
41  700. 

.0413 
.0328 

.408 

48.4 
38-4 

150. 
94.2 

3090. 
2450. 

5 

182. 

33  ioo. 

.0260 

•514 

304 

59-2 

1950. 

6 

162. 

26  300. 

.0206 

.648 

24.1 

37-2 

1540. 

7 

144. 

20  800. 

.0164 

.817 

19.1 

23-4 

1220. 

8 

128. 

1  6  500. 

.0130 

1.03 

15.2 

14.7 

970. 

9 

114. 

13  ioo. 

.0103 

1.30 

12.0 

9.26 

770. 

10 

IO2. 

10400. 

.008  15 

1.64 

9-55 

5.83 

610. 

ii 

9I. 

8230. 

.00647 

2.07 

7-57 

3.66 

484. 

12 

81. 

6530- 

•005  I3 

2.61 

6.00 

2.30 

384- 

13 

72. 

5180. 

.004  07 

3-29 

4.76 

1-45 

3°4- 

14 

64. 

4110. 

.003  23 

4.14 

3.78 

0.911 

241. 

'5 

57. 

3260. 

.OO2  56 

5.22 

2-99 

•573 

191. 

16 

2580. 

.002  03 

6.59 

2-37 

.360 

152. 

17 

45- 

2050. 

.001  61 

8.31 

1.88 

.227 

120. 

18 

40. 

1620. 

.001  28 

10.5 

1.49 

•143 

95-5 

19 

36. 

1290. 

.001  01 

13.2 

1.18 

.0897 

75-7 

20 

32- 

IO2O. 

.000  802 

16.7 

0-939 

.0564 

60.0 

21 

28.5 

810. 

.000  636 

21.0 

•745 

•0355 

47.6 

22 

25-3 

642. 

.000  505 

26.5 

•591 

.0223 

37-8 

23 

22.6 

509- 

.000  400 

33-4 

.468 

.0140 

29.9 

24 

2O.  I 

404. 

.000  317 

42.1 

•371 

.008  82 

2^-7 

25 

17.9 

320. 

.000  252 

53.1 

.295 

•005  55 

18.8 

26 

15-9 

254- 

.OOO  2OO 

67.0 

•234 

.003  49 

14.9 

27 

14.2 

202. 

.000  158 

84.4 

.185 

.002  19 

11.8 

28 

12.6 

160. 

.000  126 

106. 

.147 

.001  38 

9-39 

29 

"•3 

127. 

.000  099  5 

134- 

.117 

.000868 

7-45 

30 

1  0.0 

IOI. 

.000  078  9 

169. 

.0924 

.000  546 

5-91 

31 
32 

8.9 

8.0 

79-7 
63.2 

.000  062  6 
.000  049  6 

213. 
269. 

•0733 
.0581 

.000343 

.000  2l6 

4.68 
3-72 

33 

7.1 

50.1 

.000  039  4 

339- 

.0461 

.000  136 

2-95 

34 

6-3 

39-8 

.OOO  031   2 

428. 

•0365 

.000  085  4 

2-34 

35 

5-6 

3:-5 

.000  024  8 

540. 

.0290 

.000  053  7 

1.85 

36 
37 

4-5 

25.0 
19.8 

.000  019  6 
.000  015  6 

681. 
858. 

.0230 
.0182 

.000  033  8 

.000  021  2 

1.47 
1.17 

38 

4.0 

15.7 

.000012  3 

1080. 

.0145 

.000  013  4 

0.924 

39 

3-5 

12.5 

.000  009  79 

1360. 

.0115 

.000  008  40 

•733 

40 

9-9 

.000  007  77 

1720. 

.0091 

.000  005  28 

.58. 

SMITHSONIAN  TABLES. 


METRIC. 


TABLE  322. -ALUMINUM  WIRE  TABLE. 

Hard-Drawn  Aluminum  Wire  at  20°  0. 
American  Wire  Gage  (B.  &  S.)    Metric  Units. 


293 


Gage 
No. 

Diameter 
in  mm. 

Cross  Section 
in  mm.3 

Ohms  per 
Kilometer. 

Kilograms  pe 
Kilometer. 

Grams  per 
Ohm. 

Ohms  per 
Meter. 

0000 

II.7 

I07. 

0.264 

289. 

I    100  000. 

3790. 

000 

10.4. 

85.0 

•333 

230. 

690  ooo. 

3010. 

00 

9-3 

67.4 

.419 

182. 

434  ooo. 

2380. 

o 

8-3 

53-5 

.529 

144. 

273  ooo. 

1890. 

I 

7-3 

42.4 

.667 

114. 

172  ooo. 

1500. 

2 

6.5 

33-6 

.841 

90.8 

108  ooo. 

1190. 

3 

5.8 

26.7 

i.  06 

72.0 

67  900. 

943- 

4 

5-2 

21.2 

i-34 

57-1 

42  700. 

748. 

5 

4.6 

1  6.8 

1.69 

45-3 

26  900. 

593- 

6 

4.1 

13-3 

2.17 

35-9 

1  6  900. 

470. 

7 

3-7 

10.5 

2.68 

10  600. 

373- 

8 

3-3 

8.37 

3.38 

22.6 

6680. 

+Jf  O 

296. 

9 

2.91 

6.63 

4.26 

17.9 

4200. 

235- 

10 

2.59 

5.26 

5.38 

14.2 

2640. 

1  86. 

ii 

2.30 

4.17 

6.78 

1660. 

148. 

12 

2.05 

3-3i 

8-55 

8.93 

1050. 

117. 

13 

1.83 

2.62 

10.8 

7.0§ 

657. 

92.8 

14 

1.63 

2.08 

13-6 

5.62 

413- 

73-6 

I5 

i.45 

1.65 

17.1 

4.46 

260. 

584 

16 

1.29 

21.6 

3-53 

164. 

46.3 

17 

"•*5 

1.04 

27.3 

2.80 

103. 

36.7 

10 

1.02 

0.823 

344 

2.22 

64.7 

29.1 

'9 

20 

0.91 
.81 

.653 
48 

43-3 
54-6 

I.76 
1.40 

40.7 
.25.6 

23.1 
18.3 

21 

.72 

.411 

68.9 

I.  II 

16.1 

14-5 

22 

.64 

.326 

86.9 

0.879 

10.  1 

23 

•57 

.258 

no. 

.697 

6.36 

9-13 

24 

•45 

.205 
.162 

138. 
174. 

•553 
438 

4.00 

2.52 

7.24 

5-74 

26 

.40 

.129 

220. 

.348 

1.58 

4-55 

3 

•36 
•32 

.102 
.O8l0 

277. 

349- 

.276 
.219 

°-995 
.626 

3-6i 
2.86 

29 

.29 

.0642 

440. 

•J73 

•394 

2.27 

30 

•25 

.0509 

555- 

.138 

.248 

1.80 

3i 

.227 

.0404 

700. 

•I09 

.156 

143 

32 

.202 

.0320 

883. 

.0865 

.0979 

1-13 

33 

.ISO 

.0254 

1  1  10. 

.0686 

.0616 

0.899 

34 

.160 

.O2OI 

1400. 

•0544 

.0387 

.712 

35 

•143 

.0160 

1770. 

.0431 

.0244 

.565 

36 

.127 

.0127 

2230. 

.0342 

•0153 

448 

•"3 
.101 

.OIOO 
.0080 

2820. 
3550- 

.0271 
.0215 

.00963 
.00606 

•355 
.282 

39 

.090 

.0063 

4480. 

.0171 

.003  8  1 

.223 

40 

.080 

.OO5O 

5640. 

•0135 

.002  40 

.177 

SMITHSONIAN   TABLES. 


2Q4  TABLES  323,  324. 

DIELECTRIC   STRENGTH. 

TABLE  323.  -  Steady  Potential  Difference  in  Volts  required  to  produce  a  Spark  in  Air  with  Ball  Electrodes. 


Spark 
length, 
cm. 

/f  =  0. 

Points. 

R  =  0.25 
cm. 

R  =  0.5 
cm. 

R  —  i  cm. 

R  =  2  cm. 

R  =  3  cm. 

.ff  =  00. 

Plates. 

O.O2 

_ 

_ 

1560 

J53° 

0.04 

— 

— 

2460 

2430 

2340 

0.06 

_ 

— 

33°° 

3240 

3060 

0.08 

— 

— 

4050 

3990 

3810 

O.I 

O.2 

3720 
4680 

5010 
8610 

4740 
8490 

4560 
8490 

4560 
8370 

4500 
7770 

4350 
7590 

0-3 

5310 

11140 

11460 

11340 

11190 

10560 

10650 

0.4 
0-5 

5970 
6300 

14040 
15990 

I43IO 
16950 

14340 
17220 

14250 
16650 

13140 
16470 

13560 
16320 

o.o 

6840 

17130 

19740 

20070 

20070 

19380 

I9IIO 

0.8 

8070 

18960 

23790 

24780 

25830 

26220 

24960 

I.O 

8670 

20670 

26190 

27810 

29850 

32760 

30840 

J-S 

9960 

22770 

29970 

37260 

2.O 

IOI40 

24570 

33060 

45480 

3-o 

11250 

28380 

4.0 

I22IO 

29580 

5-o 

13050 

Based  on" the  results  of  Bailie,  Bichat-Blondot,  Freyburg,  Liebig,  Macfarlane,  Orgler,  Paschen,  Quincke,  de  la  Rue, 
Wolff.  For  spark  lengths  from  i  to  200  wave-lengths  of  sodium  light,  see  Earhart,  Phys.  Rev.  15,  p.  163;  Hobbs, 
Phil.  Mag.  10,  p.  607,  1905. 


TABLE  324.  —  Alternating  Current  Potentials  required  to  produce  a  Spark  in  Air  with  various  Bail  Elec- 
trodes. 

The  potentials  given  are  the  maxima  of  the  alternating  waves  used.     Frequency,  33  cycles  per 

second. 


Spark  length. 
cm. 

R  =  i  cm. 

R  =  1.92 

*-, 

.-,, 

,-„ 

,-„ 

0.08 

3770 

.10 

4400 

4380 

4330 

4290 

4245 

4230 

•15 

5990 

5940 

5830 

5790 

5800 

578o 

.20 

7510 

7440 

7340 

7250 

7320 

733° 

•25 

9045 

8970 

8850 

8710 

8760 

8760 

0.30 

10480 

10400 

10270 

10130 

10180 

10150 

•35 

11980 

11890 

11670 

11570 

11610 

11590 

.40 

13360 

13300 

13100 

12930 

12980 

12970 

•45 

•50 

14770 
16140 

14700 
16070 

14400 
15890 

14290 

15640 

14330 
15690 

14320 
15690 

0.6 

18700 

18730 

l855Q 

18300 

l835° 

18400 

•7 

2135° 

21380 

21140 

20980 

20990 

2IOOO 

.8 

23820 

24070 

23740 

23490 

23540 

23550 

0.9 

26190 

26640 

26400 

26130 

26110 

26090 

I.O 

28380 

29170 

28950 

28770 

28680 

28610 

1.2 

32400 

34100 

33790 

33660 

33640 

33620 

'1 

35850 

38850 

38850 

38580 

38620 

38580 

1.6 

38750 

43400 

43570 

43250 

43520 

1.8 

40900 

— 

48300 

479oo 

2.0 

42950 

52400 

SMITHSONIAN  TABLES. 


Based  upon  the  results  of  Kawalski,  Phil.  Mag.  18,  p.  699,  1909. 


TABLES  325,  326.  295 

DIELECTRIC  STRENGTH. 

TABLE  325.  —  Potential  Necessary  to  produce  a  Spark  in  Air  between  more  widely  Separated  Electrodes. 


a 

1 

Steady  potentials. 

fj 

6 

Steady  potentials. 

<  a 

0 

^  ^ 

JS 

JZ 

£ 

w> 

<2   3 

Ball  electrodes. 

Cup  electrodes. 

I 

Ball  electrodes. 

M 

c  u 

•S  £J, 

t 

13 

Projection. 

M 

E,s 

S. 

18 

R=i  cm. 

R-=2.5cm. 

£ 

•3  S 

R=i  cm. 

R=2.scm. 

4.5  mm. 

i.  5  mm. 

o-3 

_ 

_ 

_ 

_ 

II280 

6.0 

61000 

_ 

86830 

- 

17610 

17620 

- 

17420 

7.0 

- 

52000 

0.7 

I.O 

12000 

30240 

23050 
31390 

31400 

22950 
31260 

8.0 

IO.O 

67000 
73000 

52400 
74300 

90200 
91930 

1.2 

- 

33800 

36810 

- 

36700 

12.0 

82600 

- 

93300 

2.0 

2-5 

3-o 

29200 
40000 

37930 
42320 
45000 
46710 

44310 
56000 
65180 
71200 

56500 
80400 

445  10 
56530 
68720 
81140 

14.0 

15.0 

16.0 

20.0 

92000 

IOIOOO 

119000 

- 

94400 
94700 
IOIOOO 

3-5 

— 

— 

75300 

— 

92400 

25.0 

140600 

4.0 

48500 

49100 

78600 

IOI700 

103800 

30.0 

165700 

4-5 

— 

— 

81540 

— 

114600 

35-O 

190900 

56500 

50310 

83800 

- 

126500 

5-5 

— 

— 

— 

— 

135700 

-.* 

This  table  for  longer  spark  lengths  contains  the  results  of  Voege,  Ann.  der  Phys.  14,  1904,  using  alternating  current 
and  "dull  point"  electrodes,  and  the  results  with  steady  potential  found  in  the  recent  very  careful  work  of  C.  Milt 
!  ler,  Ann.  d.  Phys.  28,  p.  585,  1909. 

The  specially  constructed  elec- 
trodes for  the  columns  headed 
"  cup  electrodes  "  had  the  form  of 
a  projecting  knob  3  cm.  in  diame- 
ter and  having  a  height  of  4.5  mm. 
and  1.5  mm.  respectively,  attached 
to  the  plane  face  of  the  electrodes. 
These  electrodes  give  a  very  satis- 
factory linear  relation  between  the  ,  i 
spark  lengths  and  the  voltage 
throughout  the  range  studied. 


TABLE  326. -Effect  of  the  Pressure  of  the  Gas  on  the  Dielectric  Strength. 
Voltages  are  given  for  different  spark  lengths  /. 


Pressure, 
cm.  Hg. 

£=0.04 

/=o.o6 

/=o.o8 

/=O.IO 

/=0.20 

l=o  30 

£=0.40 

7=0.50 

2 

_ 

_ 

_ 

744 

939 

IIIO 

1266 

4 

„ 

483 

567 

648 

1015 

1350 

1645 

1915 

6 

„ 

582 

690 

795 

1290 

1740 

2140 

2505 

10 

- 

771 

933 

1090 

1840 

2450 

3015 

3580 

15 

_ 

1060 

1280 

1490 

2460 

3300 

4080 

4850 

'  25 
35 
45 

IIIO 

1375 
1640 

1420 
1820 
2150 

1725 

222O 
2660 

2040 
2615 
3120 

35°° 
4505 
5475 

4800 
6270 
7650 

6000 

7870 

9620 

7120 

9340 

11420 

55 

1820 

2420 

3025 

3610 

6375 

8950 

11290 

13455 

65 
75 

2040 
2255 

2720 
3035 

3400 
3805 

4060 
4565 

7245 
8200 

I02IO 
II570 

12950 

14650 

15470 
17450 

This  table  is  based  upon  the  results  of  Orgler,  1899.    See  this  paper  for  work  on  other  gases  (or  Landolt-B3rnstein- 

Fo^long'sp'ark  lengths  in  various  gases  see  Voege,  Electrotechn.  Z.  28,  1907.    For  dielectric  strength  of  air  and  CO8 
in  cylindrical  air  condensers,  see  Wien,  Ann.  d.  Phys.  29,  p.  679,  1909. 

SMITHSONIAN  TABLES. 


296  TABLES  327,  328. 

DIELECTRIC  STRENGTH. 

TABLE  327.  —  Dielectric  Strength  of  Materials. 
Potential  necessary  for  puncture  expressed  in  kilovolts  per  centimeter  thickness  of  the  dielectric. 


Substance. 

Kilovolts 
per  cm 

Substance. 

Kilovolts 
per  cm. 

Substance. 

Kilovolts 
per  cm. 

Ebonite    .... 
Empire  cloth    .     . 
paper  .     . 
Fibre 

300-1100 
80-300 

45° 
2O 

Oils  :                           Thickness 
Castor                 0.2  mm. 

I.O      " 

Cottonseed 

190 
130 

7O 

Papers  : 
Beeswaxed  .     . 
Blotting   .     .     . 
Manilla 

770 
ISO 

Fuller  board      .     . 
Glass 

200-300 

too-  i  coo 

Lard                    0.2     " 

"                                I.O      " 

140 

4.O 

Paraffined     .     . 
Varnished 

Z5 
500 

IOO—  2  CO 

Granite  (fused) 
Guttapercha  .     .     . 
Impregnated  jute  . 
Leatheroid    .    .     . 
Linen,  varnished   . 

90 

80-200 

20 
30-60 
I  OO—2OO 

Linseed,  raw       0.2     " 

"              "            I.O      " 

"        boiled  0.2     " 

"                 "          I.O      " 

Lubricating  .... 

I85 
90 

CO 

Paraffine  : 
Melted     .     .     . 
Melt  point. 
Solid          43° 
"               47° 

75 

350 
400 

Liquid  air      ... 
Mica  :           Thickness. 
Madras  o.i  mm. 

1.0      " 

Bengal    o.i     " 

"           1.0      " 

Canada  o.i     " 

"           I.O      " 

South  America  . 
Micanite    .    .    . 

40-90 

I600 
300 
22OO 
700 
1500 
500 
1500 
400 

Neatsfoot            0.2     " 

I.O      " 

Olive                   0.2     " 

1.0      " 

Paraffin               0.2     ' 

I.O      ' 

Sperm,  mineral  0.2    * 

I.O      ' 

"       natural  0.2     * 

I.O      ' 

Turpentine          0.2     ' 

"                        I.O      ' 

200 
90 
IJO 

75 

2I5 
1  60 

180 
85 
195 
90 
160 
no 

52° 

70° 
Presspaper  .     .     . 
Rubber   .... 
Vaseline  .... 
Thickness. 
Xylol        0.2  mm. 

1.0      " 

230 
45° 
45-75 
160-500 
90-130 

140 

80 

TABLE  328.  —Potentials  in  Volts  to  Produce  a  Spark  In  Kerosene. 


Electrodes  Balls  of  Diam.  d. 

Spark  length. 

mm. 

0.5  cm. 

i  cm. 

2  cm. 

3  cm. 

O.I 

3800 

3400 

2750 

2200 

.2 

7500 

6450 

4800 

3500 

•3 

10250 

945° 

745° 

4600 

•4 

11750 

10750 

9100 

5600 

i 

13050 
14000 

12400 
'355° 

1  1000 

12250 

6900 
8250 

.8 

15500 

15100 

13850 

10450 

I.O 

16750 

16400 

15250 

12350 

Determinations  of  the  dielectric  strength  of  the  same  substance  by  different  observers  do  not  agree  well.  For  a  dis- 
cussion of  the  sources  of  error  see  Mos'cicki,  Electrotechn.  Z.  25,  1904. 

For  more  detailed  information  on  the  dependence  of  the  sparking  distance  in  oils  as  a  function  of  the  nature  of  the 
electrodes,  see  Edmondson,  Phys.  Review  6,  p.  65,  1898. 

SMITHSONIAN  TABLES. 


TABLES  329,  330. 

TABLE  329.  — Electrical  Resistance  of  Straight  Wires  with  Alternating  Currents 
of  Different  Frequencies. 


297 


This  table  gives  the  ratio  of  the  resistance  of  straight  copper  wires  with  alternating  currents  of 
different  frequencies  to  the  value  of  the  resistance  with  direct  currents. 


Diameter  of 
wire  in 
millimeters. 

Frequency  «  = 

60 

100 

IOOO 

10  000 

100  000 

IOOO  000 

0.05 
O.I 

- 

- 

- 

- 

*I.OOI 

*I.OOI 

1.  008 

0.25 
0-5 

— 

— 

— 

*I.OOI 

1.003 
1.047 

1.247 
2.240 

I.O 

2 

: 

— 

1.  001 

I.OOS 
1.  120 

1-503 
2.756 

4.19 

3 

_ 

- 

1.  006 

1-437 

4.00 

4 

. 

- 

1.  02  1 

1.842 

5 

- 

*I.OOI 

1.047 

2.240 

7-5 

1.  001 

I.OO2 

1.  210 

3.22 

10 

15 

1.003 

I.OIO 

1.008 
1.038 

I-503 
2.136 

4.19 

20 
25 

1.044 
1.105 

1.  1  20 

1.247 

2.756 
3.38 

40 

1.474 

1.842 

100 

3-3  l 

4.19 

Values  between  i.ooo  and  i.ooi  are  indicated  by  *i.ooi. 

The  change  of  resistance  of  wires  other  than  copper  (iron  wires  excepted)  may  be  calculated 
from  the  above  table,  making  use  of  the  fact  that  the  change  of  resistance  is  a  function  of  the 
argument  /  =  2irrf2n\  where  r  =  radius  of  cross-section,  «  =  frequency,  X  =  conductivity. 

If  a  given  wire  be  wound  into  a  solenoid,  its  resistance,  at  a  given  frequency,  will  be  greater  than 
the  values  in  the  table,  which  apply  to  straight  wires  only.  The  resistance  in  this  case  is  a  com- 
plicated function  of  the  pitch  and  radius  of  the  winding,  the  frequency,  and  the  diameter  of  the 
wire,  and  is  found  by  experiment  to  be  sometimes  as  much  as  twice  the  value  for  a  straight  wire. 


TABLE  330.  — Electrical  Resistance  for  High  Frequencies. 

For  which  the  high  frequency  resistance  will  be  less  than  i  per  cent  greater  than 
direct  current  resistance. 


Constantan  or  Advance 

Wave-length. 

Wire. 

Manganin 
Diameter. 

Platinum 
Diameter. 

Copper 
Diameter. 

Diameter. 

Maximum 
Current. 

m. 

mm. 

amp. 

mm. 

mm. 

mm. 

100 

0.30 

3-5 

0.29 

0.13 

0.006 

200 

0.46 

4-5 

0.40 

0.29 

0.045 

300 

0.57 

5-5 

0.50 

0.27 

0.09 

400 

0.66 

7.0 

O.6o 

0.30 

O.IO 

600 

0.83 

8.0 

0-75 

0.37 

0.15 

800 

0.98 

IO.O 

0.88 

0.42 

O.2O 

IOOO 

1.  10 

"•5 

0.99 

0.50 

O.2I 

I2OO 

1.20 

12.5 

I.IO 

o-57 

O.22 

1500 

1.30 

14.0 

1.  21 

0.63 

O.26 

2000 

1.52 

17.0 

1.38 

0-73 

0.30 

3000 

' 

24.0 

,.62 

0.80 

0-33 

Advance  wire  is  practically  identical  electrically  with  constantan,  while  for  high  resistance  Ger- 
man silver  the  values  are  nearly  the  same  as  for  manganin.  The  column  of  the  table  under  maxi- 
mum current  gives  the  approximate  current  which  may  be  carried  by  the  various  sizes  without 
undue  heating.     The  current  capacity  of  the  manganin  is  very  nearly  the  same. 
From  Austin,  Jour.  Wash.  Acad.  of  Sci.  2,  p.  190,  1911. 


SMITHSONIAN  TABLES. 


298  TABLE  331. 

WIRELESS  TELEGRAPHY. 

Wave-Length  in  Meters,  Frequency  in  periods  per  second,  and  Oscillation  Constant  LC  in 
Microhenries  and  Microfarads. 


Meters. 

n 

LC 

Meters. 

n 

LC 

Meters. 

n 

LC 

IOO 

3,000,000 

0.00282 

600 

5OO,OOO 

O.IOI 

I  IOO 

272,700 

0.341 

no 

2,727,000 

0.00341 

610 

491,800 

0.105 

IIIO 

270,300 

0-347 

120 

2,500,000 

0.00405 

620 

485,500 

0.1  08 

1120 

267,900 

°-353 

130 

2,308,000 

0.00476 

630 

476,200 

O.III 

II3O 

265,500 

o-359 

1  140 

2,I43,OOO 

0.00552 

640 

468,700 

0.115 

II4O 

263,100 

0.366 

!5° 

2,OOO,OOO 

0.00633 

650 

461,500 

0.119 

1150 

260,900 

0.372 

!  160 

1,875,000 

0.00721 

660 

454,500 

0.123 

1160 

258,600 

o-379 

170 

1,765,000 

0.00813 

670 

447,800 

0.126 

1170 

256,400 

0-385 

180 

I,667,OOO 

0.00912 

680 

441,200 

0.130 

1180 

254,200 

0.392 

190 

1,579,000 

0.01016 

690 

434,800 

0.134 

1190 

252,100 

0-399 

200 

1,500,000 

0.0113 

700 

428,600 

0.138 

1200 

250,000 

0.405 

210 

1,429,000 

0.0124 

710 

422,500 

0.142 

I2IO 

247,900 

0.412 

22O 

1,364,000 

0.0136 

720 

416,700 

0.146 

I22O 

245,900 

0.419 

230 

1,304,000 

0.0149 

730 

411,000 

0.150 

1230 

243,900 

0.426 

240 

1,250,000 

0.0162 

740 

405,400 

0.154 

I24O 

241,900 

0-433 

250 

1,200,000 

0.0176 

75° 

400,000 

0.158 

1250 

240,000 

0.440 

260 

I,I54,OOO 

0.0190 

760 

394,700 

0.163 

1260 

238,100 

0.447 

270 

I,  III,OOO 

0.0205 

770 

389,600 

0.167 

1270 

236,200 

0-454 

280 

1,071,000 

0.0221 

780 

384,600 

0.171 

1280 

234,400 

0.461 

20X) 

1,034,000  ^ 

0.0237 

790 

379,800 

0.176 

I20X) 

232,600 

0.468 

300 

1,000,000 

0.0253 

800 

375,ooo 

0.180 

1300 

230,800 

0.476 

3IO 

967,700 

0.0270 

810 

370,400 

0.185 

I3IO 

229,000 

0.483 

320 

937,500 

0.0288 

820 

365,900 

0.189 

1320 

227,300 

0.490 

330 

909,100 

0.0307 

830 

361,400 

0.194 

1330 

225,600 

0.498 

340 

882,400 

0.0326 

840 

357,ioo 

0.199 

1340 

223,900 

0-505 

350 

859,100 

0.0345 

850 

352,900 

0.203 

'35° 

222,2OO 

360 

833,300 

0.0365 

.860 

348,800 

0.208 

1360 

220,600 

0.521 

370 

810,800 

0.0385 

870 

344,8oo 

0.213 

1370 

218,900 

0.529 

380 

789,500 

0.0406 

880 

340,900 

0.2  18 

1380 

217,400 

390 

769,200 

0.0428 

890 

337,ioo 

0.223 

1390 

215,800 

0-544 

400 

750,000 

0.0450 

900 

333,300 

0.228 

1400 

214,300 

0-552 

410 

731,700 

0.0473 

910 

329,700 

0.233 

1410 

2I2,8OO 

0-559 

420 

714,300 

0.0496 

920 

326,100 

0.238 

1420 

211,300 

0.567 

430 

697,700 

0.0520 

930 

322,600 

0.243 

143° 

209,800 

0.576 

440 

681,800 

0.0545 

940 

319,100 

0.249 

1440 

208,300 

0.584 

45° 
460 

666,700 

652,200 

0.0570 
0.0596 

950 
960 

315,900 
312,500 

0.254 

0.259 

145° 
1460 

206,900 
205,500 

0.592 
0.600 

470 

638,300 

0.0622 

970 

309,300 

0.265 

1470 

204,100 

0.608 

480 

625,000 

0.0649 

980 

306,100 

0.270 

1480 

202,700 

0.617 

490 

612,200 

0.0676 

990 

303,000 

0.276 

1490 

201,300 

0.625 

500 

600,000 

0.0704 

IOOO 

300,000 

0.281 

1500 

200,000 

0-633 

588,200 

0.0732 

IOIO 

297,000 

0.287 

1510 

198,700 

0.642 

520 

576,900 

0.0761 

1020 

294,100 

0.293 

1520 

197,400 

0.650 

530 

566,000 

0.0791 

1030 

291,300 

0.299 

1530 

196,100 

0.659 

540 

555,600 

0.0821 

IO4O 

288,400 

0-305 

1540 

I94,8OO 

0.668 

550 
560 

545,500 
535,700 

0.0851 

0.0883 

1050 
1060 

285,700 
283,600 

0.310 
0.316 

1550 
1560 

193,600 
192,300 

0.676 
0.685 

57° 

526,300 

0.0915 

1070 

280,400 

0.322 

1570 

I9I,IOO 

0.694 

580 

517,200 

0.0947 

I080 

277,800 

0.328 

1580 

189,900 

0-703 

590 

508,500 

0.0981 

1090 

275,200 

0.335 

1590 

l88,7OO 

0.712 

Prepared  by  Greenleaf  W.  Picard;  copyright  by  Wireless  Specialty  Apparatus  Company,  New  York.   Computed  on 
basis  of  300,000  kilometers  per  second  for  the  velocity  of  propagation  of  electromagnetic  waves. 

SMITHSONIAN  TABLES. 


TABLE  331  (concluded). 
WIRELESS  TELEGRAPHY. 

Wave-Length,  Frequency  and  Oscillation  Constant. 


299 


Meters. 

u 

LC 

Meters. 

n 

LC 

Meters. 

n 

LC 

1600 

187,500 

0.721 

2000 

150,000 

I-I3 

6OOO 

50,000 

IO.I 

1610 

186,300 

0.730 

2IOO 

142,900 

1.24 

6lOO 

49,l8o 

10.5 

1620 

185,200 

0-739 

22OO 

136,400 

1.36 

6200 

48,550 

10.8 

I  1630 

184,100 

0.748 

2300 

130,400 

6300 

47,620 

u.  i 

1640 
1650 

182,900 

181,800 

°-757 
0.766 

2400 
2500 

125,000 
120,000 

5:76 

6400 
6500 

46,870 
46,150 

"•5 
11.9  | 

1660 

180,700 

0.776 

2600 

1  1  5,400 

1.90 

6600 

45,450 

12.3 

1670 

179,600 

0.785 

2700 

III,IOO 

2.05 

6700 

44»780 

12.6 

1680 

178,600 

0.794 

2800 

107,100 

2.21 

6800 

44,120 

13.0 

1690 

177,500 

0.804 

2900 

103,400 

2-37 

6900 

43-48o 

13-4 

1700 

176,500 

0.813 

3000 

100,000 

2-53 

7000 

42,860 

13.8 

1710 

175,400 

0.823 

3100 

96,770 

2.70 

7IOO 

42,250 

14.2 

1720 

174,400 

0-833 

3200 

93.75° 

2.88 

72OO 

41,670 

14.6 

1730 

173,400 

0.842 

3300 

90,910 

3-07 

7300 

41,100 

15.0 

1740 

172,400 

0.852 

3400 

88,240 

3-26 

7400 

40,540 

15.4 

!75o 
1760 

171,400 

170,500 

0.862 
0.872 

3500 
3600 

85,910 
83.330 

3-45 
3-65 

7500 
7600 

40,000 
39.470 

15.8 
16.3 

1770 
1780 
1790 

169,400 
168,500 
167,600 

0.882 
0.892 
0.902 

3700 
3800 
3900 

81,080 

78,950 
76,920 

4.06 
4.28 

7700 
7800 
7900 

38,960 
38,460 
37,98o 

16.7 
17.1 

17.6 

1800 

166,700 

0.912 

4OOO 

75,000 

4-50 

8000 

37,500 

1  8.0 

1810 

165,700 

0.923 

4100 

73»*7o 

4-73 

8lOO 

37,040 

18.5 

1820 

164,800 

o-933 

4200 

71,43° 

4-96 

8200 

36,590 

18.9 

1830 

163,900 

0.943 

4300 

69,770 

5.20 

8300 

36,140 

19.4 

1840 

163,000 

0-953 

4400 

68,180 

5-45 

8400 

35.7io 

19.9 

1850 
1860 

162,200 
161,300 

0.963 
0.974 

4500 
4600 

66,670 
65,220 

570 
5-96 

8500 
8600 

iSE 

20.3 

20.8 

1870 

160,400 

0.985 

4700 

63,830 

6.22 

8700 

34,480 

21.3 

1880 

159,600 

0-995 

4800 

62,500 

6.49 

8800 

34,090 

21.8 

1890 

158,700 

i.  006 

4900 

61,220 

6.76 

8900 

33,7io 

22.3 

1900 

157,900 

.016 

5000 

60,000 

7.04 

9000 

33,330 

22.8 

1910 

157,100 

.026 

5100 

58,820 

7-32 

9100 

32,970 

23-3 

1920 

156,300 

-037 

52OO 

57»690 

7.6l 

9200 

32,610 

23.8 

1930 

155,400 

.048 

53°° 

56,600 

7.91 

9300 

32,260 

24-3 

1940 

154,600 

.059 

5400 

55,56o 

8.21 

9400 

31.910 

24.9 

1950 

153,800 

.070 

55°0 

54,550 

Si1 

9500 

3!.59o 

25-4  ! 

1960 

153,100 

.081 

5600 

53.570 

8.83 

9600 

3'»*S° 

25-9 

1970 

152,300 

.092 

5700 

52,630 

9-15 

9700 

30,930 

26.5 

1980 

iSM00 

.103 

5800 

51,720 

9-47 

9800 

30,610 

27.0 

1990 

1  50,800 

.114 

5900 

50,850 

Pi 

9900 

30,310 

27-6 

IOOOO 

30,000 

28.1 

SMITHSONIAN  TABLES. 


2OO  TABLE  332. 

WIRELESS  TELEGRAPHY. 

Radiation  Resistances  lor  Various  Wave-Lengths  and  Antenna  Heights. 

The  radiation  theory  of  Hertz  shows  that  the  radiated  energy  of  an  oscillator  may  be  repre- 
sented by  E  =  constant  (h2/A2)  I2,  where  h  is  the  length  of  the  oscillator,  A,  the  wave-length  and 
I  the  current  at  its  center.  For  a  flat-top  antenna  E  =  1600  (h2/  A2)  I2  watts ;  1600  h2/  A2  is  called 
the  radiation  resistance. 

(h  =  height  to  center  of  capacity  of  conducting  system.) 


Length  A 

40  Ft. 

60  Ft. 

80  Ft. 

too  Ft. 

120  Ft. 

i6oFt. 

200  Ft. 

300  Ft. 

450  Ft. 

600  Ft. 

1200  Ft. 

IN 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

ohm 

2OO 

6.0 

134 

24.0 

37-o 

S4-o 

95-0 

300 

2.7 

6.0 

10.6 

16.5 

23.8 

42.4 

400 
600 

0.66 

34 
1-5 

6.0 
2.7 

9-3 
4.1 

'34 
6.0 

23.8 

10.6 

I6.4 

374 

84.0 

149.0 

800 

o.37 

0.84 

2-3 

34 

6.0 

9.2 

21.0 

47.0 

84.0 

1000 
I2OO 
1500 

0.24 
0.17 

O.I  I 

o-54 
0-37 
0.24 

°3J 

0.42 

1.03 
0.66 

2.1 

o-95 

3-J 

2.6 

1-7 

6.0 

'3-5 
9-3 
6.0 

30.0 
21.0 
134 

37-o 
24.0 

215.0 
149-0 

95-o 

2000 
2500 

0.13 

0.24 
0.15 

o-37 
0.24 

0-54 
0-34 

0.61 

0-95 

34 

2.2 

n 

134 

8.6 

54-0 
34-0 

3000 
4000 

O.I  I 

0.06 

0.17 
0.09 

0.24 
0.13 

0.42 
0.24 

0.66 
o.37 

0.84 

34 
1.9 

6.0 

34 

24.0 

5OOO 

0.24 

°-53 

i.  20 

2.2 

8.6 

6OOO 

0.16 

0.37 

0.84 

1.5 

6.0 

7000 

0.12 

0.27 

0.61 

I.I 

44 

Austin,  Jour.  Wash.  Acad.  of  Sci.  i,  p.  190,  1911. 


SMITHSONIAN  TABLES. 


v 


TABLE   333.  301 

INTERNATIONAL    ATOMIC   WEIGHTS.    ELECTROCHEMICAL 
EQUIVALENTS. 

The  International  Atomic  Weights  are  quoted  from  the  report  of  the  International  Committee 
on  Atomic  Weights  (Journal  American  Chemical  Society,  35,  p.  1807,  1913). 

The  Electrochemical  equivalent  of  Silver  is  0.0011180  gram,  sec."1  amp."1.  (See  definition  of 
International  Ampere,  p.  xxxiii.)  The  electrochemical  equivalent  for  any  other  element  is 

atomic  weight  element      .0011180 

: ^— : r. X ; gm.  S6C."1  amp."1. 

atomic  weight  silver        valency 

The  equivalent  for  iodine  has  been  recently  (1913)  determined  at  the  Bureau  of  Standards  as 
1.3150.  The  valencies  given  are  only  those  commonly  shown  by  the  elements. 


Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =  1  6. 

Valency. 

Substance. 

Symbol. 

Relative 
atomic  wt. 
Oxygen  =16. 

Valency. 

Aluminum 

Al 

27.1 

3. 

Mercury 

Hg 

2OO.6 

I,  2. 

Antimony 
Argon 

Sb 
A 

120.2 
39.88 

3,5- 
o. 

Molybdenum 
Neodymium 

Mo 

Nd 

96.0 
144-3 

4,6. 
3- 

Arsenic 

As 

74.96 

3>  5« 

Neon 

Ne 

20.2 

0. 

Barium     ' 

Ba 

137.37 

2. 

Nickel 

Ni 

58.68 

2,3. 

[ation) 

Bismuth 

Bi 

208.0 

3»  5- 

Niton  (Raeman- 

Nt. 

222.4 

— 

Boron 
Bromine 

B 
Br 

II.O 

79.92 

3- 
i. 

Nitrogen 
Osmium 

N 
Os 

14.01 
190.9 

ti 

Cadmium 
Caesium 

Cd 
Cs 

112.40 
I32.8I 

2. 
I. 

Oxygen 
Palladium 

0 

Pd 

16.00 
106.7 

2. 
2,4. 

Calcium 

Ca 

40.07 

2. 

Phosphorus 

P 

31.04 

3>5- 

Carbon 

C 

12.00 

4- 

Platinum 

Pt 

195.2 

2,4. 

Cerium 

Ce 

140.25 

3>4- 

Potassium 

K 

39.10 

Chlorine 

Cl 

3S46 

i. 

Praseodymium 

Pr 

140.6 

3- 

Chromium 

Cr 

52.0 

2,  3,  6. 

Radium 

Ra 

226.4 

2. 

Cobalt 

Co 

58.97 

2,  3- 

Rhodium 

Rh 

102.9 

3- 

Columbium 

Cb 

93-  5 

5. 

Rubidium 

Rb 

85-45 

i. 

Copper 

Cu 

63-57 

1,2. 

Ruthenium 

Ru 

101.7 

6,8. 

Dysprosium 

Dy 

162.5 

3- 

Samarium 

Sa 

150.4 

3- 

Erbium 

Er 

167.7 

3- 

Scandium 

Sc 

44.1 

3- 

Europium 

Eu 

152.0 

3- 

Selenium 

Se 

79.2 

2,  4.  6. 

Fluorine 

F 

19.0 

Silicon 

Si 

28.3 

4- 

Gadolinium 

Gd 

J57-3 

3- 

Silver 

Ag 

107.88 

Gallium 

Ga 

69.9 

3. 

Sodium  , 

Na 

23.00 

i. 

Germanium 

Ge 

72.S 

4- 

Strontium 

Sr 

87.63 

2. 

Glucinum 

Gl 

9.1 

2. 

Sulphur 

S 

32.07 

2,  4>  6. 

Gold 

Au 

197.2 

r>  3- 

Tantalum 

Ta 

181.5 

5- 

Helium 

He 

3-99 

0. 

Tellurium 

Te 

127.5 

2,  4,  6. 

Holmium 

Ho 

163.5 

3. 

Terbium 

Tb 

159.2 

3- 

Hydrogen 

H 

1.008 

i. 

Thallium 

Tl 

204.0 

1.3- 

Thorium 

Th 

232.4 

4- 

Indium 

In 

114.8 

3. 

Iodine 

I 

126.92 

i. 

Thulium 

Tm 

168.5 

3- 

Indium 

Ir 

^S-1 

4. 

Tin 

Sn 

119.0 

2,4. 

Iron 

Fe 

55-84 

2,3. 

Titanium 

Ti 

48.1 

4- 

Krypton 

Kr 

82.92 

o. 

Tungsten 

W 

184.0 

6. 

Uranium 

U 

238.5 

4,6. 

Lanthanum 

La 

139.0 

3. 

Lead 

Pb 

207.10 

2,  4- 

Vanadium 

V 

51-0 

3,5- 

Lithium 

Li 

6-94 

I. 

Xenon 

Xe 

130.2 

o. 

Lutecium 

Lu 

174.0 

3. 

Ytterbium 

Yb 

173.0 

3- 

Magnesium 

Mg 

24.32 

2. 

Yttrium 

Yt 

89.0 

3- 

Manganese 

Mn 

54-93 

2,  3»    7« 

Zinc 

Zn 

65.37 

2. 

Zirconium 

Zr 

90.6 

4- 

SMITHSONIAN  TABLES. 


302  TABLES  334,  335. 

CONDUCTIVITY   OF   ELECTROLYTIC  SOLUTIONS. 

This  subject  has  occupied  the  attention  of  a  considerable  number  of  eminent  workers  in 
molecular  physics,  and  a  few  results  are  here  tabulated.  It  has  seemed  better  to  confine  the 
examples  to  the  work  of  one  experimenter,  and  the  tables  are  quoted  from  a  paper  by  F.  Kohl- 
rausch,*  who  has  been  one  of  the  most  reliable  and  successful  workers  in  this  field. 

The  study  of  electrolytic  conductivity,  especially  in  the  case  of  very  dilute  solutions,  has  fur- 
nished material  for  generalizations,  which  may  to  some  extent  help  in  the  formation  of  a  sound 
theory  of  the  mechanism  of  such  conduction.  If  the  solutions  are  made  such  that  per  unit 
volume  of  the  solvent  medium  there  are  contained  amounts  of  the  salt  proportional  to  its  electro- 
chemical equivalent,  some  simple  relations  become  apparent.  The  solutions  used  by  Kohlrausch 
were  therefore  made  by  taking  numbers  of  grams  of  the  pure  salts  proportional  to  their  elec- 
trochemical equivalent,  and  using  a  liter  of  water  as  the  standard  of  quantity  of  the  solvent.  Tak- 
ing the  electrochemical  equivalent  number  as  the  chemical  equivalent  or  atomic  weight  divided 
by  the  valence,  and  using  this  number  of  grams  to  the  liter  of  water,  we  get  what  is  called 
the  normal  or  gram  molecule  per  liter  solution.  In  the  table,  m  is  used  to  represent  the 
number  of  gram  molecules  to  the  liter  of  water  in  the  solution  for  which  the  conductivities 
are  tabulated.  The  conductivities  were  obtained  by  measuring  the  resistance  of  a  cell  filled  with 
the  solution  by  means  of  a  Wheatstone  bridge  alternating  current  and  telephone  arrangement. 
The  results  are  for  18°  C.,  and  relative  to  mercury  at  o°  C.,  the  cell  having  been  standardized  by 
filling  with  mercury  and  measuring  the  resistance.  They  are  supposed  to  be  accurate  to  within 
one  per  cent  of  the  true  value. 

The  tabular  numbers  were  obtained  from  the  measurements  in  the  following  manner  :  — 

Let  A"18  =  conductivity  of  the  solution  at  18°  C.  relative  to  mercury  at  o°  C. 

K*z  =  conductivity  of  the  solvent  water  at  18°  C.  relative  to  mercury  at  o°  C. 

Then  A"18  — K™%  =  krB  =  conductivity  of  the  electrolyte  in  the  solution  measured. 

-H-  =  fj.  =  conductivity  of  the  electrolyte  in  the  solution  per  molecule,  or  the  "  specific 
m 

molecular  conductivity." 

TABLE  334.  -Value  oi  *18  for  a  few  Electrolytes. 

This  short  table  illustrates  the  apparent  law  that  the  conductivity  in  very  dilute  solutions  is  proportional  to  the 

amount  of  salt  dissolved. 


in 

KC1 

NaCl 

AgN03 

KC2H3O2 

K2S04 

MgSO4 

0.00000  1 

1.216 

I.O24 

I.oSo 

0-939 

1-275 

1.056 

O.OOOO2 
O.OOOO6 

2.434 
7.272 

2.056 
6.162 

2.146 
6.462 

5.610 

2-532 
7.524 

2.104 
6.216 

0.000  1 

12.09 

IO.29 

10.78 

9-34 

12.49 

10.34 

TABLE  335.— Electro-Chemical  Equivalents  and  Normal  Solutions. 

The  following  table  of  the  electro-chemical  equivalent  numbers  and  the  densities  of  approximately  normal  solutions 
of  the  salts  quoted  in  Table  271  maybe  convenient.  They  represent  grams  per  cubic  centimeter  of  the  solution 
at  the  temperature  given. 


Salt  dissolved. 

Grams 
per  liter. 

m 

Temp. 
C. 

Density. 

S 

lit  dissolved. 

Grams 
per  liter. 

m 

Temp. 
C. 

Density. 

KC1    .    .    . 

74-59 

I.O 

15.2 

1-0457 

j 

-K2S04     . 

87.16 

I.O 

18.9 

1.0658 

NH4C1    .     . 
NaCl  .     .     . 

53-55 
58.50 

1.0009 
I.O 

18.6 
18.4 

1.0152 
1.0391 

] 

NaaSCU  . 
-Li2SO4     . 

71.09 
55-09 

1.0003 
1.0007 

18.6 
18.6 

1.  0002 
1.0445 

LiCl    .     .     . 

42.48 

I.O 

18.4 

I.O227 

i 

MgS04    . 

60.17 

I.OO23 

18.6 

1-0573 

£BaCl2    .     . 

104.0 

I.O 

1  8.6 

1.0888 

I 

ZnSO4     . 

80.58 

.O 

5-3 

1.0794 

£ZnCl2    .     . 

68.0 

I.OI2 

15.0 

1.0592 

i 

CuSO4     . 

79-9 

.001 

18.2 

1.0776 

KI.     .     .     . 

165.9 

I.O 

1  8.6 

1.1183 

K2C03     . 

69.17 

.0006 

18.3 

1.0576 

KN08     .    . 

101.17 

I.O 

18.6 

1.  060  1 

i 

-Na2CO8  . 

53-04 

.0 

17.9 

1.0517 

NaN03    .     . 

85.08 

I.O 

18.7 

1.0542 

] 

[COH    .     . 

56.27 

.0025 

18.8 

1.0477 

AgN03    •     • 
lBa(N08)a  . 
KC1O3     .     . 

169.9 
65.28 
61.29 

I.O 

o-5 
°-5 

18.3 

1.0367 

1 
1 
| 

-IC1      .     . 
1NO8  .     . 
-H2S04     . 

36-51 
63-13 
49-06 

.0041 
.0014 
.0006 

18.6 
18.6 
18.9 

1.0161 
1.0318 
1.0300 

KC2H3O2     . 

98.18 

1.0005 

1  8.6 

1.0467 

SMITHSONIAN  TABLES. 


*  "  Wied.  Ann."  vol.  26,  pp.  161-226,  1885. 


TABLE  336. 
SPECIFIC    MOLECULAR    CONDUCTIVITY  /x  :   MERCURY=1O". 


303 


Salt  dissolved. 

*=,o 

5 

3 

« 

OS 

O.I 

.05 

•03 

.01 

iK2S04   . 

_ 

_ 

_ 

_ 

672 

736 

897 

959 

1098 

KC1 

- 

— 

827 

919 

958 

1047 

1083 

1107 

"47 

KI  . 

— 

770 

900 

968 

1069 

IIO2 

1123 

1161 

NH4C1     . 

- 

752 

82S 

948 

I035 

1078 

IIOI 

1142 

KNO3      . 

— 

572 

752 

839 

983 

1037 

1067 

1122 

iBaC!2     . 

- 

- 

487 

658 

725 

86  1 

904 

939 

1006 

KC1O3     . 

- 

- 

- 

- 

799 

927 

(976) 

1006 

1053 

^Ba2N2Og 

—  • 

— 

— 

— 

53J 

755 

828 

(870) 

951 

|CuS04  . 

— 

— 

J50 

241 

288 

424 

479 

537 

675 

AgN03    .        .        . 

— 

351 

448 

635 

728 

886 

936 

1017 

^ZnSO4   . 

- 

82 

146 

249 

302 

43  i 

500 

556 

685 

^MgSO4  . 

- 

82 

151 

270 

330 

474 

532 

587 

ijNa2SO4 

— 

— 

— 

475 

559 

734 

784 

828 

906 

*ZnCl2     . 

60 

180 

280 

60  1 

768 

817 

851 

QJ    P 

NaCl        . 

- 

398 

528 

695 

757 

865 

897 

(920) 

962 

NaNO3    . 

_ 

_ 

430 

617 

694 

817 

855 

877 

907 

KC2H302 

30 

240 

381 

594 

671 

784 

820 

841 

879 

^•Na2CO3 

— 

254 

427 

510 

682 

751 

799 

899 

^H2SO4  .        .        . 

660 

1270 

1560 

1820 

1899 

2084 

2343 

2515 

2855 

C2H40     . 

o-5 

2.6 

5-2 

12 

«9 

43 

62 

79 

132 

HC1         ... 
HNO8     . 

600 
610 

1420 
1470 

2010 
2O7O 

2780 
2770 

3OI7 
2991 

3244 
3225 

3330 
3289 

3369 
3328 

3395 

iH3PO4  . 

148 

160 

170 

200 

250 

43° 

540 

620 

790 

KOH       . 

423 

990 

13*4 

I7l8 

1841 

1986 

2045 

2078 

2124 

NH3 

0-5 

2.4 

3-3 

8.4 

12 

31 

43 

50 

92 

Salt  dissolved. 

.006 

.002 

.001 

.0006 

.0002 

.0001 

.00006 

.00002 

.00001 

£K2S04  .        .        . 
KC1         ... 

1130 
1162 

1181 
"85 

1207 
"93 

1  220 
"99 

1241 
1209 

1249 
1209 

1254 

1212 

1266 
1217 

1275 

1216 

KI   . 

1176 

"97 

1203 

1209 

1214 

1216 

1216 

1216 

I2O7 

NH4C1     . 

"57 

1180 

1190 

"97 

I2O4 

1209 

1215 

1209 

I2O5 

KNO3      . 

1140 

"73 

1180 

1190 

"99 

1207 

I22O 

1198 

I2I5 

£BaCl2     . 

1031 

1074 

1092 

1  102 

1118 

1126 

"33 

"44 

1142 

KC1O8     . 

1068 

1091 

IIOI 

1109 

1119 

1122 

1126 

"35 

II4I 

£Ba2N206 

982 

1033 

1054 

1066 

1084 

1096 

IIOO 

1114 

III4 

ACuSO4  . 

740 

873 

95° 

987 

1039 

IO62 

1074 

1084 

1086 

AgN03    .        .        . 

I033 

1057 

1068 

1009 

1077 

1078 

1077 

1073 

1080 

!SnSO4   . 

744 

861 

919 

953 

IOOI 

1023 

1032 

1047 

I06o 

^IgSO4  . 
^a2SO4 

773 
933 

88  1 
980 

935 
998 

967 
1009 

1015 
1026 

1034 
1034 

1036 

1038 

1052 
1056 

1056 

1054 

aci2   !     ! 

939 
976 

979 
998 

i«3 

1004 
1014 

1020 

1018 

1029 
1029 

1031 

1027 

1035 
1028 

1036 
IO24 

NaN03    . 

921 

942 

952 

956 

966 

975 

970 

972 

975 

KC2H3O2 

891 

913 

919 

923 

933 

934 

935 

943 

939 

ijNa2CO3 

956 

IOIO 

1037 

1046 

988 

874 

790 

71S 

697* 

|H2SO4  . 

3001 

3240 

3342 

3280  • 

3"8 

2927 

2077 

1413* 

C2H40     . 

170 

283 

338o 

470 

796 

995 

"33 

1328 

1304* 

HC1 
HN03     . 

3438 
342i 
858 

3448 
945 

3455 
3427 
968 

3440 
3408 
977 

3340 
3285 
920 

3*70 
3088 
837 

2968 
2863 
746 

2057 
1904 

497 

1254* 

"44* 
402* 

KO3H   *  .'        !        ! 

2141 

2140 

2IIO 

2074 

1892 

1689 

H74 

845 

747* 

NH3 

116 

190 

260 

330 

500 

610 

690 

700 

560* 

*  Acids  and  alkaline  salts  show  peculiar  irregularities. 


SMITHSONIAN  TABLES. 


304  TABLES  337,338. 

LIMITING  VALUES  OF  fi.    TEMPERATURE  COEFFICIENTS. 
TABLE  337.  —  Limiting  Values  of  p. 

This  table  shows  limiting  values  of  ft  =  —  .10*  for  infinite  dilution  for  neutral  salts,  calculated  from  Table  271. 

JMI 


Salt. 

f- 

Salt. 

M 

Salt. 

M 

Salt. 

P. 

*K2S04     . 

1280 

iBaC!2       . 

1150 

|MgS04     . 

1080 

|H2S04    . 

3700 

KC1.    .    . 

1220 

iKC108     . 

1150 

iNa2SO4  . 

1060 

HC1      .    . 

3500 

KI    .    .     . 

I22O 

!BaN2O6  . 

1120 

iZnCl    .    . 

1040 

HNO3  .    . 

3500 

NH4C1.     . 

I2IO 

iCuSO4     . 

1  100 

NaCl     .    . 

1030 

£H3P04    . 

IIOO 

KNO3  .     . 

1210 

AgNOs     . 

lOQO 

NaNO3     . 

980 

KOH    .    . 

2200 

- 

- 

iZnSO4     . 

I080 

K2C2H8O2 

940 

|Na2CO3  . 

1400 

If  the  quantities  in  Table  336  be  represented  by  curves,  it  appears  that  the  values  of  the 
specific  molecular  conductivities  tend  toward  a  limiting  value  as  the  solution  is  made 
more  and  more  dilute.  Although  these  values  are  of  the  same  order  of  magnitude,  they 
are  not  equal,  but  depend  on  the  nature  of  both  the  ions  forming  the  electrolyte. 

When  the  numbers  in  Table  337  are  multiplied  by  Hittorf's  constant,  or  0.00011,  quan- 
tities ranging  between  0.14  and  o.io  are  obtained  which  represent  the  velocities  in  milli- 
metres per  second  of  the  ions  when  the  electromotive  force  gradient  is  one  volt  per 
millimetre. 

Specific  molecular  conductivities  in  general  become  less  as  the  concentration  is  in- 
creased, which  may  be  due  to  mutual  interference.  The  decrease  is  not  the  same  for 
different  salts,  but  becomes  much  more  rapid  in  salts  of  high  valence. 

Salts  having  acid  or  alkaline  reactions  show  marked  differences.  They  have  small 
specific  molecular  conductivity  in  very  dilute  solutions,  but  as  the  concentration  is  in- 
creased the  conductivity  rises,  reaches  a  maximum  and  again  falls  off.  Kohlrausch  does 
not  believe  that  this  can  be  explained  by  impurities.  H3PO4  in  dilute  solution  seems  to 
approach  a  monobasic  acid,  while  H2SO4  shows  two  maxima,  and  like  H3PO4  approaches 
in  very  weak  solution  to  a  monobasic  acid. 

Kohlrausch  concludes  that  the  law  of  independent  migration  of  the  ions  in  media  like 
water  is  sustained. 


TABLE  338. -Temperature  Coefficients. 

The  temperature  coefficient  in  general  diminishes  with  dilution,  and  for  very  dilute  solutions  appears  to  approach  a 
common  value.  The  following  table  gives  the  temperature  coefficient  for  solutions  containing  o.oi  gram  mole- 
cule of  the  salt. 


Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

Salt. 

Temp. 
Coeff. 

KC1  .    .    . 
NH4C1  .    . 
NaCl     .    . 
LiCl.    .    . 

iBaCl2  .    . 
iZnC!2  .     . 
iMgCl2      . 

0.0221 
0.0226 
0.0238 
0.0232 
0.0234 
0.0239 
0.0241 

KI    .    .    . 
KN03  .    . 
NaN03.    . 

AgNOg.      . 

iBa(N08)2 

KClOg    .      . 

KC2H302  . 

0.0219 

0.0216 

0.0226 
0.0221 
O.O224 
0.0219 
O.O229 

|K2S04      . 
|Na2S04    . 
iLi2S04     . 
iMgS04     . 
|ZnSOs     . 
|CuSO4     . 

0.0223 
0.0240 
0.0242 
0.0236 
0.0234 
0.0229 

iK2C03     .    . 
iNa2CO3  .    . 

0.0249 
0.0265 

KOH    .    , 
HC1      .    .    . 
HN03  .    .    . 
iH2S04     .    . 

0.0194 
0.0159 
0.0l62 
0.0125 

*H2S04         ) 
for  m  =  .001  J 

0.0159 

SMITHSONIAN  TABLES. 


TABLE  339. 


305 


THE    EQUIVALENT    CONDUCTIVITY    OF    SALTS,    ACIDS  AND    BASES    IN 

AQUEOUS  SOLUTIONS. 

In  the  following  table  the  equivalent  conductance  is  expressed  in  reciprocal  ohms.  The  con- 
centration is  expressed  in  milli-equivalents  of  solute  per  litre  of  solution  at  the  temperature  to  which 
the  conductance  refers.  (In  the  cases  of  potassium  hydrogen  sulphate  and  phosphoric  acid  the 
concentration  is  expressed  in  milli-formula-weights  of  solute,  KHSO4  or  H8PO4,  per  liter  of  solu- 
tion, and  the  values  are  correspondingly  the  modal,  or  "  formal,"  conductances.)  Except  in  the 
cases  of  the  strong  acids  the  conductance  of  the  water  was  subtracted,  and  for  sodium  acetate, 
ammonium  acetate  and  ammonium  chloride  the  values  have  been  corrected  for  the  hydrolysis  of 
the  salts.  The  atomic  weights  used  were  those  of  the  International  Commission  for  1905,  referred 
to  oxygen  as  16.00.  Temperatures  are  on  the  hydrogen  gas  scale. 

Concentration  in  Sram  equivalents, 
i  coo  liter 


Equivalent  conductance  in 


reciprocal  ohms  per  centimeter  cube 
gram  equivalents  per  cubic  centimeter 


Substance. 

Concen-  1 
tration.  1 

Equivalent  conductance  at  the  following  °  C  temperatures. 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

218° 

281° 

3060 

Potassium  chloride  . 

0 

130.1 

(152.1) 

(232.5) 

(321.5) 

414 

(519) 

625 

825 

1005 

II2O 

"                «        t 

2 

126.3 

146.4 

393 

588 

779 

930 

I008 

«                « 

10 

122.4 

141-5 

215.2 

295-2 

377 

470 

560 

74i 

874 

910 

a                u 

80 

H3-5 

— 

342 

498 

638 

723 

720 

"                " 

IOO 

II2.0 

129.0 

I94-5 

264.6 

415 

49° 

Sodium  chloride  .     . 

0 

109.0 

- 

- 

- 

362 

- 

555 

760 

970 

I080 

"             "        . 

2 

105.6 

— 

— 

— 

349 

— 

534 

722 

895 

955 

"             **        •    « 

10 

IO2.O 

— 

— 

— 

336 

— 

SI1. 

685 

820 

860 

"             " 

80 

93-5 

— 

— 

— 

301 

— 

500 

674 

680 

"             " 

IOO 

92.0 

— 

— 

— 

296 

— 

442 

Silver  nitrate  .    .    . 

0 

115.8 

- 

- 

- 

367 

- 

570 

780 

965 

1065 

"                   ... 

2 

II2.2 

— 

— 

— 

353 

— 

539 

727 

877 

935 

M 

10 

108.0 

— 

— 

— 

337 

- 

507 

673 

790 

"                                 ... 

20 

I05.I 

— 

— 

— 

326 

— 

488 

639 

"                                 ... 

40 

IOI.3 

— 

— 

— 

312 

— 

462 

599 

680 

680 

"                                  ... 

80 

96.5 

- 

- 

- 

- 

432 

552 

614 

604 

M 

IOO 

94-6 

— 

_ 

_ 

289 

Sodium  acetate    .    . 

0 

78.1 

_ 

_ 

• 

283 

- 

45° 

660 

- 

924 

"            "         .    . 

2 

74-5 

- 

- 

- 

268 

- 

421 

578 

- 

§01 

"           "         .    . 

IO 

71.2 

— 

— 

— 

253 

— 

396 

542 

— 

702 

tt           «         f 

80 

634 

— 

_ 

— 

221 

- 

340 

Magnesium  sulphate 

0 

II4.I 

- 

- 

- 

426 

- 

690 

1080 

U                                  M 

2 
10 

94-3 
76.1 

_ 

_ 

_ 

302 
234 

_ 

377 
241 

260 

U                               U 

2O 

67.5 

— 

— 

— 

190 

— 

195 

no 

(1                         « 

40 

59-3 

- 

- 

- 

160 

- 

158 

88 

"                 " 

80 

52.0 

- 

- 

- 

136 

- 

133 

75 

«                    « 

IOO 

49-8 

— 

— 

- 

130 

— 

126 

«                         <« 

2OO 

43-  r 

_ 

_ 

— 

no 

— 

109 

Ammonium  chloride 

O 

131.1 

152.0 

. 

- 

(415) 

- 

(628) 

(841) 

- 

(1176) 

"                  " 

2 

126.5 

146.5 

- 

- 

399 

- 

601 

801 

- 

1031 

«<                         u 

10 

122.5 

141.7 

— 

— 

382 

— 

573 

758 

— 

925 

<«                  « 

3° 

118.1 

_. 

— 

— 

— 

— 

828 

Ammonium  acetate  . 

0 

(99.8) 

- 

- 

- 

(338) 

- 

(523) 

«               « 

10 

91.7 

_ 

_ 

— 

300 

— 

456 

" 

25 

88.2 

— 

** 

~ 

286 

426 

From  the  investigations  of  Noyes,  Melcher,  Cooper,  Eastman  and  Kato;  Journal  of  the  American  Chemical  Society, 

30,  p.  33Si  1908. 
SMITHSONIAN  TABLES. 


306  TABLE  339  (continued). 

THE    EQUIVALENT    CONDUCTIVITY    OF    SALTS,    ACIDS    AND    BASES    IN 

AQUEOUS    SOLUTIONS. 


Substance. 

Concen-  1 
tration.  1 

Equivalent  conductance  at  the  following  °  C  temperatures. 

18° 

25° 

50° 

75° 

100° 

128° 

156° 

218° 

281° 

306° 

Barium  nitrate  .    . 

0 

116.9 

_ 

_ 

_ 

385 

_ 

600 

840 

1120 

1300 

"           " 

2 

109.7 

— 

— 

— 

352 

— 

536 

7i5 

828 

824 

"           " 

IO 

IOI.O 

— 

— 

— 

322 

— 

481 

618 

658 

615 

"           "      .    . 

40 

88.7 

- 

- 

- 

280 

- 

412 

5°7 

5°3 

448 

"           "      .    . 

80 

8l.6 

- 

- 

- 

258 

- 

372 

449 

430 

" 

100 

79.1 

— 

— 

— 

249 

Potassium  sulphate 

0 

132.8 

- 

- 

- 

455 

- 

715 

1065 

1460 

1725 

a               44 

2 

I24.8 

— 

— 

— 

402 

- 

605 

806 

893 

867 

(4                               44 

10 

II5-7 

- 

- 

- 

365 

- 

537 

672 

687 

637 

4O 

104.2 

320 

455 

545 

S19 

400 

(«                               4<         ^ 

80 

97.2 

- 

- 

- 

294 

- 

482 

448 

396 

"         . 

100 

95-o 

mm 

— 

— 

286 

Hydrochloric  acid 

0 

379-o 

- 

- 

- 

850 

- 

1085 

1265 

1380 

1424 

"             "  ! 

2 
IO 

373-6 
368.1 

_ 

: 

™" 

826 
807 

: 

1048 
1016 

1217 
1168 

1332 
1226 

1337 
Il62 

"             "  . 

80 

353-o 

- 

- 

- 

762 

- 

946 

1044    1046 

862 

"             "  . 

100 

35°-6 

— 

— 

— 

754 

_ 

929 

1006 

Nitric  acid        .    . 

o 

377-0 

42I.O 

570 

706 

826 

945 

1047 

(1230) 

- 

(1380) 

«(                  U 

2 

371.2 

4137 

559 

690 

806 

919 

IOI2 

life 

— 

1156 

(4                  U 

10 

365-0 

406.0 

548 

676 

786 

893 

978 

44                  U 

50 

100 

353-7 
346-4 

393-3 
385-0 

528 
516 

649 
632 

75° 
728 

845 
817 

917 

880 

_ 

_ 

454* 

Sulphuric  acid  .     . 

0 

383-0 

(429) 

(590 

(746) 

891 

(1041) 

1176 

'5°5 

- 

(2030) 

"    . 

2 

353-9 

390.8 

55i 

536 

563 

- 

637 

'    . 

10 

309.0 

337.0 

406 

435 

446 

460 

48l 

533 

"    . 

50 

253-5 

273.0 

323 

356 

384 

417 

448 

502 

Potassium  hydrogen  \ 
sulphate    .    .     .    ) 

Phosphoric  acid    . 

100 
2 

50 
100 
0 

233-3 
455-3 
295-5 
263.7 

338.3 

251.2 
506.0 
318.3 
283.1 
376 

636°i°o 

374-4 
329.1 

336 
754 
403 
354 
631 

369 
784 
422 

375 
730 

404 

773 
446 
402 
839 

435 
754 
477 
435 
930 

483 

474* 

"      « 

2 

283.1 

3"-9 

401 

464 

498 

508 

489 

" 

IO 

203.0 

222.O 

273 

300 

308 

298 

274 

44                         4( 

50 

122.7 

132.6 

157-8 

168.6 

168 

158 

142 

" 

100 

96.5 

IO4.O 

122.7 

129.9 

128 

120 

1  08 

Acetic  acid  . 

o 

(347-0) 

- 

(773) 

- 

(980) 

("65) 

- 

(1268) 

. 

IO 

14.50 

— 

— 

— 

25.1 

— 

22.2 

14.7 

44                (4 

30 

8.50 

— 

— 

— 

14.7 

— 

13.0 

8.65 

44                44 

80 

5.22 

- 

- 

- 

9-05 

- 

8.00 

5-34 

44                 44 

100 

4.67 

— 

_ 

_ 

8.10 

_ 

— 

4.82 

_ 

1.57 

Sodium  hydroxide 

0 

216.5 

- 

- 

- 

594 

- 

835 

1060 

" 

2 

2I2.I 

— 

— 

— 

582 

— 

814 

44                              44 

2O 

205.8 

- 

- 

- 

559 

- 

771 

930 

" 

5° 

200.6 

— 

_ 

_ 

540 

_ 

738 

873 

Barium  hydroxide 

0 

222 

256 

389 

(520) 

JT 

645 

(760) 

847 

it                            ii 

2 

215 

— 

359 

4 

591 

It                           tt 

10 

207 

235 

342 

449 

548 

664 

722 

ti                    tt 

50 

I9I.I 

2I5.I 

308 

399 

478 

549 

593 

*i                    ft 

100 

ISO.I 

2O4.2 

291 

373 

443 

5°3 

531 

Ammonium  hydrox-  J 

o 

IO 

(238) 
9.66 

(27I) 

(404) 

(526) 

(647) 
23.2 

(764) 

(908) 
22.3 

(1141) 
15-6 

— 

(1406) 

ide  1 

IO 

«;.66 

— 

n  6 

1 

100 

3  •*-«"' 
3.10 

3.62 

5-35 

6.70 

1J.VJ 

7-47 

- 

7.17 

4.82 

- 

-.33 

SMITHSONIAN  TABLES. 


These  values  are  at  the  concentration  Sao, 


TABLE  340. 


307 


THE     EQUIVALENT    CONDUCTIVITY    OF    SOME    ADDITIONAL    SALTS    IN 

AQUEOUS  SOLUTION. 

Conditions  similar  to  those  of  the  preceding  table  except  that  the  atomic  weights  for  1908  were  used. 


Substance. 

Concen- 
tration. 

Equivalent  conductance  at  the  following  °  C  temperature. 

0° 

18° 

*5° 

50° 

75° 

100° 

128° 

156° 

Potassium  nitrate  .    .    . 

O 

80.8 

126.3 

I45-1 

219 

299 

384 

485 

580 

"             "... 

2 

78.6 

122.5 

140.7 

212.7 

289.9 

370.3 

460.7 

«        <"    ;  ;  ; 

12.5 

50 

75-3 
70.7 

117.2 
109.7 

134.9 
126.3 

202-9 
189.5 

276.4 
2574 

351.5 

326.1 

435-4 
402.9 

520.4 
476.1 

41        "... 

IOO 

67.2 

104.5 

120.3 

180.2 

244.1 

308.5 

379-5 

447-3 

Potassium  oxalate  .    .    . 

O 

794 

127.6 

147.5 

230 

322 

419 

653 

"              "... 

2 

74.9 

119.9 

139.2 

21  5-9 

300.2 

389.3 

489.1 

587 

"              "... 

I2.S 

69-3 

III.  I 

129.2 

199.1 

275-1 

354-1 

438.8 

524.3 

"              "... 

50 

63 

101 

116.5 

178.6 

244.9 

3^2.2 

383-8 

449-5 

"      ... 

IOO 

59-3 

94.6 

109.5 

167 

227.5 

288.9 

353-2 

409.7 

"              "... 

200 

55-8 

88.4 

102.3 

155 

210.9 

265.1 

321.9 

37  2-  i 

Calcium  nitrate     .    .    . 

0 

70.4 

II2.7 

130.6 

202 

282 

369 

474 

575 

"           "          ... 

2 

66.5 

123.7 

I9I.9 

266.7 

346.5 

438.4 

529.8 

"            "          ... 

I2.5 

61.6 

98.6 

"4-5 

176.2 

244 

314.6 

394-5 

473-7 

"            "          ... 

5° 

55-6 

88.6 

102.6 

I57-2 

216.2 

276.8 

343 

405.1 

"           "          ... 

IOO 

82.6 

95-8 

146.1 

199.9 

255.5 

3*5.1 

369.1 

"            "          ... 

200 

48.3 

76.7 

88.8 

J354 

184.7 

2344 

288 

334-7 

Potassium  ferrocyanide  . 

0 

98.4 

159.6 

185-5 

288 

403 

527 

" 

O*5 

91.6 

171.1 

«                                       4« 

2. 

84.8 

137 

158.9 

243.8 

335-2 

427.6 

. 

I2-5 

7i 

"34 

131.6 

200.3 

271 

340 

" 

50 

58.2 

93-7 

1  08.6 

163-3 

219.5 

272.4 

" 

IOO 

53 

84.9 

984 

148.1 

I98.I 

245 

«                                    44 

200 

48.8 

77-8 

90.1 

*3S'7 

180.6 

222.3 

Barium  ferrocyanide  .     . 

400 
0 

454 

72.1 
150 

83-3 
176 

124.8 
277 

1657 

393 

203.1 
521 

"                "            . 

2 

46.9 

73 

86.2 

127.5 

166.2 

202.3 

"                "            . 

12.5 

304 

48.8 

56.5 

83-1 

107 

129.8 

Calcium  ferrocyanide     . 

0 

88 

146 

271 

386 

5" 

. 

2 

47.1 

75-5 

86.2 

130 

"                "         .    . 

I2-5 

31.2 

49-9 

574 

"                "         .    . 

24.1 

38.5 

444 

64.6 

81.9 

"                "         .    . 

IOO 

21.9 

35-1 

40.2 

58.4 

73-7 

84-3 

" 

200 

20.6 

32.9 

37.8 

55 

6B.7 

77.5 

" 

400 

20.2 

32.2 

37-i 

54 

67.5 

76.2 

Potassium  citrate       .    . 

0 

76.4 

124.6 

144.5 

228 

320 

420 

"           .    . 

0.S 

— 

1  20.  i 

1394 

"              "           .    . 

2 

71 

n  54 

134.5 

2IO.I 

293.8 

381.2 

«              « 

5 

67.6 

109.9 

128.2 

198.7 

276.5 

357-2 

"              "           .    . 

I2-5 

62.9 

101.8 

118.7 

183.6 

254.2 

326 

"              "           .    . 

50 

544 

87.8 

IO2.I 

157-5 

215-5 

273 

"              "           .    . 

IOO 

50.2 

80.8 

93'9 

1437 

196.5 

247-5 

"              "           . 

300 

43-5 

69.8 

81 

I23-5 

167 

209.5 

Lanthanum  nitrate    .    . 

0 

754 

122.7 

142.6 

223 

534 

651 

44                             (4 

•     2 
12-5 

614 

1  10.8 

128.9 
114.4 

200.5 
176.7 

279.8 
2434 

363-5 
311.2 

457.5 
383.4 

549 
447-8 

44                             44 

50 
IOO 

54 
49-9 

794 

99.7 
91.8 

152.5 

207.6 
189.1 

261.4 
236.7 

3I5-8 
282.5 

3577 
3l6-3 

<4                             <4 

200 

46 

72.1 

83.5 

126.4 

170.2 

210.8 

249.6 

276.2 

From  the  investigations  of  Noyes  and  Johnston,  Journal  of  the  American  Chemical  Society,  31,  p.  287,  1909. 
SMITHSONIAN  TABLES. 


308  TABLES  341 ,  342. 

CONDUCTANCE  OF  IONS.  -  HYDROLYSIS  OF  AMMONIUM  ACETATE. 

TABLE  341.  —  The  Equivalent  Conductance  of  the  Separate  Ions. 


Ion. 

0° 

18° 

25° 

So° 

75° 

100° 

128° 

156° 

K  

40.4 

64.6 

74-5 

"5 

:59 

206 

263 

317 

Na    

26 

4\>$ 

C.O.9 

82 

i?6 

155 

207 

249 

NH4      

4.0.2 

64.1; 

74.  c. 

115 

i  eg 

207 

264 

719 

Ag    

12.9 

54.3 

63.5 

101 

143 

188 

245 

299 

*Ba 

M 

CC2 

65 

104 

140 

200 

262 

722 

JCa  .             .    .    . 

T.O 

5i3 

60 

98 

142 

191 

252 

312 

iLa                ,    .    . 

7C 

61 

72 

IIQ 

177 

2^t; 

712 

388 

Cl     

4I.I 

65.5 

7C.c 

116 

1  60 

207 

264 

3l8 

NO3  

4O.4 

61.7 

'  O  J 

70.0 

104 

140 

178 

222 

263 

C2H802     .... 
^SO* 

20.3 
Al 

', 

34.6 

682 

40.8 
70 

67 

I2C 

^~. 
96 

177 

130 
214 

171 

•?O7 

211 
77O 

iC204    
|C6H507    .... 
jFe(CN)6  .... 

H      .    . 

39 
36 
58 

240 

632 
60 

95 
^14 

73 
70 
in 

•5  CQ 

"5 
"3 

173 

46  c 

'63 

161 

244 

c6i; 

2I3 
214 
32I 

644 

275 
722 

J    /- 
336 

777 

OH  

IOC 

172 

IQ2 

& 

j"j 
^60 

4"3Q 

C2C 

C.Q2 

From  Johnson,  Journ.  Amer.  Chem.  Soc.,  31,  p.  1010,  1909. 


TABLE  342.— Hydrolysis  of  Ammonium  Acetate  and  lonizatlon  of  Water. 


Temperature. 

Percentage 
hydrolysis. 

loiiization  constant 
of  water. 

Hydrogen-ion  concen- 
tration in  pure  water. 
Equivalents  per  liter. 

t 

I00h 

KwXio" 

CHXio' 

O 

- 

0.089 

0.30 

18 

(0-35) 

0.46 

0.68 

25 

- 

0.82 

0.91 

100 

4.8 

48. 

6.9 

156 

18.6 

223. 

14.9 

218 

527 

46l. 

21-5 

306 

91.5 

168. 

I3.0 

Noyes,  Kato,  Kanolt,  Sosman,  No.  63  Publ.  Carnegie  lust.,  Washington. 
SMITHSONIAN  TABLES. 


TABLES  343,  344.  309 

DIELECTRIC   CONSTANTS. 

TABLE  343.  — Dielectric  Constant  (Specific  Inductive  Capacity)  of  Gases. 

Atmospheric  Pressure. 
Wave-lengths  of  the  measuring  current  greater  than  10000  cm. 


Gas. 

Temp. 
°C. 

Dielectric  constant 
referred  to 

Authority. 

Vacuum=  i 

Air=i 

Air  

0 

20 

0 
ICO 

0 
0 

o 
o 

0 
0 

100 
0 

o 

0 

o 
o 

0 

o 
o 

145 

1.000590 
1.000586 

I.OOJiS 

1.00290 
1.00239 

1.000946 
1.000985 

1.000690 
1.000695 

I.OOI3I 
1.00146 

1.00258 

1.000264 
1  .000264 

1.000944 
1.000953 

I.OOII6 
1.00099 

1.00993 
1.00905 

1.00705 

I.OOOOOO 
1.  000000 

1  .00659 

1.00231 
1.00180 

1.000356 

1.000399 

1.  000  1  00 

1.000109 

1.00072 
1.00087 

1.00199 

0.999674 
0.999678 

1.000354 
1.000367 

1.00057 
1.00041 

1.00934 

1  .00846 
1.00646 

Boltzmann,  1875. 
KlemenCiC,  1885. 

Badeker,  1901. 

KlemenCiC. 
Badeker. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenCiC. 

Badeker. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenCiC. 

Boltzmann. 
KlemenCiC. 

Badeker. 
KlemenCiC. 

Badeker. 

14 

Ammonia      .     .    .     .     .    . 

Carbon  bisulphide     .    .    . 

Carbon  dioxide      .... 
«            « 

Carbon  monoxide  .... 
«              « 

Ethylene  .          

Hydrochloric  acid      .     .    . 

«< 

Nitrous  oxide  (N2O)      .     . 

(«                   ((                   u 

Sulphur  dioxide     .... 
«            « 

Water  vapor,  4  atmospheres 

TABLE  344.  —Variation  of  the  Dielectric  Constant  with  the  Temperature. 

For  variation  with  the  pressure  see  next  table. 

If  Z?0  =  the  dielectric  constant  at  the  temperature  8°  C.,  Dt  at  the  tempera- 
ture t°  C.,  and  a  and  )3  are  quantities  given  in  the  following  table,  then 

DQ  =  Dt  [i  —  a(t  —  0)  +  j8(f— 0)a]. 
The  temperature  coefficients  are  due  to  Badeker. 


Gas. 

a 

0 

Range  of 
temp.  °  C. 

Ammonia     .     . 

5.45  X  io-* 

2.59  X  icr7 

10  —  110 

Sulphur  dioxide 

6.19  X  ior» 

1.86  X  io-7 

0  —  110 

Water  vapor     . 

1.4X10-* 

- 

145 

The  dielectric  constant  of  air  at  atmospheric  pressure  but  with  varying  tem- 
perature may  also  be  calculated  from  the  fact  that  D  —  i  is  approximately  pro- 
portional to  the  density. 
SMITHSONIAN  TABLES. 


3  IO  TABLES  345,  346. 

DIELECTRIC  CONSTANTS  (.continued), 
TABLE  345.  — Change  of  the  Dielectric  Constant  of  Gases  with  the  Pressure. 


Gas. 

Temper- 
ature,0 C. 

Pressure 
atmos. 

Dielectric 
constant. 

Authority. 

Air   .         .... 

IQ 

2O 

I.OIO8 

Tangl,  1907. 

« 

40 

I.  O2l8 

« 

60 

I.O77O 

«          « 

80 

I.O47Q 

«          <« 

IOO 

i  o«u8 

«          «« 

II 

20 

I  OIOI 

Occhia.li.ni    190^ 

40 

1.0196 

«< 

60 

I.O2Q4. 

4< 

80 

I  O787 

u 

IOO 

l.WJU/ 

1.0482 

«« 

1  20 

I  OS7Q 

M 

M 

I4O 

I  o6?d. 

<« 

« 

160 

I  O76o 

« 

M 

1  80 

i  084.  <; 

«<              « 

Carbon  dioxide  .    . 

«           « 

«            « 

Nitrous  oxide,  N2O 
«           ««         « 

«           <«         « 

15 

IS 

10 
20 
40 
10 

20 

40 

i.  008 
i.  020 
i.  060 

I.OIO 

1.025 
1.070 

Linde,  1895. 

«        «( 
(< 
<« 
«« 

TABLE  346.— Dielectric  Constants  of  Liquids. 
A  wave-length  greater  than  10000  centimeters  is  denoted  by  co . 


Substance. 

Temp. 

°c: 

Wave- 
length, 
cm. 

Dielectric 
constant. 

~  >> 

r 

Substance. 

Temp. 

°c; 

Wave- 
length, 
cm. 

Dielectric 
constant. 

1* 

< 

Alcohol  : 

Alcohol  : 

Amyl  .     .     . 

frozen 

00 

2.4 

Methyl      .     . 

—50 

CO 

45-3 

"      ... 

—  IOO 

u 

30.1 

« 

0 

M 

35-° 

a 

—50 

<« 

23.0 

<« 

+20 

« 

31.2 

« 

0 

u 

17.4 

H 

17 

75 

33-2 

n 

+  20 

«« 

16.0 

Propyl      .     . 

—  120 

00 

46.2 

(t 

18 

200 

10.8 

<i 

—60 

« 

33-7 

u 

18 

73 

4-7 

« 

O 

(« 

24.8 

Ethyl  !    !    '. 

frozen 

00 

2.7 

H 

+  20 

M 

22.2 

« 

—  120 
-80 

«( 
(« 

54-6 
44-3 

M 

Acetone  .     .    . 

-& 

75 

00 

12.7 

33-8 

2 

5 

u 

—40 

u 

35-3 

(« 

0 

H 

26.6 

5 

« 

O 

<« 

28.4 

« 

15 

1200 

21.85 

6 

« 

+20 

<« 

25.8 

« 

17 

73 

20.7 

7 

'       ... 

17 

200 

24.4 

2 

Acetic  acid 

18 

00 

9-7 

8 

< 

«< 

75 

23.0 

2 

"         "     .    . 

IS 

1200 

10.3 

6 

t 

« 

S3 

2O.6 

3 

«         « 

17 

200 

7.07 

2 

f       ... 

« 

4 

8.8 

3 

«         «« 

X9 

75 

6.29 

2 

Methyl'    .'    .' 
« 

« 
frozen 
—  IOO 

0.4 

00 

M 

5-0 
58.0 

4 
i 

Amyl  acetate    . 
Amylene      .     . 

!9 

16 

00 
«« 

4.81 

2.20 

9 

10 

References  on  page  311. 


SMITHSONIAN  TABLES. 


TABLE  346  (continued). 
DIELECTRIC  CONSTANTS  OF  LIQUIDS. 

A  wave-length  greater  than  10000  centimeters  is  designated  by  oo . 


Substance. 

Temp. 

Wave- 
length 
cm. 

Diel. 
const. 

£ 

o 

•s  >, 

Substance. 

Temp. 

Wave- 
length 
cm. 

Diel. 

const. 

1      ' 

(frozen) 

Anilin 

18 

oo 

*?    IT  f\ 

j  i 

Nitrobenzol 

—  IO 

oo 

c\  c\ 

I 

Benzol  (benzene)  . 

18 

t< 

2.*288 

42.0 

H 

«                              H 

19 

73 

2.26 

2 

. 

O 

41.0 

It 

Bromine  .... 

23 

84 

3.18 

12 

.     . 

-|-i  e 

37-8 

It 

Carbon  bisulphide 

20 

00 

2.626 

13 

. 

3° 

u 

«            (i 

17 

73 

2.64 

2 

.     . 

18 

36.45 

II 

Chloroform  .     .    . 

18 

OO 

5-2 

II 

.     .     . 

17 

73 

34-o 

2 

u 

!7 

73 

4-95 

2 

Octane     .... 

17 

00 

1.949 

16 

Decane    .... 

14 

00 

1.97 

IO 

Oils: 

Decylene      .    .     . 

17 

" 

2.24 

M 

Almond     .    .     . 

20 

OO 

2.83 

18 

Ethyl  ether       .    . 

—80 

00 

7-05 

5 

Castor  .... 

II 

" 

4-67 

19 

((                 U 

—40 

" 

5.67 

Colza    .... 

2O 

" 

3-11 

20 

"        "... 

0 

" 

4.68 

« 

Cottonseed    .    . 

14 

" 

3.10 

21 

"       ... 

18 

" 

4.368 

ii 

Lemon  .... 

21 

M 

2.25 

22 

44 

20 

M 

4-30 

I3 

Linseed     .    .     . 

13 

M 

3-35 

21 

44      ... 

60 

U 

3-65 

«• 

Neatsfoot  .    .     . 

- 

" 

3.02 

2O 

"       ... 

100 

» 

3.12 

M 

Olive     .... 

2O 

" 

3-" 

23 

«       ... 

140 

» 

2.66 

H 

Peanut.     .    .    . 

II.4 

«' 

3-03 

21 

«<          "... 

1  80 

u 

2.12 

« 

Petroleum      .     . 

2OOO 

2-13 

24 

Crit. 

Petroleum  ether 

20 

00 

1.92 

2O 

temp. 

Rape  seed     .     . 

16 

M 

2.85 

21 

Formic  acid      .     . 

«        « 
Glycerine      .    .    . 

192 

18 

+  2 
(frozen) 

15 
15 

83 

73 
1  200 
73 

1200 
200 

4-35 
19.0 

62.0 
58.5 
56.2 
39-i 

2 

6 

2 

6 

2 

Sesame     .    .     . 
Sperm  .... 
Turpentine    .     . 
Vaseline    .     .     . 
Phenol      .... 
Toluol      .... 

134 

20 
20 

48 
—83 

+  16 
19 

73 

oo 

7-7 

3.02 

3-17 
2.23 
2.17 
9.68 
2.51 

2-33 
2.31 

u 

20 
tt 

25 

2 

5 

2 

M 

M 

15 

875 

25-4 

I  e 

Meta-xylol    .     .     . 

18 

/  J 

J     A 

2.376 

II 

44     .  .  .  ! 

_ 

0.4 

26 

*  j 
4 

.     . 

17 

73 

2-37 

2 

Hexane    .... 

17 

oo 

1.880 

16 

Hydrogen  perox-  ) 
ide  46  %  in  H2O  J 

18 

75 

84.7 

^7 

Water      .... 
for  temp,  coeff. 

18 

oo 

2OO 

81.07 
80.6 

II 
2 

see  Table  344. 

17 

74 

8l.7 

M 

17 

38 

83.6 

U 

i  Abegg-Seitz,  1899.             10  Landolt-Jahn,  1892.                  18  Hasenohrl,  1896. 
2  Drude,  1896.                       n  Turner,  1900.                             19  Arons-  Rubens,  1892. 

3  Marx,  1898.                         12  Schlundt.                                   20  Hopkinson,  1881. 

4  Lampa,  1896.                      13  Tangl,  1903.                              21  Salvioni,  1888. 
5  Abegg,  1897.                       14  Coolidge,  1899.                         22  Tomaszewski,  1888. 
6  Thwing,  1894.                     15  v.  Lang,  1896.                           23  Heinke,  1896. 

7  Drude,  1898.                       16  Nemst,  1894.                            24  Marx. 

8  Francke,  1893.                    17  Calvert,  1900.                           25  Fuchs. 

9  Lowe,  1898. 

SMITHSONIAN  TABLES. 


312 


TABLES  347,  348. 

DIELECTRIC  CONSTANTS  OF   LIQUIDS  (.continued). 
TABLE  347.  -  Temperature  Coefficients  of  the  Formula : 


Substance. 

a 

ft 

Temp, 
range,  6  C. 

Authority. 

Amyl  acetate  .     .     . 
Aniline  

0.0024 

O.OOT<;I 

- 

- 

Lowe. 
Ratz. 

Benzol   

0.00106 

O.OOOOO87 

10-40 

Hasenohrl. 

Carbon  bisulphide  . 
«             « 

Chloroform     .     .     . 
Ethyl  ether     .     .     . 
Methyl  alcohol    .     . 
Oils  :   Almond    .     . 
Castor  .     .     . 
Olive    .     .     . 
Paraffine  .     . 
Toluol 

0.000966 
0.000922 
0.00410 
0.00459 
0.0057 
0.00163 
0.01067 
0.00364 
0.000738 
o  00092  1 

0.00000060 
O.OOOOI5 

O.OOOO26 
0.0000072 

20-181 

22-l8l 
O—I3 

Ratz. 
Tangl. 

Ratz. 
Drude. 
Hasenohrl. 
Heinke,  1896. 

Hasenohrl. 
Ratz 

« 

0.000977 

O.OOOOOO46 

20-181 

Tangl. 

Water         .... 

O.OO4474 

H-2O 

Heerwagen. 

u 

O.OO4  "$"? 

O.OOOOII7 

•)       .fcW 

O-76 

Drude. 

it 

0.00436 

4-25 

Coolidge. 

Meta-xylol      .    .     . 

0.0008l7 

— 

20-181 

Tangl. 

(See  Table  344  for  the  signification  of  the  letters.) 


TABLE  348. -Dielectric  Constants  of  Liquified  Oases. 
A  wave-length  greater  than  10000  centimeters  is  designated  by  oo. 


Substance. 

Temp. 

ll 

Dial. 

constant. 

o 

Substance. 

Temp. 
°C 

il 

Dial. 

constant. 

! 

*! 

3 

c 

9 

Air    

—  IQI 

OO 

1.4-7.2 

I 

Nitrous  oxide 

u 

1.  47-  1.  CO 

2 

N2O 

—88 

OO 

1.933 

8 

Ammonia  .     .     . 

—34 

7S 

21-23 

3 

—5 

M 

1.630 

5 

"      .... 

16.2 

4 

+  S 

" 

1.573 

Carbon  dioxide  . 

—5 
o 

+  10 

00 
M 

i.6o8 
1.583 
i-54o 

5 

u           « 
Oxygen      .     .     . 

±& 

M 

1.520 
1.491 
1.465 

H 

" 

+15 

" 

1-526 

" 

Sulphur  dioxide  . 

14-5 

I  2O 

1375 

4 

Chi  rine    .    .     . 

—60 

2.150 

2O 

00 

14.0 

6 

—  20 

2.030 

«             « 

40 

" 

12.5 

• 

. 

0 

" 

i-97o 

<« 

««             « 

60 

" 

10.8 

i 

.    .     . 

+10 

N 

i-94o 

" 

«             « 

80 

" 

9.2 

' 

.     .    . 

0 

M 

2.08 

6 

"             " 

100 

u 

7.8 

1 

... 

+14 

100 

1.88 

4 

««             « 

1  20 

M 

6.4 

1 

Cyanogen  .     .     . 

23 

84 

2.52 

7 

«             « 

140 

M 

4.8 

• 

Hydrocyanic  acid 
Hydrogen  sulph. 

21 
10 

ti 

OO 

about  95 
5-93 

6 

Critical.    .    .    . 

154.2 

' 

2.1 

" 

50 

4.92 

« 

• 

90 

376 

i  v.  Pirani,  1903.                                4  Coolidge,  1899.                7  Schlundt,,  1901. 
2  Bahn-Kiebitz,  1904.                         5  Linde,  1895.                      8  Hasenohrl,  1900. 
3  Goodwin-Thompson,  1899.           o  Eversheim,  1904."            9  Fleming-Dewar,  1896. 

SMITHSONIAN  TABLES. 


TABLES  349,  350. -DIELECTRIC  CONSTANTS  (continued).  313 

TABLE  349.  —  Standard  Solutions  for  the  Calibration  of  Apparatus  for  the  Measuring  of  Dielectric  Constants. 


Turner. 

Drude. 

Nernst. 

Substance. 

Diel.  const. 

at  18°. 

\=  00. 

Acetone  in  benzol  at  19°.    A  =  75  cm. 

Ethyl  alcohol  in 
water  at  19.5°. 
A=  oo. 

Per  cent 
by  weight. 

Density  16°. 

Dielectric 

constant. 

Temp, 
coefficient. 

Benzol  

2.288 

2.376 

4.36' 
7.298 

10.90 

27.71 

3645 
81.07 

Per  cent 
by  weight. 

Dielectric 
constant. 

Meta-xylol     .... 
Ethyl  ether   .... 
Aniline      
Ethyl  chloride  .     .     . 
O-nitro  toluol     .     .     . 
Nitrobenzol  .... 
Water  (conduct.  lO"6) 

o 

2O 
40 
60 
80 
IOO 

0.885 
0.866 
0.847 
0.830 
0.813 
0.797 

2.26 
£10 

»43 

12.1 

16.2 

20.5 

0.1% 

o-3 
0.4 

o-5 

°*1 

0.6 

IOO 
90 
80 

jo 

00 

26.0 
29-3 

38.0 
43-1 

Water  in  acetone  at  19°.    A  =  75  cm. 

0 
2O 
40 
60 
80 
IOO 

0.797 
0.856 
0.903 
0.940 

0-973 
0.999 

20.5 
31-5 

43-5 
57-0 
70.6 
80.9 

0.6% 
o-S 
o-S 
o-S 
o-5 
0.4 

TABLE  350.  —Dielectric  Constants  of  Solids. 


Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Dielectric 

constant. 

i* 

Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Dielectric 

constant. 

J* 

Asphalt      .     . 

_ 

CO 

2.68 

i 

Temp. 

Barium      sul- 

Iodine (cryst.)  . 

23 

75 

4.00 

2 

phate      .    . 

_ 

75 

10.2 

2 

Lead  chloride  . 

Caoutchouc    . 

_ 

CO 

2.22 

3 

(powder) 

_ 

M 

42 

2 

Diamond   .    . 

_ 

(( 

16.5 

i 

"     nitrate     . 

_ 

* 

16 

2 

"           .     . 

_ 

75 

5-5° 

2 

"     sulphate  . 

- 

" 

28 

2 

Ebonite      .    . 

- 

CO 

2.72 

4 

"     molybde- 

. 

- 

" 

2.86 

5 

nate  .     . 

— 

" 

24 

2 

"           .    . 

_ 

1000 

2-55 

6 

Marble 

Glass* 

Density. 

(Carrara) 

_ 

« 

8.3 

2 

Flint  (extra 

Mica   .... 

_ 

CO 

5 

heavy) 

4-5 

CO 

9.90 

7 

M 

_ 

" 

5.80-6.62 

15 

Flint    (very 

Madras,  brown 

_ 

M 

2.5-3-4 

16 

light)  .     . 

2.87 

« 

6.61 

7 

"        green 

_. 

«« 

3-9-5-5 

16 

Hard  crown 
Mirror    .    . 

2.48 

M 

M 

6.96 
6.44-746 

7 
5 

"        ruby  . 
Bengal,  yellow 

_ 

M 

a 

16 
16 

"        , 

— 

" 

5-37-5-90 

8 

"       white  . 

— 

" 

4.2 

16 

"        4 

— 

600 

5.42-6.20 

8 

"      ruby    . 

_ 

" 

4-2-4-7 

16 

Lead  (Pow- 

Canadian   am- 

ell).    .    . 

3-0-3-5 

CO 

5.4-8.0 

9 

ber  .     ... 

- 

" 

3-o 

16 

Jena 

South  America 

— 

" 

5-9 

16 

Boron 

_ 

" 

5.5-8.1 

10 

Ozokerite  (raw) 

_ 

M 

2.21 

i 

Barium    . 

_ 

" 

7.8-8.5 

TO 

Paper         (tele- 

Borosili- 

phone) 

_ 

" 

2.O 

17 

cate      . 

_ 

" 

6.4-7.7 

I 

"      (cable)    . 

_ 

" 

2.O-2.5 

i 

Gutta  percha  . 

- 

- 

3-3-4-9 

II 

Paraffine  .     .    . 

Melting 

M 

2.46 

18 

Temp. 

"        ... 

point. 

" 

2.32 

19 

Ice    .... 

C 

1200 

2.85 

12 

"        ... 

44-46 

« 

2.10 

20 

"<  :  :  :  : 

—190 

5000 

75 

3.16 
1.76-1.88 

13 
14 

«    :  :  : 

54-56 
74-76 

(i 

2.14 
2.16 

20 
2O 

References  on  p.  314. 

*  For  the  effect  of  temperature,  see  Gray-Dobbie,  Pr.  Roy.  Soc.  63,  1898;  67,  1900. 
"  wave-length,  see  K.  F.  Lowe,  Wied.  Ann.  66,  1898. 

SMITHSONIAN  TABLES. 


TABLES  350,  351. 

DIELECTRIC  CONSTANTS  (continued). 
TABLE  350.  —  Dielectric  Constants  of  Solids  (continued). 


Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Diel. 
constant. 

o 
•S  & 
s.^ 
<! 

Substance. 

Condi- 
tion. 

Wave- 
length, 
cm. 

Diel. 

constant. 

•5  ^ 
1^ 

Paraffine    .    . 

47-°6 

61 

2.16 

21 

Sulphur 

ii 

56.°2 

61 

2.25 

21 

Amorphous 

- 

00 

3.98 

I 

Phosphorus  : 

tt 

— 

75 

3.80 

2 

Yellow    .     . 

- 

75 

3-60 

2 

Cast,  fresh 

- 

00 

4.22 

I 

Solid  .    .     . 

— 

80 

4.1 

22 

«        « 

— 

M 

4-05 

18 

Liquid     .     . 
Porcelain  : 

- 

80 

3-85 

22 

«        « 
Cast,  old     . 

- 

75 

00 

3.60 

2 

18 

Hard 

i<        it 

- 

75 

3-9° 

2 

(Royal  B'l'n) 
Seger   "  "     . 

_ 

00 
« 

III 

15 
15 

Liquid     .   1 

near 
melting- 

L 

3-42 

I 

Figure"  "    . 

— 

II 

6.84 

15 

( 

point 

) 

Selenium   .     . 

— 

(« 

744 

I 

Strontium 

"           .     . 

- 

75 

6.60 

2 

sulphate 

- 

75 

"•3 

2 

<i 

— 

00 

6.13 

23 

Thallium 

«< 

_ 

1000 

6.14 

23 

carbonate 

- 

75 

17 

2 

Shellac  .     !    '. 

_ 

00 

3.10 

4 

"  nitrate 

_ 

-75 

16.5 

2 

ii 

_ 

(( 

2-95-3-73 

24 

Wood 

dried 

i< 

- 

(I 

3-67 

25 

Red  beech  . 

||  fibres 

00 

4.83-2.51 

- 

«        « 

_L    " 

II 

7-73-3-63 

— 

Oak  .     .     1 

II      " 

It 

4.22-2.46 

— 

it 

J_    « 

u 

6.84-3.64 

— 

i  v.  Pirani,  1903.                         10  Lowe,  1898.                              18  Fallinger,  1902. 

2  Schmidt,  1903.                         n  (submarine-data).                     19  Boltzmann,  1875. 

3  Gordon,  1879.                           I2  Thwing,  1894.                           20  Zietkowski,  1900. 

4  Winklemann,  1889.                 13  Abegg,  1897.                            21  Hormell,  1902. 

5  Elsas,  1891.                               14  Behn-Kiebitz,  1904.                 22  Schlundt,  1904. 

6  Ferry,  1897.                             15  Starke,  1897.                            23  Vonwiller-Mason,  1907. 
7  Hopkinson,  1891.                     16  E.  Wilson.                                 24  Wiillner,  1887. 

8  Arons-Rubens,  1891.              17  Campbell,  1906.                       25  Donle. 
9  Gray-Dobbie,  1898. 

TABLE  351.— Dielectric  Constants  of  Crystals. 
Do,  D)8,  Dy  are  the  dielectric  constants  along  the  brachy,  macro  and  vertical  axes  respectively. 


Substance. 

Wave- 
length, 
cm. 

Diel.  const. 

i 

•5  £• 
< 

Substance. 

Wave- 
length, 
cm. 

Diel.  const. 

I* 

j_  Axis. 

I  Axis. 

Da 

D/3 

Dy 

UNIAXIAL  : 
Apatite    .... 
Beryl   .... 

75 

oo 

75 

00 

75 
75 

00 

ii 

1000 

75 
75 

CO 

75 
75 

» 

7.10 

6.05 
8.49 

F 

4.69 
4-38 
4.27 

4-32 
89 

7-'3 
6-75 

12.8 

7.40 

7-44 
6.05 

5-52 
7.56 
8.29 
6.80 
8.00 

5.06 

4.46 

4.60 

173 
6.54 
5-65 

12.6 

2 

3 
i 

4 
5 
i 
i 

4 
6 
6 

i 

4 
i 
i 

RHOMBIC  : 
Arragonite   .     .     . 

Barite 

oo 

75 
oo 

75 
75 
75 
oo 

II 

75 
75 

9.14 
9.80 
6.97 

7-65 
7.70 

25-4 
|.26 
6.09 
6.70 
3.8l 
3-65 

665 

7.68 
10.09 

12.  2O 
I8.5 
23.2 

6.05 

5.08 

6.92 
3-97 

$ 

6.70 

7-13 
6-55 
7.00 
7.70 
8-30 
19.2 
8.28 
4.48 
8.89 

4-77 
4.66 
4.66 
6.30 

4 
i 

4 

i 
i 
7 
7 

I 

7 

i 
i 

ii 
Calcspar  .... 

M 

Dolomite  .,_  .     .     . 
Iceland  spar     .     . 
Quartz     .... 

i< 

« 

Coelestin  .... 
Cerussite  .  .  . 
MgS04+7HaO  . 
K2S04  .... 
Rochelle  salt  .  . 
Sulphur  .... 

it 

it 

ii 

Rutil  (Ti62).     .    . 
Tourmaline  .     .     . 
ii 

Zircon  

Topaz  

I  Schmidt,  1903.                        4  Fallinger,  1902.                     7  Borel,  1893. 
2  Starke,  1897.                          5  v.  Pirani,  1903.                     8  Boltzmann,  1875. 
3  Curie,  1889.                            6  Ferry,  1897. 

SMITHSONIAN  TABLES. 


TABLES  352,  353. 
PERMEABILITY  OF  IRON. 


315 


TABLE  352.— Permeability  of  Iron  Rings  and  Wire. 

This  table  gives,  for  a  few  specimens  of  iron,  the  magnetic  induction  B,  and  permeability  p,  corresponding  to  the 
magneto-motive  forces  H  recorded  in  the  first  column.  The  first  specimen  is  taken  from  a  paper  by  Rowland,* 
and  refers  to  a  welded  and  annealed  ring  of  "Burden's  Best"  wrought  iron.  The  ring  was  6.77  cms.  in  mean 
diameter,  and  the  bar  had  a  cross  sectional  area  of  0.916  sq.  cms.  Specimens  2-4  are  taken  from  a  paper  by 
Bosanquet,t  and  also  refers  to  soft  iron  rings.  The  mean  diameters  were  21.5,  22.1,  and  22.725  cms.,  and  the 
thickness  of  the  bars  2.535,  1.295,  and  .7544  cms.  respectively.  These  experiments  were  intended  to  illustrate  the 
effect  of  thickness  of  bar  on  the  induction.  Specimen  5  is  from  Ewing's  book,t  and  refers  to  one  of  his  own 
experiments  on  a  soft  iron  wire  .077  cms.  diameter  and  30.5  cms.  long. 


Specimen  1 

2 

3 

4 

6 

.ci:>,c 

'*  gS  §  A 

B 

* 

B 

pi 

B 

P 

B 

f- 

B 

M 

0.2 

o-5 

I.O 

2.0 

80 
330 

145° 
4840 
9880 

400 
660 

145° 
2420 
1976 

126 

377 
1449 

4564 
9900 

630 

754 
1449 
2282 
1980 

65 

224 
840 

3533 
8293 

325 
448 
840 
1766 

85 
214 

885 
2417 
8884 

g 

1208 
1777 

22 

74 

246 
950 
12430 

110 

I48 
246 

475 
2486 

fl^l 

Is  |'c.s 

SfBJl 

43  C  rt  'Crt 

*%m 

1  0.0 
2O.O 
5O.O 
1  00.0 

12970 
14740 
16390 

1297 

737 
328 

13023 
14911 
16217 
17148 

1302 
746 

324 
171 

12540 
14710 
16062 
17900 

1254 
735 
321 
179 

11388 

13273 
13890 

14837 

IJ39 

278 
148 

15020 

15790 

1502 
789 

Bill 

Bill 

TABLE  363.  -Permeability  of  Transformer  Iron.§ 

This  table  contains  the  results  of  some  experiments  on  transformers  of  the  Westinghouse  and  Thomson-Houston 
types.  Referring  to  the  headings  of  the  different  columns,  Mis  the  total  magneto-motive  force  applied  to  the  iron ; 
M/  /  the  magneto-motive  force  per  centimetre  length  of  the  iron  circuit ;  B  the  total  induction  through  the  mag- 
netizing coil ;  B  /  a  the  induction  per  square  centimetre  of  the  mean  section  of  the  iron  core  ;  M I B  the  magnetic 
reluctance  of  the  iron  circuit ;  Bl/Ma  the  permeability  of  the  iron,  a  being  taken  as  the  mean  cross  section  of  the 
iron  circuit  as  it  exists  in  the  transformer,  which  is  thus  slightly  greater  than  the  actual  cross  section  of  the  iron. 


(a)  WESTINGHOUSB  No.  8  TRANSFORMERS  (ABOUT  2500  WATTS  CAPACITY). 

First  specimen. 

Second  specimen. 

M 

M 

~T 

B 

M 

Bl 

B 

M 

Bl 

B 

a 

B 

Ma 

B 

a 

~B 

~M~a 

20 

0-597 

2I8XI08 

1406 

0.917  X  IO"4 

2360 

16X10* 

1032 

1.  25XIO-4 

1730 

£ 

1.194 
1.791 

587        '« 
878        " 

3790 
5660 

0.681         ' 
0.683         ' 

3120 
3180 

49      « 
82      " 

3HO 
5290 

0.82        " 
0.73        " 

2640 
2970 

80 

100 

2.338 
2.985 

1091        " 
1219       " 

7040 
7860 

0.734 
0.819        « 

2960 
2640 

104      « 
118      " 

6710 
7610 

0-77      " 
0.85      " 

2820 
2560 

1  20 

140 
1  60 

3-582 
4.179 
4.776 

1330 
1405        " 

1475 

8580 
9060 
9510 

0.903         ' 
0.994         || 

2410 
2186 
2000 

124      " 
131      " 
135      " 

8000 
8450 
8710 

0.97      " 
.07 
.18      " 

2250 
2036 
1830 

180 

5-373 

!532 

9880 

I.lSo        " 

1850 

140      " 

9030 

•29  ;; 

1690 

200 

5-970 

1581       " 

IO2OO 

1.270         " 

I72O 

142      " 

9160 

.41 

1540 

220 

6.^67 

1618      " 

10430 

1.360        " 

'59° 

144      " 

9290 

•53 

I4IO 

260 

7.761 

1692      " 

I09IO 

1.540        « 

1410 

*  "  Phil.  Mag.v  4th  series,  vol.  xlv.  p.  151. 

t  Ibid,  sth  series,  vol.  xix.  p.  73. 

J  "  Magnetic  Induction  in  Iron  and  Other  Metals." 

§  T.  Gray,  from  special  experiments. 


SMITHSONIAN  TABLES. 


316 


TABLE  353  (continued). 

PERMEABILITY    OF    TRANSFORMER    IRON, 


(to)  WESTINGHOUSE  No.  6  TRANSFORMERS  (ABOUT  :8oo  WATTS  CAPACITY). 

First  specimen. 

Second  specimen. 

M 

M 
I 

B 

M 

Bl 

B 

M 

Bl 

B 

a 

B 

Ma 

B 

a 

B 

Ma 

20 

0.62 

I47XI08 

1320 

I.36XIO-4 

2140 

2i5Xio3 

1940 

0.93X10-* 

3J4Q 

g 

1.23 

i.8s 

442     'I 

6280 

0.91      " 

0.86    " 

3260 

339° 

615  " 
826  " 

5540 
7440 

0.64       " 
0.72       " 

449° 
4030 

80 

2.46 

862 

7770 

0.93    « 

3T40 

986  " 

8880 

0.8  1     " 

3590 

100 

3.08 

949 

8550 

1.05     " 

2770 

1050   " 

9460 

0.95     " 

3060 

1  20 

3-70 

1010 

9106 

1.19    " 

2450 

1  100     " 

9910 

1.09     « 

2670 

140 

4-31 

1060 

955° 

i-33    " 

22IO 

1140  " 

10300 

1.23     « 

2430 

160 

4-93 

1090 

9820 

1.47    « 

1990 

1170    " 

IO5OO 

1-37     " 

2180 

1  80 

5-55 

1  1  20 

IOIOO 

1.61     " 

1830 

1190  " 

10700 

1.51     " 

1970 

200 

6.16 

1150 

10400 

1.74    ' 

1680 

(C)  WESTINGHOUSE  No.  4  TRANSFORMER 
(ABOUT  1200  WATTS  CAPACITY). 

(d)  THOMSON-HOUSTON  1500  WATTS  TRANSFORMER. 

M 

B 

M 

Bl 

M 

B 

If 

Bl 

M 

T 

B 

a 

B 

Ma 

M 

I 

B 

a 

y 

Ma 

20 

0.69 

i47Xio8 

1470 

1.36X10-^ 

2140 

20 

0.42 

7oXio3 

1560 

2.86X10-4 

3730 

40 

0.84 

142  " 

3160 

2.81     " 

37»0 

40 

1.38 

406    " 

4066 

0.98      " 

2940 

60 

1.26 

214    « 

4770 

2.81     " 

3790 

80 

1.68 

265  « 

5910 

3.02  « 

3520 

60 

2.07 

573    " 

S73° 

I.OS      « 

2770 

100 

2.10 

309  •« 

6890 

3-24  u 

3280 

1  20 

2.52 

348  " 

7760 

3-45    " 

3080 

80 

2.76 

659    « 

6590 

I.2I       " 

2390 

160 

3.36 

408   " 

9IOO 

3.92    ' 

2710 

200 

4.20 

456  " 

10200 

4-39    " 

2430 

100 

34  S 

714    tt 

7140 

1.40      " 

2070 

240 

5-°4 

495    " 

IIOOO 

4.87     « 

2190 

280 

5.88 

524    ' 

11690 

5-35    " 

1990 

120 

4.14 

748    " 

7490 

1.  60      " 

1810 

320 

6.72 

550    " 

12270 

5.82    " 

1820 

360 

7-S6 

573    " 

12780 

6.29    " 

1690 

140 

4-8,3 

777    " 

7770 

1.  80       " 

1610 

4OO 

8.40 

59i 

13180 

6.78    « 

1570 

440 

9.24 

504    " 

13470 

7.28    « 

1460 

TABLES  354-356.    MAGNETIC  PROPERTIES  OF  IRON.  317 

TABLE  354.  — Magnetic  Properties  o!  Iron  and  Steel. 


Electro- 
lytic 
Iron. 

Good 
Cast 

Steel. 

Poor 
Cast 
Steel. 

Steel. 

Cast 
Iron. 

Electrical  Sheets. 

Ordinary. 

Silicon 
Steel. 

c 

Chemical  composi-     ^ 
tion  in  per  cent       p 

(s 

0.024 
0.004 
0.008 

0.008 

O.OOI 

0.044 
0.004 
0.40 
0.044 
0.027 

0.56 

0.18 
0.29 
0.076 
o-035 

0.99 

O.IO 

0.40 
0.04 
0.07 

3-1  1 

3-27 
0.56 
I.0| 
O.o6 

0.036 
0.330 
0.200 
0.040 
0.068 

0.036 
3-90 
0.090 
0.009 
O.OO6 

Coercive  force    .    .     .    < 

2.83 
[0.36] 

"-51 

[0.37] 

(44-*3) 

16.7 
(52-4) 

II.4 
[4-6] 

[1-30] 

[0.77] 

Residual  B     .    .    .    .    j 

11400 
[10800] 

10600 
[nooo] 

10500 
(10500) 

13000 
(7500) 

5100 
[5350] 

[9400] 

[9850] 

Maximum  permeability  j 

1850 
[14400] 

3550 

[14800] 

700 
(170) 

<§ 

240 
[600] 

[3270] 

[6I30] 

B  for  H=i50     ...    | 

19200 

[18900] 

18800 
[19100] 

17400 
(15400) 

16700 
(11700) 

10400 

[iiooo] 

[18200] 

[17550] 

4irl  for  saturation        .    j 

21620 

[21630] 

21420 

[21420] 

20600 
(20200) 

19800 
(18000) 

16400 

[16800] 

[20500] 

[19260] 

E.  Gumlich,  Zs.  fur  Electrochemie,  15,  p.  599;  1909. 
Brackett  indicate  annealing  at  800°  C  in  vacuum.  Partntheses  indicate  hardening  by  quenching  from  cherry-red. 

TABLE  355. -Cast  Iron  in  Intense  Fields. 


Soft  Cast  Iron. 

Hard  Cast  Iron. 

H 

B 

I 

/* 

H 

B 

I 

p 

114 

172 

9950 

10800 

782 
846 

87.3 
62.8 

142 

254 

7860 
9700 

614 

752 

g 

433 

13900 

1070 

32.1 

239 

10850 

836 

30.6 

744 

15750 

1  200 

21.2 

684 

1305° 

983 

19.1 

1234 
1820 

17300 
18170 

1280 
1300 

I4.O 
1  0.0 

915 

1570 

14050 
15900 

1044 
1138 

154 
IO.I 

12700 

31100 

1465 

2-5 

2020 

16800 

1176 

8.3 

13550 

32100 

1475 

2.4 

lOOXX) 

26540 

1245 

2.4 

13800 

32500 

1488 

2.4 

I32OO 

28600 

1226 

2.2 

15100 

33650 

1472 

2.2 

14800 

30200 

1226 

2.O 

B.  O.  Peirce,  Proc.  Am.  Acad.  44,  1909. 
TABLE  3 56. -Corrections  for  Ring  Specimens. 


In  the  case  of  ring  specimens,  the  average  magnetizing  force  is  not  the  value  at  the  mean  radius, 
the  ratio  of  the  two  being  given  in  the  table.     The  flux  density  consequently  is  not  uniform,  and 
the  measured  hysteresis  is  less  than  it  would  be  for  a  uniform  distribution.    This  ratio  is  also  given 
for  the  case  of  constant  permeability,  the  values  being  applicable  for  magnetizations  in  the  neigh- 
borhood of  the  maximum  permeability.     For  higher  magnetizations  the  flux  density  is  more  uni- 
form, for  lower  it  is  less,  and  the  correction  greater. 

Ratio  of 
Radial 
Width  to 
Diameter 
of  Ring. 

Ratio  of  Average  H  to 
H  at  Mean  Radius. 

Ratio  of  Hysteresis  for  Uniform 
Distribution  to  Actual  Hysteresis. 

Rectangular 
Cross-section. 

Circular 
Cross-section. 

Rectangular 
Cross-section. 

Circular 
Cross-section. 

lit 

& 
ft 

i/7 
1/8 

I/IO 

1/19 

1.0986 
1-0397 

1.0216 

1.0137 
1.0094 

1.0069 
1.0052 

1.0033 

1.0009 

1.0718 
1.0294 
1.0162 
I.OIO2 
1.0070 
1.0052 
1.0040 
1.0025 
I.OOO7 

1.  112 

1.045 
1.024 
I.OI5 
I.OIO 
I.OOS 
1.  006 
1.003 
1.  00  1 

1.084 
1.033 

1.018 

I.OII 
1.008 
1.  006 
1.004 
1.002 
1.  001 

M.  G.  Lloyd,  Bull.  Bur.  Standards,  5,  p.  435.  *9o8. 


SMITHSONIAN  TABLES. 


TABLE  357. 


COMPOSITION   AND   MAGNETIC 

This  table  and  Table  358  below  are  taken  from  a  paper  by  Dr.  Hopkinson  *  on  the  magnetic  properties  of  iron  and  steel, 
which  is  stated  in  the  paper  to  have  been  240.  The  maximum  magnetization  is  not  tabulated ;  but  as  stated  in  the 
by  4»r.  "  Coercive  force  "  is  the  magnetizing  force  required  to  reduce  the  magnetization  to  zero.  The  "demag- 
previous  magnetization  in  the  opposite  direction  to  the  "  maximum  induction  "  stated  in  the  table.  The  "  energy 
which,  however,  was  only  found  to  agree  roughly  with  the  results  of  experiment. 


No. 
of 
Test 

Description  of 
specimen. 

Temper. 

Chemical  analysis. 

Total 
Carbon 

Manga 
nese. 

Sulphur. 

Silicon 

Phos- 
phorus 

Other 
substances. 

j 

Wrought  iron    . 

Annealed 

_ 

_ 

_ 

2 

Malleable  cast  iron   . 

« 

_ 

_ 

_ 

_ 

_ 

_ 

1    3 

Gray  cast  iron  . 

_ 

- 

- 

- 

_ 

_ 

_ 

4 

i 

Bessemer  steel  . 
Whitworth  mild  steel 

u                      « 

Annealed 

« 

0.045 
0.090 
0.320 

0.200 

0.153 
0.438 

0.030 

0.016 
0.017 

None. 

H 

O.O42 

0.040 
0.042 
0-035 

- 

tt 

(  Oil-hard- 

<t 

u 

7 

• 

(    ened 

— 

8 

"              " 

Annealed 

0.890 

0.165 

0.005 

0.081 

0.019 

- 

«                  « 

(  Oil-hard- 

|| 

n 

(< 

(( 

9 

{    ened 

" 

10 

Hadfield's  manganese  ) 
steel                           {    ' 

- 

1.005 

12.360 

0.038 

O.2O4 

0.070 

- 

ii 

12 

Manganese  steel 

As  forged 
Annealed 

0.674 

4.730 

0.023 
« 

0.608 

0.078 
« 

- 

u 

(  Oil-hard- 

(t 

X3 

*        • 

(    ened 

— 

15 

'.        '. 

As  forged 
Annealed 

1.298 

8-740 

0.024 

H 

0.094 

0.072 

-   ' 

u                u 

(  Oil-hard- 

(( 

{< 

U 

' 

u 

*               * 

l    ened 

•• 

3 

Silicon  steel 

As  forged 
Annealed 

0.685 

0.694 

ft 
tt 

3438 

0.123 
« 

- 

«         » 

(  Oil-hard- 

H 

tt 

|| 

*9 

*        •        . 

{    ened 

~ 

20 

21 

Chrome  steel    .        . 

As  forged 
Annealed 

0.532 

0.393 

O.O2O 

O.22O 

0.041 

0.621  Cr. 

M 

tt 

(  Oil-hard- 

u 

(t 

22 

... 

(    ened 

" 

" 

" 

23 
24 

"    "   ;    ;    ! 

As  forged 
Annealed 

0.687 

0.028 

H 

0.134 

0.043 

1.195  Cr. 

Of 

u        « 

(  Oil-hard- 

<« 

(( 

25 

*       *       • 

(    ened 

26 
27 

Tungsten  steel  . 

As  forged 
Annealed 

J-357 

0.036 

None. 

O-043 

tt 

0.047 

4.649  W. 

(  Hardened 

28 

"           "... 

<    in  cold 

tt 

f 

« 

tt 

« 

H 

(    water 

f  Hardened 

29 

"           "... 

<    in  tepid 

" 

" 

« 

" 

« 

tt 

(    water 

30 

"    (French)   . 

(  Oil-hard- 
{    ened 

0.511 

0.625 

None. 

0.021 

O.O28 

3.444  W. 

32 

33 
34 

35 

««            tt 
Gray  cast  iron   . 
Mottled  cast  iron 
White      "       "         . 
Spiegeleisen 

Very  hard 

0.855 

3-455 
2.581 
2.036 
4.510 

0.312 
0.173 

0.610 
0.386 
7.970 

0.042 
0.105 
0.467 
Trace. 

O.I5I 

2.044 
1.476 
0.764 
0.502 

0.089 
0.151 

0-435 
0.458 
0.128 

IJgw 

1-477  C.t 

*  Phil.  Trans.  Roy.  Soc.  vol.  176. 
SMITHSONIAN  TABLES. 


t  Graphitic  carbon. 


TABLE  357  (continued). 

PROPERTIES  OF  IRON  AND  STEEL. 


The  numbers  in  the  columns  headed  "magnetic  properties"  give  the  results  for  the  highest  magnetizing  force  used, 
paper,  it  may  be  obtained  by  subtracting  the  magnetizing  force  (240)  from  the  maximum  induction  and  then  dividing 
netizing  force  "  is  the  magnetizing  force  which  had  to  be  applied  in  order  to  leave  no  residual  magnetization  after 
dissipated"  was  calculated  from  the  formula: — Energy  dissipated  =:  coercive  force  X  maximum  induction  -j-  ir 


No. 
of 
Test. 

Description  of 
specimen. 

Temper. 

Specific 
electri- 
al  resis- 
tance. 

Magnetic  properties. 

Energy  dis- 
sipated per 
cycle. 

Maxi- 
mum in- 
luction. 

Residual 
induc- 
tion. 

Coer- 
cive 
force. 

Demag- 
netizive 
force. 

I 

Wrought  iron    . 

Annealed 

.01378 

18251 

7248 

2.30 

_ 

13356 

2 

3 

Malleable  cast  iron  . 
Gray  cast  iron  . 

_ 

.03254 
.10560 

12408 
10783 

7479 
3928 

8.80 
3-80 

_ 

34742 
13037 

4 

Bessemer  steel  . 
Whitworth  mild  steel 

Annealed 

.01050 
.OI080 

18196 
19840 

7860 
7080 

2.06 
1.63 

— 

I7I37 
10289 

6 

"               " 

" 

.01446 

18736 

9840 

6-73 

- 

40120 

7 

« 

(  Oil-hard- 
|    ened 

.01390 

18796 

11040 

11.00 

- 

65786 

8 

"               " 

Annealed 

.01559 

l6l20 

10740 

8.26 

- 

42366 

9 

" 

(  Oil-hard- 
(    ened 

.01695 

l6l20 

8736 

19.38 

- 

99401 

10 

Hadfield's  manganese  ) 
steel                             J  ' 

- 

•06554 

3IO 

- 

- 

- 

ii 

12 

Manganese  steel 

((                          U 

As  forged 
Annealed 

.05368 
.03928 

4623 
10578 

2202 
5848 

23-50 
33-86 

37.13 
46.10 

34567 
113963 

I3 

" 

(  Oil-hard- 
(    ened 

.05556 

4769 

2158 

27.64 

40.29 

41941 

14 

"            " 

As  forged 

.06993 

747 

- 

- 

- 

- 

15 

"           " 

Annealed 

.06316 

1985 

540 

24.50 

5°-39 

15474 

(  Oil-hard- 

16 

• 

j    ened 

.07066 

733 

~ 

~ 

"  • 

™ 

17 

Silicon  steel 

As  forged 

.06163 

15148 

II073 

9-49 

12.60 

45740 

18 

"        "          ... 

Annealed 

.06185 

14701 

8149 

7.80 

10.74 

36485 

19 

«                   ... 

(  Oil-hard- 
\    ened 

.06195 

14696 

8084 

12.75 

17.14 

59619 

20 

Chrome  steel     . 

As  forged 

.O2Ol6 

15778 

9318 

12.24 

13-87 

61439 

21 

"         "... 

Annealed 

.01942 

14848 

7570 

8.98 

12.24 

42425 

22 

"... 

(  Oil-hard- 
(    ened 

.02708 

13960 

8595 

38-15 

48-45 

169455 

23 

"         "... 

As  forged 

.01791 

14680 

7568 

18.40 

22.03 

85944 

24 

"         "... 

Annealed 

.01849 

13233 

6489 

15.40 

19.79 

64842 

25 

"... 

(  Oil-hard- 
\    ened 

•03035 

12868 

7891 

40.80 

56.70 

167050 

26 

27 

Tungsten  steel  . 

As  forged 
Annealed 

.02249 
.02250 

15718 
16498 

IOI44 
II008 

15-71 

17-75 
16.93 

78568 
80315 

(  Hardenec 

28 

"           "     .        .        . 

}    in  cold 

.02274 

- 

- 

- 

- 

- 

(    water 

(  Hardenec 

29 

"           "... 

<    in  tepid 

.02249 

15610 

9482 

30.10 

34-70 

149500 

(    water 

30 

"    (French)   . 

]  Oil  hard- 
(    ened 

.03604 

14480 

8643 

47-07 

64.46 

216864 

31 

"            " 

Very  hard 

.04427 

12133 

68l8 

51.20 

70.69 

197660 

32 

Gray  cast  iron    . 

_ 

.II4OO 

9148 

3l6l 

13.67 

17-03 

39789 

33 

Mottled  cast  iron 

- 

.06286 

10546 

5108 

12.24 

- 

41072 

34 

White 

- 

.05661 

9342 

5554 

12.24 

20.40 

36383 

35 

Spiegeleisen 

.10520 

385 

77 

SMITHSONIAN  TABLES. 


32O  TABLES  358-360. 

PERMEABILITY  OF  SOME  OF  THE  SPECIMENS  IN  TABLE  357. 

TABLE  358. 

This  table  gives  the  induction  and  the  permeability  for  different  values  of  the  magnetizing  force  of  some  of  the  sped- 
mens  in  Table  w.  The  specimen  numbers  refer  to  the  same  table.  The  numbers  in  this  table  have  been  taken 
from  the  curves  given  by  Dr.  Hopkinson,  and  may  therefore  be  slightly  in  error ;  they  are  the  mean  values  for 
rising  and  falling  magnetizations. 


Magnetiz- 

Specimen i  (iron). 

Specimen  8 
(annealed  steel). 

Specimen  9  (same  as 
8  tempered). 

Specimen  3 
(cast  iron). 

ing  ^rce 

B 

M 

B 

/* 

B 

/* 

B 

M 

I 

_ 

_ 

_ 

_ 

_ 

265 

265 

2 

200 

IOO 

— 

— 

— 

— 

700 

350 

3 

- 

- 

- 

- 

1625 

542 

5 

10050 

2OIO 

1525 

300 

750 

150 

3OOO 

600 

10 

12550 

I255 

9000 

900 

1650 

165 

5000 

500 

20 

30 
40 

!455° 
15200 
15800 

727 
507 
395 

11500 
12650 
13300 

575 
422 

332 

5875 
9875 
Il6oo 

294 

329 

290 

6000 
6500 
7100 

300 
217 
177 

5° 

16000 

320 

13800 

276 

I2OOO 

240 

735° 

149 

70 

16360 

234 

!435° 

205 

13400 

191 

7900 

"3 

IOO 

16800 

168 

14900 

149 

14500 

145 

8500 

85 

150 

17400 

116 

15700 

'25 

15800 

I0.5 

9500 

63 

200 

17950 

90 

16100 

80 

IOIOO 

80 

10190 

51 

Tables  359-363  give  the  results  of  some  experiments  by  Du  Bois,*  on  the  magnetic  properties  of  iron,  nickel,  and 
cobalt  under  strong  magnetizing  forces.  The  experiments  were  made  on  ovoids  of  the  metals  18  centimeters  long 
and  0.6  centimeters  diameter.  The  specimens  were  as  follows:  (i)  Soft  Swedish  iron  carefully  annealed  and 
having  a  density  7.82.  (2)  Hard  English  cast  steel  yellow  tempered  at  230°  C. ;  density  7.78.  (3)  Hard  drawn 
best  nickel  containing  99  %  Ni  with  some  SiO2  and  traces  of  Fe  and  Cu ;  density  8.82.  (4)  Cast  cobalt  giving 
the  following  composition  on  analysis :  Co  =  93. i.  Ni  =  5.8,  Fe  =  0.8,  Cu  =  0.2,  Si  =  o. i,  and  C  =  0.3.  The  speci- 
men was  very  brittle  and  broke  in  the  lathe,  and  hence  contained  a  surfaced  joint  held  together  by  clamps  during 
the  experiment.  Referring  to  the  columns,  H,  B,  and  /ut  have  the  same  meaning  as  in  the  other  tables,  ^  is  t|v 
magnetic  moment  per  gram,  and  /  the  magnetic  moment  per  cubic  centimeter.  H  and  S  are  taken  from  tne 
curves  published  by  Du  Bois ;  the  others  have  been  calculated  using  the  densities  given. 

MAGNETIC  PROPERTIES  OF  SOFT  IRON  AT  O°  AND  100°  C. 

TABLE  359. 


Soft  iron  at  o°  C. 

Soft  iron  at  100°  C. 

H 

i 

7 

B 

M 

H 

S 

7 

B 

M 

IOO 

180.0 

1408 

17790 

177.9 

IOO 

1  80.0 

1402 

17720 

177.2 

2OO 
400 

194-5 
208.0 

152! 
1627 

I93IO 
20830 

96.5 
52.1 

200 
400 

194.0 
2O7.O 

T1 
1613 

ig\T 
20660 

96.0 
51.6 

700 

•  2I3'5 

1685 

21870 

31.2 

700 

2134 

l663 

21590 

29.8 

IOOO 

218.0 

1705 

22420 

22.4 

IOOO 

215.0 

1674 

22040 

2I.O 

1200 

218.5 

1709 

22670 

18.9 

I2OO 

215-5 

1679 

22300 

18.6 

MAGNETIC  PROPERTIES  OF  STEEL  AT  0°  AND  100°  C. 

TABLE  360. 


Steel  at  o°  C. 

Steel  at  100°  C. 

H 

s 

7 

B 

P 

H 

S 

7 

B 

M 

IOO 

165.0 

1283 

16240 

162.4 

IOO 

165.0 

1278 

16170 

l6l.7 

200 

181.0 

1408 

17900 

89.5 

200 

180.0 

1395 

17730 

88.6 

4OO 

193.0 

1500 

19250 

48.1 

400 

191.0 

1480 

I9OOO 

47-5 

700 

199-5 

'552 

2O2IO 

28.9 

700 

197.0 

1527 

19890 

28.4 

IOOO 

203-5 

iJb 

2O9OO 

2O-9 

IOOO 

199.0 

1543 

20380 

20.4 

I2OO 

205.0 

!595 

21240 

17.7 

1500 

203.0 

1573 

2I27O 

14.2 

375°t 

2I2.O 

1650 

24470 

6.5 

3000 
5OOO 

205.5 
208.0 

1593 

1612 

23020 
25260 

7-7 
5-i 

"  Phil.  Mag."  5  series,  vol.  xxix. 

t  The  results  in  this  and  the  other  tables  for  forces  above  1200  were  not  obtained  from  the  ovoids  above  referred 
to,  but  from  a  small  piece  of  the  metal  provided  with  a  polished  mirror  surface  and  placed,  with  its  polished  face  nor- 
mal to  the  lines  of  force,  between  the  poles  of  a  powerful  electromagnet.  The  induction  was  then  inferred  from 
the  rotation  of  the  plane  of  a  polarized  ray  of  red  light  reflected  normally  from  the  surface.  (See  Kerr's  "  Constants," 
P- 33i.) 

SMITHSONIAN  TABLES. 


TABLES  361-367. 
MAGNETIC    PROPERTIES    OF    METALS. 

TABLE  361.  -  Cobalt  at  100°  0.  TABLE  362.— Nickel  at  100°  0. 


321 


H 

S 

/   |    B 

P 

2OO 

1  06 

848 

10850 

54.2 

300 

116 

928 

11960 

39-9 

500 
700 

127 
J3i 

1016 
1048 

13260 
13870 

19.8 

1000 

*34 

1076 

14520 

14-5 

1500 

138 

1104 

i538o 

10.3 

2500 

H3 

1144 

16870 

6.7 

4OOO 

*45 

1164 

18630 

4-7 

6OOO 

M7 

1176 

20780 

3-5 

9000 

149 

1192 

23980 

2.6 

At  o°  C.  this  specimen  gave  the  fol- 

lowing results  : 

7900  |  154 

1232  |  23380 

3-o 

H 

5 

/ 

B 

M 

100 

35-o 

309 

3980 

39-8 

200 
300 
500 

43-o 
46.0 
50.0 

380 
406 
441 

4966 

5399 
6043 

24.8 
1  8.0 

I2.I 

700 

51.5 

454 

6409 

9-1 

IOOO 

53.0 

468 

6875 

6.9 

1500 

56.0 

494 

7707 

5-1 

2500 

58.4 

8973 

3-6 

4000 

59-O 

520 

10540 

2.6 

6000 

59-2 

522 

12561 

2.1 

9000 

59-4 

524 

15585 

1-7 

I2OOO 

Ato°C 

.  this  sj 
low 

526 
Decimer 
ng  resn 

gave  th 
Its: 

e  fol- 

12300 

67-5 

595 

19782 

1.6 

TABLE  363.  —Magnetite. 

The  following  results  are  given  by  Du  Bois  *  for  a  specimen  of  magnetite. 


H 

/ 

B 

M 

500 
IOOO 
2000 
I2OOO 

325 

345 
350 
350 

8361 
9041 
10084 
20084 

I6.7 
9-0 

5-o 
i-7 

Professor  Ewing  has  investigated  the  effects  of  very  intense  fields  on  the  induction  in  iron  and  other  metals.f  The 
results  show  that  the  intensity  of  magnetization  does  not  increase  much  in  iron  after  the  field  has  reached  an  in- 
tensity of  looo  c.  g.  s.  units,  the  increase  of  induction  above  this  being  almost  the  same  as  if  the  iron  were  not 
there,  that  is  to  say,  dBf  dH  is  practically  unity.  For  hard  steels,  and  particularly  manganese  steels,  much  higher 
forces  are  required  to  produce  saturation.  Hadfield's  manganese  steel  seems  to  have  nearly  constant  susceptibility 
up  to  a  magnetizing  force  of  10,000.  The  following  tables,  taken  from  E  wing's  papers,  illustrate  the  effects  of 
strong  fields  on  iron  and  steel.  The  results  for  nickel  and  cobalt  do  not  differ  greatly  from  those  given  above. 


TABLE  364.  —  Lowmoor 
Wrought  Iron. 


TABLE  365.-Vlcker's 
Tool  Steel. 


TABLE  366. -Hadfield's 
Manganese  Steel. 


H 

/ 

B 

0 

3080 
6450 
10450 
13600 
16390 
18760 
18980 

1680 
1740 
1730 
1720 
1630 
1680 
1730 

24130 
28300 
32250 
35200 
36810 
39900 
40730 

7.83 
4-39 
3-09 
2-59 
2.25 
2.13 
2.15 

H 

/ 

B 

ft 

6210 

I  530 

25480 

4.10 

9970 

1570 

29650 

2.97 

I2I2O 

I55O 

31620 

2.60 

14660 

15530 

1610 

34550 
35820 

2.36 
2.3I 

H 

/ 

B 

M 

1930 

55 

2620 

I.36 

2380 

84 

3430 

1.44 

3350 

84 

4400 

I.3I 

5920 
6620 

in 
187 

73'o 
8970 

1.24 

i-35 

7800 

191 

10290 

1.30 

8^90 
9810 

Si 

11690 
14790 

i-39 
J-51 

TABLE  367. -Saturation  Values  for  Steels  of  Different  Kinds. 


- 

H 

/ 

B 

M 

I 

2 

3 

Bessemer  steel  containing  about  0.4  per  cent  carbon  .  .  . 
Siemens-Marten  steel  containing  about  0.5  per  cent  carbon 
Crucible  steel  for  making  chisels,  containing  about  0.6  per 

17600 
18000 

19470 

1770 
1660 

1480 

39880 
38860 

38010 

2.27 
2.l6 

!-95 

4 

Finer  quality  of  3  containing  about  0.8  per  cent  carbon  .  . 

18330 
19620 

1580 
1440 

38190 
77600 

2.0§ 
I.Q2 

5 

18700 

i  fjoo 

l87IO 

2.  07 

*  "  Phil.  Mag."  5  series,  vol.  xxix,  1890. 
SMITHSONIAN  TABLES. 


t  "  Phil.  Trans.  Roy.  Soc."  1885  and  1889. 


322  TABLES  368-370. 

TABLE  368. -MAGNETIC   PROPERTIES   OF  IRON   IN  VERY  WEAK   FIELDS. 

The  effect  of  very  small  magnetizing  forces  has  been  studied  by  C.  Baur *  and  by  Lord  Ray leigh.f  The  following 
short  table  is  taken  from  Baur's  paper,  and  is  taken  by  him  to  indicate  that  the  susceptibility  is  finite  for  zero  values 
of  H  and  for  a  finite  range  increases  in  simple  proportion  to  H.  He  gives  the  formula  £=15  +  100  ff,  or  /= 
je  ff-\-  loo  H2.  The  experiments  were  made  on  an  annealed  ring  of  round  bar  1.013  cms.  radius,  the  ring  having 
a  radius  of  9.432  cms.  Lord  Rayleigh's  results  for  an  iron  wire  not  annealed  give  k  =  6.4  +  5.  r  ff,  or  /  =  6.4  H 
-f  5  i  Hz.  The  forces  were  reduced  as  low  as  0.00004  c.  g.  s.,  the  relation  of  k  to  H  remaining  constant. 


First  experiment. 

Second  experiment. 

H 

k 

/ 

H 

k 

.01  580 

16.46 

2.63 

.0130 

13.5° 

.03081 
.07083 
.13188 

I7-65 
23.00 
28.90 

547 
16.33 
38.15 

.0847 
.0946 
.1864 

18.38 
20.49 
25.07 

.23011 

39.81 

91.56 

.2903 

32.40 

.38422 

58.56 

224.87 

•3397 

35-20 

TABLES  369,  370.-DISSIPATION  OF  ENERGY  IN  CYCLIC  MAGNETIZATION 
OF  MAGNETIC  SUBSTANCES. 

When  a  piece  of  iron  or  other  magnetic  metal  is  made  to  pass  through  a  closed  cycle  of 
magnetization  dissipation  of  energy  results.  Let  us  suppose  the  iron  to  pass  from  zero  magneti- 
zation to  strong  magnetization  in  one  direction  and  then  gradually  back  through  zero  to  strong 
magnetization  in  the  other  direction  and  thence  back  to  zero,  and  this  operation  to  be  repeated 
several  times.  The  iron  will  be  found  to  assume  the  same  magnetization  when  the  same  magne- 
tizing force  is  reached  from  the  same  direction  of  change,  but  not  when  it  is  reached  from  the 
oiher  direction.  This  has  been  long  known,  and  is  particularly  well  illustrated  in  the  permanency  of 
hard  steel  magnets.  That  this  fact  involves  a  dissipation  of  energy  which  can  be  calculated  from 
the  open  loop  formed  by  the  curves  giving  the  relation  of  magnetization  to  magnetizing  force  was 
pointed  out  by  Warburg  \  in  1881,  reference  being  made  to  experiments  of  Thomson,  §  where  such 
curves  are  illustrated  for  magnetism,  and  to  E.  Cohn,  ||  where  similar  curves  are  given  for  thermo- 
electricity. The  results  of  a  number  of  experiments  and  calculations  of  the  energy  dissipated 
are  given  by  Warburg.  The  subject  was  investigated  about  the  same  time  by  Ewing,  who  pub- 
lished results  somewhat  later.  T  Extensive  investigations  have  since  been  made  by  a  number  of 
investigators. 


TABLE  369.  -  Soft  Iron  Wire. 

(From  E  wing's  1885  paper.) 


Horse- 

Total 
induction 

Dissipation 
of  energy 

power 
wasted  per 

per  sq.  cm. 

in  ergs  per 

ton  at  100 

B 

cu.  cm. 

cycles  per 

sec. 

2000 

420 

0-74 

3OOO 

800 

1.41 

4000 

I230 

2.18 

5OOO 

1700 

3.01 

6OOO 

22OO 

3-89 

7000 

2760 

4.88 

8000 

3450 

6.10 

9000 

4200 

7-43 

10000 

5000 

8.84 

IIOOO 

5820 

10.30 

12000 

6720 

11.89 

13000 

7650 

13-53 

14000 

8650 

i5»3° 

15000 

9670 

17.10 

"Wied.  Ann."  vol.  xi. 
$  "  Wied.  Ann.;'  vol.  xiii.  p.  141. 
II  "  Wied.  Ann."  vol.  6. 

SMITHSONIAN  TABLES. 


TABLE  370.  —  Cable  Transformers. 

This  table  gives  the  results  obtained  by  Alexander  Siemens  with  one  of 
Siemens'  cable  transformers.  The  transformer  core  consisted  of  900 
soft  iron  wires  i  mm.  diameter  and  6  meters  long.**  The  dissipation 
of  energy  in  watts  is  for  100  complete  cycles  per  second. 


Mean  maxi- 
mum induc- 
tion density 
in  core. 
B 

Total  ob- 
served dis- 
sipation of 
energy  in  the 
core  in  watts 
per  112  Ibs. 

Calculated 
eddy  current 
loss  in  watts 
per  112  Ibs. 

Hysteresis 
loss  of 
energy  in 
watts  per 
112  Ibs. 

Hysteresis 
loss  of 
energy  in 
ergs  per 
cu.  cm. 
per  cycle. 

IOOO 
2000 

96.2 

.2 

39-2 
80.2 

602 
1231 

3000 

158.0 

36 

122.0 

1874 

4000 

231.2 

64 

167.2 

2566 

5000 

309-5 

100 

209.5 

3217 

6000 

390.1 

144 

246.1 

3779 

t  "  Phil.  Mag."  vol.  xxiii. 
§  "  Phil.  Trans.  Roy.  Soc."  vol. 
1T  "  Proc.  Roy.  Soc.*'  1882,  and  " 
"  Proc.  Inst.  of  Elect.  Eng."  Lond.,  1892. 


ins.  Roy.  Soc."  1885. 


TABLES  371-372.  323 

DEMAGNETIZING  FACTORS  FOR  RODS. 

TABLE  371. 

J7=true  intensity  o*  magnetizing  field,  H'  =  intensity  of  applied  field,  /=  in- 
tensity of  magnetization,  H=H' — NI. 

Shuddemagen  says :  The  demagnetizing  factor  is  not  a  constant,  falling  for 
highest  values  of  /to  about  1/7  the  value  when  unsaturated;  for  values  of  B 
(=H-\-\ic /)  less  than  10000,  N  is  approximately  constant;  using  a  solenoid 
wound  on  an  insulating  tube,  or  a  tube  of  split  brass,  the  reversal  method  gives 
values  for  A7"  which  are  considerably  lower  than  those  given  by  the  step-by-step 
method  ;  if  the  solenoid  is  wound  on  a  thick  brass  tube,  the  two  methods  prac- 
tically agree. 


Values  of  NX  10*. 

Cylinder. 

Ratio 
of 

Ballistic  Step  Method. 

Length 
to 
Diameter. 

Ellipsoid. 

Uniform 
Magneti- 

Magneto- 
metric 

Dubois. 

Shuddemagen  for  Range  of 
Practical  Constancy. 

zation. 

(Mann). 

Diameter. 

o.i  58  cm. 

0.3175  cm. 

i.i  1  1  cm. 

1.905  cm. 

5 

7015 

_ 

6800 

IO 

2549 

630 

2550 

2l6o 

- 

- 

1960 

15 

135° 

280 

1400 

I2O6 

— 

— 

1075 

20 

848 

160 

898 

775 

— 

— 

67I 

3° 

432 

70 

460 

393 

388 

350 

343 

40 

266 

39 

274 

238 

234 

212 

209 

g 

181 
132 

25 
18 

182 

162 
118 

116 

106 

149 
106 

11 

101 

80 

'98 

99 
78 

89 
69 

88 

66 

63 

90 

65 

7.8 

63  o 

55 

56 

100 

150 

It 

6.3 

2.8 

51.8 
25.1 

45 

20 

46 
23 

4i 

21 

21 

200 

16 

1.57 

15.2 

II 

12.5 

II 

II 

300 

7.5 

0.70 

7.5 

5-O 

4OO 

4-5 

0-39 

2.8 

C.  R.  Mann,  Physical  Review,  3,  p.  359;  1896. 

H.  DuBois,  Wied.  Ann.  7,  p.  942 ;  1002. 

C.  L.  B.  Shuddemagen,  Proc.  Am.  Acad.  Arts  and  Sci.  43,  P-  185,  1907  (Bibliography). 


TABLE  372. 

Shuddemagen  also  gives  the  following,  where  B  is  determined  by  the  step  method 

' 


Ratio  of 

Values  of  KX  10*. 

Length 

to 
Diameter. 

Diameter 
0.3175  cm. 

Diameter 
i.i  to  2.0  cm. 

15 

_ 

85.2 

2O 

— 

53*3 

25 

- 

36.6 

3° 

30-9 

27.3 

40 

1  8.6 

1  6.6 

£ 

12.7 
9-25 

1  1.6 

8-45 

80 

5-05 

100 

3  66 

3.26 

150 

1.83 

1.67 

SMITHSONIAN  TABLES. 


324 


TABLE  373. 


DISSIPATION  OF  ENERGY  IN  THE  CYCLIC  MAGNETIZATION  OF  VARIOUS 

SUBSTANCES. 

C.  P.  Steinmetz  concludes  from  his  experiments*  that  the  dissipation  of  energy  due  to 
hysteresis  in  magnetic  metals  can  be  expressed  by  the  formula  e  =  aB1-6,  where  e  is  the  energy 
dissipated  and  a  a  constant.  He  also  concludes  that  the  dissipation  is  the  same  for  the  same 
range  of  induction,  no  matter  what  the  absolute  value  of  the  terminal  inductions  may  be.  His 
experiments  show  this  to  be  nearly  true  when  the  induction  does  not  exceed  -}-  15000  c.  g.  s. 
units  per  sq.  cm.  It  is  possible  that,  if  metallic  induction  only  be  taken,  this  may  be  true  up  to 
saturation  ;  but  it  is  not  likely  to  be  found  to  hold  for  total  inductions  much  above  the  satura- 
tion value  of  the  metal.  The  law  of  variation  of  dissipation  with  induction  range  in  the  cycle, 
stated  in  the  above  formula,  is  also  subject  to  verification.! 


Values  of  Constant  a. 

The  following  table  gives  the  values  of  the  constant  a  as  found  by  Steinmetz  for  a  number  of  different  specimens. 
The  data  are  taken  from  his  second  paper. 


Number  of 
specimen. 

Kind  of  material. 

Description  of  specimen. 

Value  of 
a. 

I 

Iron  . 

2 

Wrought  bar     

.00326 

•5 

« 

J 

4 

«      ' 

Annealed            "            "          

.00458 

s 

"      .        . 

Thin  tin  plate    

.00286 

6 

« 

OOJ.2C 

Steel  ! 

Soft  galvanized  wire          

.00349 

3 

« 

Annealed  cast  steel  

.00848 

« 

10 

« 

Very  soft  annealed  cast  steel    

ii 

" 

Same  as  8  tempered  in  cold  water   .... 

.02792 

12 

" 

Tool  steel  glass  hard  tempered  in  water 

.07476 

13 

" 

"       "     tempered  in  oil         

.O267O 

14. 

til 

"       "     annealed  

OlSoQ 

1  T" 
15 

"     '        ") 

(  Same  as  12,  13,  and  14,  after  having  been  subjected  ) 

C  .06130 

16 

*     •        •  i 

<  to  an  alternating  m.  m.  f.  of  from  4000  to  6000  > 

<  .02700 

17 

«                V 

(  ampere  turns  for  demagnetization    .        .        .        .  ) 

(  .01445 

18 

Cast  iron  . 

Gray  cast  iron  

.01300 

19 

"        "    . 

"        "      "    containing  £  %  aluminium 

.01365 

20 

"        " 

«            «          f(                    <(               1  Oi               <« 

.01459 

(  A  square  rod  6  sq.  cms.  section  and  6.5  cms.  long,  ) 

21 

Magnetite  . 

<  from  the  Tilly  Foster  mines,  Brewsters,   Putnam  > 

.02348 

(  County,  New  York,  stated  to  be  a  very  pure  sample  ; 

22 

Nickel 

Soft  wire  

.0122 

(  Annealed    wire,     calculated    by    Steinmetz    from  ) 

_/r 

23 

• 

j  Ewing's  experiments        J 

.OI5O 

24 

«< 

Hardened,  also  from  Ewing's  experiments 

.0385 

25 

Cobalt 

(  Rod  containing  about  2  %  of  iron,  also  calculated  ) 
/  from  Ewing's  experiments  by  Steinmetz          .        .  ) 

.0120 

Consisted   of  thin  needle-like  chips  obtained  by 

milling  grooves  about  8  mm.  wide  across  a  pile  of 
thin  sheets  clamped  together.     About  30  %  by  vol- 

26 

Iron  filings 

ume  of  the  specimen  was  iron, 
ist  experiment,  continuous  cyclic  variation  of  m.  m.  ) 
f.  1  80  cycles  per  second    ) 

•0457 

2d  experiment,  114  cycles  per  second 

.0396 

[  3d          "            79~9r  cycles  per  second  . 

•0373 

SMITHSONIAN  TABLES. 


*  "Trans.  Am.  Inst.  Elect.  Eng."  January  and  September,  1892. 
t  See  T.  Gray,  "  Proc.  Roy.  Soc."  vol.  Ivi. 


TABLE  374. 
ENERGY  LOSSES  IN  TRANSFORMER  STEELS. 


325 


Determined  by  the  wattmeter  method. 

Loss  per  cycle  per  cc  =  AB*-\-bnB<>,  where  #  =  flux  density  in  gausses  and  «=  frequency  in 

cycles  per  second,   x  shows  the  variation  of  hysteresis  with  B  between  5000  and  10000  gausses, 

and  y  the  same  for  eddy  currents. 


Ergs  per  Gramme  per  Cycle. 

Watts  per  Pound  at  60  Cy- 
cles and  10000  Gausses. 

Thick- 

10000 Gausses. 

5000  Gausses. 

«-    <0 

Designation. 

ness. 

X 

y 

a 

§  §f 

cm. 

i  « 

S3 

J'g't 

Hyste- 

Tntal 

Hyste- 

U   M 

Hyste- 

^ H  i 

>,t5  N 

resis. 

J.OUU* 

resis. 

%** 

resis. 

f85 

|sl 

Unannealed 

A 

0.0399 

r599 

1  86 

562 

46 

1.51 

2.O2 

0.00490 

0.41 

4-35 

4.76 

B 

.0326 

1156 

I34 

384 

36 

i»S9 

1.89 

•00358 

0.44 

3-H 

3-58 

C 

.0422 

1032 

242 

356 

70 

1.51 

1.79 

.00319 

0.47 

2.81 

3.28 

D 

.0381 

1009 

184 

353 

48 

1.52 

1.94 

.00312 

0.44 

2.74 

3-18 

Annealed 

E 
F 

.0476 
.0280 

III 

236 

100 

246 
220 

58 

27 

!:lo 

2.  02 

.88 

.00227 
.00206 

0.36 

0.44 

2.OO 

1.81 

2.36 
2.25 

G 

H* 

•0394 
.0307 

563 
4I2 

2IO 
I46 

193 
138-5 

54 
39 

1.54 

.96 

.00174 
.00127 

0.47 
0.54 

1.  12 

2.00 

1.66 

T 

.0318 

2O2 

111.5 

55 

1.62 

.88 

.00105 

0.70 

0.93 

1.63 

K* 

.0282 

394 

124 

130 

32 

1.61 

.90 

.OOI22 

0.54 

1.07 

1.61 

L 
B 

.0346 
.0338 

354 

184 
2OO 

I25 
116 

50 
57 

1.61 
1.61 

1.81 

.OOIlS 
.OOI  IO 

0.535 

0.61 

1.035 
0.96 

i-57 
'-57 

M 

N 

.0335 
.0340 

372 
321 

I78 
210 

127 
105 

46 

56 

1:11 

i'|o 

.00115 
.00099 

o-55 
0.63 

1.  01 

0.87 

1.56 
1.50 

P 

•0437 

334 

l84 

107 

50 

1.64 

1.88 

.OOIO3 

0.34 

0.91 

1-25 

Silicon  steels 

Qt 

.0361 

303 

54 

98 

15 

1.63 

- 

.00094 

0.14 

0.825 

0.965 

R 

.0315 

288 

42 

93 

ii 

1.64 

— 

.00089 

0.15 

0.78 

0-93 

S 
T 

.0452 
•0338 

278 
250 

90 

78 

18 
18 

1.63 
1.68 

: 

.00086 
.00077 

0.12 

0.18 

a685 

0.875 
0.86 

U 

.0346 

270 

42 

86 

12 

1.66 

_ 

.00084 

O.I2 

O.735 

0-855 

v* 
w* 

.0310 
•°3°5 

25I-5 
197 

47 
43 

79 
62.3 

13 

12.4 

1.68 
1.67 

- 

.00078 
.00061 

0.17 

0.16 

0.685 
0-535 

0-855 
0.695 

X 

.0430 

200 

65 

64.2 

16.6 

1.65 

~ 

.OOO62 

0.12 

0-545 

0.665 

German. 


t  English. 


. 

t  In  order  to  make  a  fair  comparison,  the  eddy  current  loss  has  been  computed  for  a  thickness  01  0.0357  cm. 
No.  29),  assuming  the  loss  proportional  to  the  thickness. 

Lloyd  and  Fisher,  Bull.  Bur.  Standards,  5,  p.  453  J  «9°9- 

Note.  —For  formula  and  tables  for  the  calculation  of  mutual  and  sell  Inductance  see  Bulletin  Bureau 
of  Standards,  vol.  8,  p.  1-237,  1912. 


SMITHSONIAN  TABLES. 


326 


TABLE  375. 
MAGNETO-OPTIC  ROTATION. 


Faraday  discovered  that,  when  a  piece  of  heavy  glass  is  placed  in  magnetic  field  and  a  beam 
of  plane  polarized  light  passed  through  it  in  a  direction  parallel  to  the  lines  of  magnetic  force, 
the  plane  of  polarization  of  the  beam  is  rotated.  This  was  subsequently  found  to  be  the  case 
with  a  large  number  of  substances,  but  the  amount  of  the  rotation  was  found  to  depend  on  the 
kind  of  matter  and  its  physical  condition,  and  on  the  strength  of  the  magnetic  field  and  the 
wave-length  of  the  polarized  light.  Verdet's  experiments  agree  fairly  well  with  the  formula  — 


where  c  is  a  constant  depending  on  the  substance  used,  /  the  length  of  the  path  through  the 
substance,  H  the  intensity  of  the  component  of  the  magnetic  field  in  the  direction  of  the  path 
of  the  beam,  r  .the  index  of  refraction,  and  A.  the  wave-length  of  the  light  in  air.  If  H  be  dif- 
ferent, at  different  parts  of  the  path,  IH  is  to  be  taken  as  the  integral  of  the  variation  of  mag- 
netic potential  between  the  two  ends  of  the  medium.  Calling  this  difference  of  potential  z>,  we 
may  write  6  =  Av,  where  A  is  constant  for  the  same  substance,  kept  under  the  same  physical 
conditions,  when  the  one  kind  of  light  is  used.  The  constant  A  has  been  called  "  Verdet's  con- 
stant," *  and  a  number  of  values  of  it  are  given  in  Tables  376-380.  For  variation  with  tempera- 
ture the  following  formula  is  given  by  Bichat  :  — 

R  =  RQ  (i  —  0.00104  1  —  O.OOOOI4*2), 

which  has  been  used  to  reduce  some  of  the  results  given  in  the  table  to  the  temperature  corre- 
sponding to  a  given  measured  density.  For  change  of  wave-length  the  following  approximate 
formula,  given  by  Verdet  and  Becquerel,  may  be  used  :  — 


where  p.  is  index  of  refraction  and  A  wave-length  of  light. 

A  large  number  of  measurements  of  what  has  been  called  molecular  rotation  have  been  made, 
particularly  for  organic  substances.  These  numbers  are  not  given  in  the  table,  but  numbers 
proportional  to  molecular  rotation  may  be  derived  from  Verdet's  constant  by  multiplying  in  the 
ratio  of  the  molecular  weight  to  the  density.  The  densities  and  chemical  formulae  are  given  in 
the  table.  In  the  case  of  solutions,  it  has  been  usual  to  assume  that  the  total  rotation  is  simply 
the  algebraic  sum  of  the  rotations  which  would  be  given  by  the  solvent  and  dissolved  substance, 
or  substances,  separately  ;  and  hence  that  determinations  of  the  rotary  power  of  the  solvent 
medium  and  of  the  solution  enable  the  rotary  power  of  the  dissolved  substance  to  be  calculated. 
Experiments  by  Quincke  and  others  do  not  support  this  view,  as  very  different  results  are 
obtained  from  different  degrees  of  saturation  and  from  different  solvent  media.  No  results  thus 
calculated  have  been  given  in  the  table,  but  the  qualitative  result,  as  to  the  sign  of  the  rotation 
produced  by  a  salt,  may  be  inferred  from  the  table.  For  example,  if  a  solution  of  a  salt  in  water 
gives  Verdet's  constant  less  than  0.0130  at  20°  C.,  Verdet's  constant  for  the  salt  is  negative. 

The  table  has  been  for  the  most  part  compiled  from  the  experiments  of  Verdet,t  H.  Becque- 
rel,f  Quincke,  §  Koepsel,||  Arons,1f  Kundt,**  Tahn,tt  Schonrock,ti  Gordon,  §§  Rayleigh  and 
Sidgewick,||||  PerkhVH  Bichat.*** 

As  a  basis  for  calculation,  Verdet's  constant  for  carbon  disulphide  and  the  sodium  line  D  has 
been  taken  as  0.0420  and  for  water  as  0.0130  at  20°  C. 

*  The  constancy  of  this  quantity  has  been  verified  through  a  wide  range  of  variation  of  magnetic  field  by 
H.  E.  J.  G.  Du  Bois  (Wied.  Ann.  vol.  35),  p.  137,  1888. 

t  "  Ann.  de  Chim.  et  de  Phys."  [3]  vol.  52,  p.  129,  1858. 

t  "  Ann.  de  Chim.  et  de  Phys."  [5]  vol.  12;  "  C.  R."  vols.  90,  p.  1407,  1880,  and  100,  p.  1374,  1885. 

§  "  Wied.  Ann."  vol.  24,  p.  606,  1885. 

II  "  Wied.  Ann."  vol.  26,  p.  456,  1885. 

IT  "Wied.  Ann."  vol.  24,  p.  161,  1885. 
**  "  Wied.  Ann."  vols.  23,  p.  228,  1884,  and  27,  p.  191.  1886. 
tt  "  Wied.  Ann."  vol.  43,  p.  280,  1891. 
it  "Zeits.  fiir  Phys.  Chem."  vol.  n,  p.  753,  1893. 
§§  "Proc.  Roy.  Soc."  36,  p.  4,  1883. 
HII  "Phil.  Trans.  R.  S."  176,  p.  343,  1885. 
Till  "Jour.  Chem.  Soc." 

de  Phys."  vols.  8,  p.  204,  1879,  and  9,  p.  204  and  p.  275,  1880. 


'Jour.  Chem.  Soc.' 
***  "  Jour. 

SMITHSONIAN  TABLES. 


TABLE  376. 
MAGNETO-OPTIC  ROTATION. 

Solids. 


Substance. 

Formula. 

Wave- 
length. 

Verdet's 
Constant. 
Minutes. 

Temp.  C. 

Authority. 

0.589 

l8-20° 

Quincke. 

Blende         

ZnS 

c 

« 
u 

0.2234 

o.oi  27 

15 
T  e 

Becquerel. 

Diamond                   .     . 

Lead  borate     .... 

PbB2O4 

« 

0.0600 

1  j 
15 

« 

Selenium     

Se 

0.687 

0.4625 

15 

" 

Sodium  borate     .     .     . 

Na2B4O7 

0.589 

O.OI7O 

15 

* 

Cu2O 

0.68? 

o.  cqo8 

1C 

« 

CaFl2 

W.V^W  j 

0.2534 
•3655 

jy^ 

0.05989 
.02526 

J 

20 

Meyer,  Ann.  der 
Physik,  30,  1909. 

4358 

.01717 

.4916 

_6_. 

.01329 

" 

•5^9 
1.  00 

.00897 
.OO3OO 

« 

2.50 

.00049 

" 

3.00 

.00030 

M 

Glass,  Jena  :  Medium  phosphate  crn. 
Heavy  crown,  01143    . 

0.589 

0.0161 

O.O22O 

18 

DuBois,  Wied.  Ann. 
51,  1894. 

Light  flint,        0451 

" 

0.0317 

" 

Heavy  flint      0500 

" 

0.0608 

" 

8163.    . 
Zeiss,  Ultraviolet  

O.7I7 

0.0888 
O.O674 

16 

Landau,    Phys.   ZS. 

JO 

"ft 

.0^69 

9,1908. 



0.436 

o  y 

.0311 

" 

Quartz,  along  axis,  i.e., 
plate  cut  1  to  axis 

SiO2 

0.2194 

•2573 
.3609 

0.1587 
.1079 
.04617 

20 

M 

Borel,Arch.  sc.phys. 
1  6,  1903. 

.4800 

.02574 

" 

.5892 

.01664 

" 

Rock  salt    

NaCl 

•6439 
0.2599 

.01368 
0.2708 

20 

Meyer,  as  above. 

.3100 

.1561 

M 

.4046 

.0775 

u 

.4916 

.0483 

" 

.6708 

.0245 

" 

I.OO 

.01050 

" 

2.00 

.00262 

M 

Sugar,  cane  :  along 
axis  HA 

C"H*°" 

4.00 
0.451 

ffi 

.00069 
.0122 
.0076 
.0066 

2O 
U 

Voigt,  Phys.  ZS.  9, 
1908. 

axisIIA1      .    . 

_ 

0.451 

0.0129 

M 

KC1 

'.626 

0.4358 
.5461 

.0084 
.0075 
0.0534 
.0316 

« 

2O 

Meyer,  as  above. 

.6708 

.02012 

.90 

.01051 

i.  20 

.00608 

" 

2.00 

.00207 

" 

4.00 

.00054 

N 

SMITHSONIAN   TABLES. 


328 


TABLE  377. 
MAGNETO-OPTIC  ROTATION. 

Liquids :  Verdet's  Constant  for  A  =  0.589/*. 


Substance. 

Chemical  formula. 

Density  in 
grams  per 
c.  c. 

Verdet's 
constant 
in  minutes. 

Temp.  C 

Authority. 

Acetone 

C8H60 

0.7947 

O.OII3 

20° 

Jahn. 

Acids  :  Acetic 

C2H402 

1.0561 

.0105 

21 

Perkin. 

"       Butyric 

C4H802 

0.9663 

.OIl6 

15 

"       Formic 

CH202 

1.2273 

.0105 

li 

"       Hydrochloric 

HC1 

1.2072 

.0224 

" 

"       Hydrobromic 

HBr 

I-7859 

•°343 

" 

"       Hydroiodic 

HI 

1-9473 

•OS1  5 

" 

"       Nitric 

HNO8 

1.5190 

.0070 

13 

* 

"       Sulphuric 

H2S04 

.0121 

15 

Becquerel. 

Alcohols  :  Amyl 

C6HUOH 

0.8107 

.0128 

20 

Jahn. 

Butyl 

C4H9OH 

0.8021 

.0124 

" 

« 

Ethyl 

C2H5OH 

0.7900 

.0112 

" 

tt 

"           Methyl 

CH3OH 

0.7920 

.0093 

" 

" 

"          Propyl 

C8H7OH 

0.8042 

.0120 

" 

" 

Benzol 

C6H6 

0.8786 

.0297 

tt 

M 

Bromides  :  Bromoform 

CHBrs 

2.9021 

.0317 

15 

Perkin. 

Ethyl 

C2H5Br 

1.4486 

.0183 

tt 

"           Ethylene 

C2H4Br2 

2.1871 

.0268 

« 

tt 

Methyl 

CH3Br 

1733! 

.0205 

0 

tt 

Methylene 

CH2Br2 

2.4971 

.0276 

15 

" 

Carbon  bisulphide 

CS2 

•°433 

0 

Gordon. 

<«               >< 

«« 

— 

.0420 

18 

Rayleigh. 

Chlorides  :  Amyl 

CHC1 

0.8740 

.0140 

20 

Jahn. 

"           Arsenic 

AsCl8 

— 

.0422 

IS 

Becquerel. 

"           Carbon 

CC14 

— 

.0321 

« 

"           Chloroform 

CHC18 

1.4823 

.0164 

20 

Jahn. 

Ethyl 

C2H5C1 

0.9169 

0.0138 

6 

Perkin. 

Ethylene 

C2H4C12 

1.2589 

.0166 

15 

t* 

"           Methyl 
Methylene 

CH3C1 
CH2C12 

1-3361 

.0170 
.0162 

«« 

Becquerel. 
Perkin. 

Sulphur  bi- 

S2C12 

•0393 

" 

Becquerel. 

"           Tin  tetra 

SnCl4 

— 

.0151 

" 

'< 

Zinc  bi- 

ZnCl2 

— 

-°437 

tt 

«< 

lodides  :  Ethyl 

C2H6I 

1.9417 

/• 
.0296 

« 

Perkin. 

Methyl 

CH3I 

2.2832 

•0336 

« 

« 

"         Propyl 

C3H7I 

1.7658 

.0271 

« 

K 

Nitrates  :  Ethyl 

C2H6O.NO2 

1.1149 

.0091 

tt 

« 

Methyl 

CH3O.NO2 

1.2157 

.0078 

« 

" 

Propyl 

C3H7O.NO2 

1.0622 

.0100 

« 

" 

Paraffins:  Heptane 

C7Hie 

0.6880 

.0125 

M 

" 

Hexane 

C6Hi4 

0.6743 

.0125 

« 

" 

Pentane 

C5H12 

0.6332 

.0118 

«« 

«< 

Phosphorus,  melted 
Sulphur,  melted 

P 

S 

.1316 

.0803 

33 
114 

Becquerel. 
it 

Toluene 
Water,  A  =  0.2496  ju 

C7H8 
H20 

0.8581 

.0269 
.1042 

28 

Schonrock. 
See  Meyer, 

0.275 

.0776 

Ann.  der 

0.3609 

.0384 

Physik,  30, 

0.4046 

.0293 

1969.  Meas- 

0.500 

.0184 

ures  by 

0.589 

.0131 

Landau, 

0.700 

.0091 

Siertsema, 

I.OOO 

.00410 

Ingersoll. 

1.300 

.00264 

Xylene 

C8H10 

0.8746 

.0263 

27 

Schonrock. 

SMITHSONIAN  TABLES. 


TABLE  378. 

MAGNETO-OPTIC  ROTATION. 

Solutions  of  acids  and  salts  in  water.    Verdet's  constant  for  A  =  0.689/u. 


329 


Chemical 
formula. 

Density, 
grams 
per  c.  c. 

Verdet's 
constant 
in  minutes. 

Temp. 

* 

Chemical 
formula. 

Density, 
grams 
per  c.  c. 

Verdet's 
constant 
in  minutes. 

Tecmp' 

* 

C8H60 

0.9715 

O.OI29 

20° 

J 

LiCl 

1.0619 

0.0145 

20° 

I 

HBr 

J-3775 

0.0244 

u 

P 

M 

1.0316 

0.0143 

" 

* 

1.1163 

0.0168 

" 

" 

MnCl2 

1.1966 

0.0167 

15 

B 

HC1 

I-I573 

O.O2O4 

" 

a 

" 

1.0876 

o.oi  50 

M 

" 

M 

1.0762 

0.0168 

" 

u 

HgCl2 

1.0381 

0.0137 

16 

S 

" 

1.0158 

O.OI4O 

u 

J 

" 

1.0349 

0.0137 

M 

11 

HI 

1.9057 

0.0499 

" 

P 

NiCl2 

1.4685 

0.0270 

y 

B 

" 

1-4495 

0.0323 

ft 

(i 

" 

1.2432 

0.0196 

" 

" 

1.1760 

O.O2O5 

tt 

" 

" 

1-1233 

O.OI62 

u 

" 

HN03 

1.3560 

O.OIO5 

" 

" 

KC1 

1.  6OOO 

0.0163 

<« 

M 

NH3 

0.8918 

0.0153 

15 

(i 

" 

1.0732 

0.0148 

20 

J 

NH4Br 

1.2805 

0.0226 

" 

NaCl 

1.2051 

O.OlSo 

15 

B 

M 

1.1576 

o.o  1  86 

" 

" 

M 

1.0546 

0.0144 

" 

BaBr2 

L5399 

0.0215 

20 

I 

" 

1.0418 

O.OI44 

u 

J 

" 

1.2855 

0.0176 

" 

SrCl2 

I.I92I 

O.OI62 

u 

CdBr2 

1.3291 

0.0192 

M 

" 

" 

1.0877 

0.0146 

M 

«< 

" 

1.1608 

0.0162 

*i 

M 

SnCl2 

1.3280 

0.0266 

15 

V 

CaBr2 

1.2491 

0.0189 

" 

" 

" 

I.III2 

0.0175 

" 

" 

I-I337 

0.0164 

" 

" 

ZnCl2 

I.285I 

0.0196 

'< 

" 

KBr 

1.1424 

0.0163 

" 

" 

" 

i-I595 

0.0161 

" 

«« 

" 

1.0876 

0.0151 

" 

'« 

K2CrO4 

I-3598 

0.0098 

tt 

« 

NaBr 

1.1351 

0.0165 

" 

" 

K2Cr2O7 

1.0786 

0.0126 

« 

" 

" 

1.0824 

0.0152 

tt 

* 

Hg(CN)a 

1.0638 

0.0136 

16 

S 

SrBr2 

1.2901 
1.1416 

o.oi  86 
0.0159 

« 

u 

NH4I 

1.0605 
1.5948 

0.0135 
0.0396 

y 

P 

K2C08 

1.1906 

0.0140 

20 

" 

(4 

1.5109 

0.0358 

" 

Na2CO3 

1.  1006 

0.0140 

" 

" 

" 

1.2341 

0.0235 

u 

" 

" 

1.0564 

0.0137 

" 

" 

Cdl 

1-5156 

0.0291 

20 

J 

NH4C1 

1.0718 

0.0178 

15 

V 

" 

1.1521 

0.0177 

" 

" 

BaCl2 

1.2897 

0.0168 
0.0149 

2O 

M 

J4 

KI 

1.6743 
1.3398 

0.0338 
0.0237 

y 

B 

CdCl2 

1.3179 

0.0185 

" 

M 

" 

1.1705 

0.0182 

" 

" 

" 

l-27SS 

0.0179 

W 

" 

Nal 

I-I939 

0.0200 

" 

J 

" 

1.1732 

0.0  1  60 

H 

" 

" 

1.1191 

0.0175 

u 

" 

4< 

'•'SS1 

0.0157 

" 

* 

NH4NO8 

1.2803 

O.OI2I 

15 

P 

CaCl2 

1.1504 

0.0165 

" 

" 

KN03 

1.0634 

O.OI3O 

20 

J 

" 

1.0832 

0.0152 

" 

" 

NaNO8 

I.III2 

O.OI3I 

" 

u 

CuCl2 

1.5158 

0.0221 

IS 

B 

U203N206 

2.0267 

0.0053 

u 

B 

<« 

1-1330 

o.oi  56 

« 

" 

tt 

1  .  1  963 

O.OII5 

* 

" 

FeCl2 

O.OO25 

15 

M 

(NH4)2S04 

1.2286 

O.OI4O 

15 

P 

" 

1.2141 

1.1093 

0.0099 
O.OIlS 

n 

H 

NH4.HSO4 
BaSO4 

I.44I7 
I.I788 

0.0085 
O.OI34 

(( 
2O 

J 

Fe2Cl6 

'•6933 

—  0.2026 

•j 

• 

" 

1.0938 

0.0133 

** 

" 

I-53I5 

—  O.II4O 

" 

" 

CdS04 

I.I762 

0.0139 

" 

" 

« 

1.3230 

—  0.0348 

" 

" 

• 

1.0890 

0.0136 

" 

44 

« 

1.1681 

—O.OOI5 

u 

" 

Li2S04 

1.1762 

0.0137 

" 

" 

«< 

1.0864 

O.OOSI 

«' 

« 

MnS04 

I.244I 

0.0138 

" 

44 

« 

1.0445 

O.OII3 

u 

" 

K2SO4 

1-0475 

0.0133 

" 

44 

1.0232 

0.0122 

NaSO4 

I.  O66l 

0.0135 

*  J,  Jahn,  P,  Perkin,  V,  Verdet,  B,  Becquerel,  S,  Schonrock;  see  p.  326  for  references. 
SMITHSONIAN  TABLES. 


330 


TABLES  379,  380. 

TABLE  379. -Magneto- Optic  Rotation. 
Gases. 


Verdet's 

Substance. 

Pressure. 

Temp. 

constant  in 

Authority. 

minutes. 

Atmospheric  air 
Carbon  dioxide 

Atmospheric 
tt 

Ordinary 

6.83  X  io-6 
13.00      " 

Becquerel. 

Carbon  disulphide  . 

74  cms. 

70°  C. 

23.49      " 

Bichat. 

Ethylene          ... 
Nitrogen          ... 

Atmospheric 

u 

Ordinary 

34-48      « 
6.92      " 

Becquerel. 

Nitrous  oxide  ... 

II 

« 

16.90      " 

ii 

Oxygen   .... 
Sulphur  dioxide 

u 
u 

i< 
ii 

6.28      " 

3J-39     " 

M 

U 

"**'"•'• 

246  cms. 

20°  C. 

3840     " 

Bichat. 

See  also  Siertsema,  Ziting.  Kon.  Akad.  Watt.,  Amsterdam,  7,  1899;  8,  1900. 

Du  Bois  shows  that  in  the  case  of  substances  like  iron,  nickel,  and  cobalt  which  have  a  variable 
magnetic  susceptibility  the  expression  in  Verdet's  equation,  which  is  constant  for  substances  of  con- 
stant susceptibility,  requires  to  be  divided  by  the  susceptibility  to  obtain  a  constant.  For  this 
expression  he  proposes  the  name  "  Kundt's  constant."  These  experiments  of  Kundt  and  Du 
Bois  show  that  it  is  not  the  difference  of  magnetic  potential  between  the  two  ends  of  the  medium, 
but  the  product  of  the  length  of  the  medium  and  the  induction  per  unit  area,  which  controls  the 
amount  of  rotation  of  the  beam. 


TABLE  380.  — Verdet's  and  Kundt's  Constants. 


The 


following  short  table  is  cjuoted  from  Du  Bois'  paper.    The  quantities  are  stated  in  c.  g.  s. 
measure  (radians)  being  used  in  the  expression  of  "  Verdet's  constant  "  and  "  Kundt's  co 


measure,  circular 
Kundt's  constant." 


Verdet's  constant. 

Name  of  substance. 

Magnetic 
susceptibility. 

Wave-length 
of  light 

Kundt's 
constant. 

Number. 

Authority. 

Cobalt      . 

_ 

_ 

6.44  X  io-6 

3-99 

Nickel     . 

_ 

_ 

_ 

g 

3-J5 

Iron 
Oxygen  :  i  atmo.    . 
Sulphur  dioxide 

+  O.OI26XICT5 

—  0.0751     " 

0.000179  X  io~6 
0.302    '       " 

Becquerel. 

« 

8 

2.63 
0.014 
—4.00 

Water      . 

—0.0694    " 

0-377 

Arons 

—  5-4 

Nitric  acid       . 

—0.0633     " 

0.356 

Becquerel. 

-5.6 

Alcohol    . 

—0.0566    " 

0.330 

De  la  Rive. 

-5.8 

Ether.      . 
Arsenic  chloride 

—  0.0541     " 

—  0.0876    " 

0-315 

1.222                ". 

M 

Becquerel. 

-5.8 
—14.9 

Carbon  disulphide  . 
Faraday's  glass 

-0.0716    " 
—0.0982    " 

1.222                " 
1.738 

Rayleigh. 
Becquerel. 

« 

—17.1 
—17.7 

SMITHSONIAN  TABLES. 


TABLES  381-383. 
TABLE  381.  —  Values  of  Kerr's  Constant.* 


331 


Du  Bois  has  shown  that  the  rotation  of  the  major  axis  of  vibration  of  radiations  normally  reflected  from  a  magnet  is 
algebraically  equal  to  the  normal  component  of  magnetization  multiplied  into  a  constant  K.  He  calls  this  con- 
stant K,  Kerr  s  constant  for  the  magnetized  substance  forming  the  magnet. 


Color  of  light. 

Spectrum 
line. 

Wave- 
length 
in  cms. 
X  io8 

Kerr's  constant  in  minutes  per  c.  g.  s.  unit  of  magnetization. 

Cobalt. 

Nickel. 

Iron. 

Magnetite. 

Red  

Li  a 

D 
b 
F 
G 

67.7 
62.O 

58-9 
51-7 
48.6 

43-1 

—  0.0208 
—0.0198 
—0.0193 
—  0.0179 
—  O.OlSo 
—0.0l82 

—0.0173 

—  0.0160 
—0.0154 
—  0.0159 
—0.0163 
—0.0175 

—0.0154 
—  0.0138 
—0.0130 
—  O.OIII 
—  O.OIOI 

—  0.0089 

+0.0096 
+0.0120 
+0.0133 
+O.OO72 
+0.0026 

1 

Red 

Yellow        .     .     . 

Green     

Blue  

Violet    . 

*  H.  E.  J.  G.  Du  Bois,  "  Phil.  Mag."  vol.  29. 


TABLE  382.— Dispersion  of  Kerr  Effect. 


Wave-length. 

0.51* 

I.O/* 

i-Sf* 

2.0/* 

2.5M 

Steel      .     .     . 

—H'. 

—  iff. 

-14'. 

—  II'. 

-C/.0 

Cobalt  .     .     . 

-9-5 

—"•5 

-9-5 

II. 

-6.5 

Nickel   .    .    . 

—  5-5 

—  4.0 

0 

+1-75 

+3-o 

Field  Intensity^  10,000  C.  G.  S.  units.     (Intensity  of  Magnetization  =  about  800  in  steel,  700  to  800  in  cobalt, 
about  400  in  nickel).     Ingersoll,  Phil.  Mag.  n,  p.  41,  1906. 


TABLE  383.  -  Dispersion  of  Kerr  Effect. 


Mirror. 

Field 
(C.  G.  S.) 

•  4'M 

•44i" 

•48** 

•  52M 

.56^ 

*» 

•64* 

.66/u. 

Iron      .     . 

21,500 

—.25 

—.26 

—.28 

—•31 

-36 

—.42 

—•44 

-•45 

Cobalt  .     . 

2O,OOO 

—36 

—•35 

—•34 

—•35 

—•35 

—•35 

—•35 

-.36 

Nickel  .     . 

19,000 

—.16 

—•iS 

—•13 

—•13 

—.14 

—.14 

—.14 

—.14 

Steel     .    . 

19,200 

—.27 

—.28 

—31 

—•35 

-.38 

.—.40 

—  44 

—45 

Invar    .    . 

19,800 

—  .22 

—.23 

—.24 

—•23 

-23 

—.22 

—•23 

—•23 

Magnetite 

16,400 

—.07 

—.02 

+.04 

+.06 

+.08 

+.06 

+.04 

+•03 

Foote,  Phys.  Rev.  34,  p.  96,  1912. 

See  also  Ingersoll,  Phys.  Rev.  35,  p.  312,  1912,  for  "The  Kerr  Rotation  for  Transverse  Magnetic  Fields,"  and 
Snow,  1.  c.  2,  p.  29,  1913,  "  Magneto-optical  Parameters  of  Iron  and  Nickel." 

SMITHSONIAN  TABLES. 


332 


TABLE  384. 
MAGNETIC   SUSCEPTIBILITY. 

If  31  is  the  intensity  of  magnetization  produced  in  a  substance  by  a  field  strength 


then  the 


magnetic  susceptibility  H  =  31  /$•  This  is  generally  referred  to  the  unit  mass;  italicized  figures 
refer  to  the  unit  volume.  The  susceptibility  depends  greatly  upon  the  purity  of  the  substance,  es- 
pecially its  freedom  from  iron.  The  mass  susceptibility  of  a  solution  containing  p  per  cent  by  weight 
of  a  water-free  substance  is,  if  H0  is  the  susceptibility  of  water,  (p/ioo)  H  +  (i  —  p/ioo)  H0. 


Substance. 

Suscep- 
tibility. 

1" 

Remarks 

Substance. 

Suscep- 
tibility. 

!° 

Remarks 

Ag         

—  O.IQ 

18° 

K2CO3  .     , 

—  O  ^O 

20° 

Sol'n 

AgCl          .... 

—  0.28 

Li      

4-o  -;8 

Air  i  Atm                . 

4-0  024. 

I  c 

Mb    .     . 

_J_o  O4. 

18 

Al          

4-0.65 

iff 

Mg   

4-o  t;c. 

18 

AlvKol  SO-i^dHoO 

—  1.0 

Crys. 

MgSO4  . 

—  o  4.0 

A,  i  Atm  .... 

—  0./0 

o 

Mn    

4-n. 

18 

As     

—  O.'* 

T8 

MnCl2  

J-I22 

18 

Sol'n 

Au             .... 

—  O.I  C 

18 

MnSO4  .         .    . 

4-ioo 

18 

«( 

B 

—0.7  1 

18 

N2  i  Atm. 

0  00/ 

16 

BaCl2    

\J./1 

—  -  O.7O 

20 

NH3      

Be    '  

~-J" 
4-O.7Q 

T  C 

Powd. 

Na 

4-o  ci 

18 

Bi 

—  1.4. 

1$ 

NaCl 

Br     

—  O.^8 

18 

NaCO3.     .    .    . 

1  —  O  IQ 

17 

Powd 

C,  arc-carbon      .    . 
C,  diamond    . 

—  2.0 
—  0.40 

18 
18 

NaCO3.  10  H2O     . 
Nb    

—  0.46 
-4-i  i 

I? 

18 

« 

CH4,  i  Atm.  .     .     . 

«•  ty 
-\-O.OOI 

16 

NiCl2    

•  '     •* 

4-4O 

18 

Sol'n 

CO2,  i  Atm.  .     .     . 

-\-Q.OO2 

16 

NiSO4  

-\-10 

20 

M 

CS2  

—  0.77 

18 

O2,  i  Atm 

~JU' 

_j_O  I2O 

20 

CaO  

—  O  27 

16 

Powd 

Os 

-I-O  OJ. 

20 

CaCl2    . 

\t»*j 

—  'O  40 

10 

« 

p  -white 

O  QO 

CaCO3,  marble  .    . 

—  O  7 

*y 

P,  red        .... 

—  O  C.O 

20 

Cd    

—  —  O  17 

18 

Pb 

—  O  I" 

20 

CeBr8    

4-6.1 

18 

PbCl3    

—  O  2C 

J  C 

Powd 

C12,  i  Atm.    .    .     . 

•—  O  HQ 

16 

Pd     .    .    . 

4-c8 

18 

CoCl2 

v-yj 

•I-QO 

18 

Sol'n 

prCl3 

Zr 

18 

Sol'n 

CoBr2   

-pyu. 
-1-4.7. 

18 

it 

Pt  

+l'l 

18 

CoI2 

J_-7-> 

18 

« 

PtCU 

o  o 

22 

Sol'n 

CoSO4  

T^JJ- 
4-C7. 

IQ 

«< 

Rh    .    .    , 

4-i.  i 

18 

Co(NO3)2.    .     .    . 

j/' 
4-S7. 

[i 

« 

S  

—  0.48 

18 

Cr     .    . 

1 
•4-1.7 

18 

SO2  i  Atm 

•~~O  "5O 

16 

CsCl      

1   O'/ 

—  0.28 

'7 

Powd 

Sb     . 

—  O  Q4 

18 

Cu    

—  O  OQ 

Se     .    . 

1  —  0  1" 

18 

CuCl2    

u.uy 
4-12. 

20 

Sol'n 

Si  

—  O.I  2 

18 

Crys 

CuSO4  .    . 

4-10 

20 

Sol'n 

SiO2,  Quartz      .    . 

—  O  44 

20 

CuS            .     . 

+0  l6 

Powd 

—  Glass 

—  o  cX 

FeCl3    

4-QO 

18 

Sol'n 

Sn     

~O_1_ 

4-O.O3 

20 

FeCl2    

-y*" 
4-QO 

18 

M 

SrCl2     . 

—  O  42 

20 

Sol'n  ! 

FeSO4  ... 

+82 

20 

«« 

Ta 

4  O  QT. 

18 

Fe2(NO3)6  . 

J-  CQ 

18 

H 

Te     

—  0.32 

20 

FeCn6K4    . 

—  0.44 

Powd. 

Th    

4-0.18 

18 

FeCn6K8  . 

4-Q.I 

«< 

Ti     

4-^.i 

T8 

He,  i  Atm. 

—O  OO2 

o 

Va    

4-i.s 

18 

H2,  i  Atm. 

O  OOO 

16 

Wo  .             .    . 

*-j 

4-O.'?'? 

20 

H2,  40  Atm. 

o.ooo 

16 

Zn     

—  O.IS 

18 

H2O  

—  O  7Q 

20 

ZnSO4  

—  0.40 

HC1  

~~~o  So 

20 

Zr 

,Q  4C 

18 

H2SO4  

-i-n  7<§ 

20 

CH3OH 

O  71 

HNO3  .    .    , 

—0.70 

20 

C2H6OH  .... 

—  0.80 

Hg    .     , 

—O  IQ 

20 

C8H7OH 

—  O.8o 

I       .    . 

20 

C2H6OC2H5 

•   o  60 

20 

In     

Oil* 

18 

CHClo 

o  c8 

Ir  

4-o  ic 

18 

CAHR 

0.78 

K.    .    . 

"pKnm'fp 

_l_r  r 

KC1  , 

—  O  CO 

20 

'     * 

o  64 

22 

KBr  .    .     , 

20 

O  C7 

KI    .     .    .     . 

—  o  18 

Paraffin 

-0'S 

KOH    .... 

—  O  1C 

22 

Sol'n 

T  —  O  Ql 

K2SO4  . 

Tnliipnp 

1  KMnO4     .... 

-f-2.O 

Wood   

—  -u.// 
—  O.2-C 

KNO3  

~^O  IT. 

2O 

Xylene 

•o  81 

W-.3J 

Valuss  are  mostly  means  taken  of  values  given  in  Landolt-Bornstein's  Physikalisch-chemische  Tabellen.    See  espe- 
cially Honda,  Annalen  der  Physik  (4),  32,  1910. 

SMITHSONIAN  TABLES. 


TABLES  385-387.     RESISTANCE   OF   METALS.     MAGNETIC  EFFECTS.    333 

TABLE  385.— Variation  of  Resistance  of  Bismuth,  with  Temperature,  in  a  Transverse  Magnetic  Field. 


Proportional  Values  of  Resistance. 

H 

-192° 

-135° 

—  100° 

-37° 

0° 

+18° 

+60° 

+  100° 

+  183° 

0 

0.40 

0.60 

0.70 

0.88 

1.  00 

1.  08 

•25 

1.42 

1.79 

200O 

1.16 

0.87 

0.86 

0.96 

1.  08 

I.  n 

.26 

1-43 

1.80 

4000 

2.32 

1.  35 

1.20 

1.  10 

1.18 

I.2I 

I.3I 

1.46 

1.82 

6000 

4.00 

2.06 

1.  60 

1.29 

1.30 

1.32 

.39 

1.51 

1.85 

8000 

S-90 

2.88 

2.OO 

1.50 

1-43 

1.42 

.46 

1.57 

1.87 

1  0000 

8.60 

3.80 

2.43 

1.72 

1.57 

1-54 

•54 

1.62 

1.89 

I20OO 

10.8 

4.76 

2.93 

1-94 

i.7i 

1.67 

.62 

1.67 

1.92 

I4OOO 
16000 

12.9 
15-2 

5-82 
6.95 

3.50 

4.11 

2.16 
2.38 

1.87 
2.02 

1.  80 
1-93 

•70 
•79 

1.73 
1.  80 

1.94 
1.96 

18000 

17-5 

8.15 

4.76 

2.60 

2.18 

2.06 

.88 

1.87 

1.99 

20000 

19.8 

9-50 

5-40 

2.81 

2.33 

2.20 

1.97 

1.95 

2.03 

25000 
3000O 

25.5 
30.7 

13-3 

18.2 

7.30 

9.8 

3-50 
4.20 

2.73 

3.17 

2.52 
2.86 

2.22 
2.46 

2.10 
2.28 

2.09 
2.17 

35000 

35-5 

20.35 

12.2 

4-95 

3.62 

3.25 

2.69 

2.45 

2.25 

TABLE 386.— Increase  of  Resistance  of  Nickel  due  to  a  Transverse  Magnetic 
Field,  expressed  as  %  of  Resistance  at  0°  and  H  —  0. 


H 

-190° 

-75° 

0° 

+18° 

+  100° 

+182° 

o 

+0 

0 

0 

O 

0 

0 

1000 

+0.20 

+0.23 

+0.07 

+0.07 

+0.96 

+0.04 

2OOO 

+0.17 

+0.16 

+0.03 

+0.03 

+0.72 

—0.07 

3000 

0.00 

—0.05 

-0.34 

—0.36 

-0.14 

—0.60 

4000 

-0.17 

—0.15 

—0.60 

—0.72 

—0.70 

-I.  IS 

6000 

—0.19 

—  O.2O 

—0.70 

—0.83 

—  1.02 

8000 

—0.19 

-0.23 

—0.76 

—0.90 

-i.  IS 

—  1.66 

1  0000 

—  0.18 

—0.27 

—0.82 

—0.95 

-1.23 

-1.76 

I2OOO 

—  0.18 

—0.30 

—0.87 

—  1.  00 

-1.30 

-1.  85 

14000 

-0.18 

—0.32 

—0.91 

-1.04 

-1.37 

-1.95 

16000 

—0.17 

-0.35 

-0.94 

—  1.09 

-1.44 

-2.05 

I800O 

-0.17 

-0.38 

—0.98 

-i.  13 

-LSI 

-2.15 

20000 

—  0.16 

—0.41 

-1.03 

—  1.17 

-1.59 

-2.25 

2500O 

-0.14 

-0.49 

—  1.  12 

-1.29 

-1.76 

-2.50 

30000 

—  0.12 

—0.56 

—  1.22 

-1.40 

-1.95 

-2.73 

35000 

—  O.IO 

—0.63 

-1.32 

-1.50 

-2.13 

-2.98 

F.  C.  Blake,  Ann.  der  Physik,  28,  p.  449;  1909. 


TABLE  387.  —  Change  of  Resistance  of  Various  Metals  in  a  Transverse  Magnetic  Field. 

Room  Temperature. 


Metal. 

Field  Strength 
in  Gausses. 

Per  cent 
Increase. 

Authority. 

Nickel 

1  0000 

—  1.2 

—  1.4 

Williams,  Phil.  Mag.  9,  1905. 
Barlow,  Pr.  Roy.  Soc.  71,  1903. 

" 

6000 

1  0000 

—  i.o 
-1.4 

Dagostino,  Atti  Ac.  Line.  17,  1908. 
Grummach,  Ann.  der  Phys.  22,  1906. 

Cobalt 

—  0.53 

Cadmium 

VO*> 

+0.03 

Zinc 

+0.01 

Copper 

+0.004 

Silver 

+0.004 

Gold 

+0.003 

Tin 

+O.OO2 

Palladium 

+O.OOI 

M 

Platinum 

+O.OOO5 

M 

Lead 

+O.0004 

•• 

Tantalum 

+0.0003 

" 

Magnesium 

6000 

+0.01 

Dagostino,  /.  c. 

Manganin 

*• 

+O.OI 

** 

Tellurium 

? 

+O.O2  tO  O.34 

Goldhammer,  Wied  Ann.  31,  1887. 

Antimony 

? 

+0.02  to  0.16 

** 

Iron 

Different  specimens  show  very 
diverse  results,  usually  an   in- 
crease in  weak  fields,  a  decrease 

Grummach,  /.  c. 
Barlow,  /.  c. 
Williams,  /.  c. 

( 

in  strong. 

Nickel  steel 

Alloys  behave  similarly  to  iron. 

Williams,  I.  c. 

i 

SMITHSONIAN  TABLES. 


334  TABLES  388,389. 

TABLE  388'  —  Transverse  Galvanomagnetic  and  Thermomagnetic  Effects. 

Effects  are  considered  positive  when,  the  magnetic  field  being  directed  away  from  the  observer, 
and  the  primary  current  of  heat  or  electricity  directed  from  left  to  right,  the  upper  edge  of  the 
specimen  has  the  higher  potential  or  higher  temperature. 

E=  difference  of  potential  produced;  T—  difference  of  temperature  produced;  7=  primary 

dt 
current;   -r-  =  primary  temperature  gradient;    B=  breadth,  and  D=  thickness,  of  specimen; 

Sf=  intensity  of  field.     C.  G.  S.  units. 

Hall  effect  (Galvanomagnetic  difference  of  Potential),  E  =  K— 


Ettingshausen  effect  (  " 
Nernst  effect  (Thermomagnetic 
Leduc  effect  ( 


"  Temperature),  T—P-^- 


"  Potential),  E  = 
"  Temperature),  T 


Substance. 

Values  of  R. 

P  X  10°. 

<2  X  I0«. 

61  X  io8. 

Tellurium      .          . 

-(-400  to  800 

•4-^OQ 

_L  760000 

-f-  O.Q       O.22 

+  2 

-(-9000  to  18000 

-J-2OO 

Steel    . 

+  012     o  cm 

—  O.O7 

—700    "    I7OO 

4-  60 

-f-.oio     0.026 

-\-i6oo  "  7000 

i  uy 

-J-.OO7     o.on 

—  O.O6 

—  1000  "  1500 

-4-^Q 

Cobalt      ... 

-{-.0016     o  0046 

-4-o  01 

-f-iSoo  "  2240 

-rjy 

_L.  T  -3 

Zinc     

—  C4.    "   24.O 

T*3 

.  1.   T-I 

Cadmium     

+  000^ 

1     *J 

-f-  .00040 

_ 

up  to  —  c.o 

4-c 

Lead    

•4-  OOOOQ 

—  CO  (?) 

Tin  

•"-.00003 

—  A.O  (?) 

—  .0002 

_ 

—  2 

Copper 

—  00052 

—  QO  tO  27O 

jg 

German  silver  .     .              . 

—  OOO  S4. 

Gold    

—  .00057  to  00071 

Constantine  

—  OOOQ 

—  .OOOQ'? 

—  OOO7  tO    OOI2 

-Leo  tO  I^O 

^—•3 

—  .0008    "  .0015 

—  4.6  "   410 

J 
—  4.1 

—  .002  "* 

—  .00094  to  .0035 

—  .000^6    "    .OO77 

Nickel      .    

—  .OO4C    "    .024. 

-f-o  04  to  o  19 

-J-200O   "    90OO 

—  AC 

—  .OI7 

4-c 

4-ioo 

Bismuth   

—  Up  to  ID. 

1     '  J 
-T-  3  to  4O 

•f"  Up  tO  I32OOO 

—  ''OO 

TABLE  369. -Variation  of  Hall  Constant  with  the  Temperature. 


Bismuth.1 

Antimony.2 

H 

—182° 

-90° 

-23° 

-HI 

.5° 

+  100° 

H 

—  186° 

-79° 

+21-5° 

+58° 

I  OOO 

62.2 

28.0 

17.0 

13-3 

7.28 

ITS 

D 

0.263 

0.249 

0.217 

2OOO 

55-0 

25.0 

1  6.0 

12.7 

7.17 

D 

0.252 

0.243 

O.2II 

3000 

49-7 

22-9 

i 

S-i 

12.  1 

7.06 

6160 

0.245 

02.35 

O.2O9 

0.203 

4OOO 

45-8 

21-5 

14-3 

II 

•s 

6.95 

5OOO 

42.6 

2O.2 

13.6 

II 

.0 

6.84 

6OOO 

40.1 

18.9 

12.9 

10.6 

6.72 

Bismuth.8 

H 

+14.5°       +104° 

125° 

189° 

212° 

239°              259° 

269° 

270° 

890 

5.28          2.57 

2.12 

1.42 

1.24 

I.  II             0.97 

0.83 

0-77* 

1  Barlow,  Ann.  der  Phys.  12,  1903.  *  Everdinsren,  Comm.  Phys.  Lab.  Leiden,  58. 

8  Traubenberg,  Ann.  der  Phys.  17,  1905.  *  Melting-point. 

Both  tables  taken  from  Jahn,  Jahrbuch  der  Radioactivitat  und  Electronik,  5,  p.  166;  1908,  who  has  collected  data  of 

all  observers  and  gives  extensive  bibliography. 
SMITHSONIAN  TABLES. 


TABLES  390-392. 
RONTGEN  (X-RAYS)  RAYS. 


335 


Rontgen  rays  are  produced  whenever  an  electric  discharge  passes  through  a  highly  exhausted 
tube.  The  disturbance  is  propagated  in  straight  lines  probably  with  the  velocity  of  light,  affects 
photographic  plates,  excites  phosphorescence,  ionizes  gases  and  suffers  neither  deviation  by  mag- 
netic forces  nor  measurable  refraction  in  passing  through  media  of  different  densities.  With  ex- 
treme exhaustion  in  the  tube  they  have  an  appreciable  effect  after  passing  through  several  milli- 
meters of  brass  or  iron.  The  quality  by  which  it  is  best  to  classify  the  rays  is  their  hardness 
which  is  the  greater  the  greater  the  exhaustion.  It  is  conveniently  measured  by  the  amount  of  ab- 
sorption which  they  suffer  in  passing  through  a  layer  of  aluminum  or  tin  foil  of  standard  thick- 
ness. The  number  of  ions  which  the  rays  produce  in  i  sec.  in  passing  through  I  cu.  cm.  of  a  gas 
depends  upon  its  nature  and  pressure.  The  absorption  of  any  substance  is  equal  to  the  sum  of 
the  absorption  of  the  individual  molecules  and  the  absorption  due  to  any  molecule  is  independent 
of  the  nature  of  the  chemical  compound  of  which  it  forms  a  part,  of  its  physical  state,  and  probably 
of  its  temperature. 

TABLE  390.  —  lonization  due  to  Rontgen  Rays  In  Various  Gases. 


Gas. 

Relative  ionization. 

Density. 

Soft  rays,  Strutt. 

Hard  rays,  Eve. 

Hydrogen 

.11 

.42 

0.069 

Air 

I.OO 

I.OO 

I.OO 

Oxygen 

!-39 

— 

I.  II 

Carbon  dioxide 

I.OO 

— 

1.53 

Cyanogen 

1.05 

— 

1.86 

Sulphur  dioxide 

7-97 

2.3 

2.19 

Chloroform 

4-6 

4-32 

Methyl  iodide 
Carbon  tetrachloride 

72.0 
45-3 

13-5 

4-9 

5-oS 
5-31 

Hydrogen  sulphide 

•9 

1.18 

Strutt,  Proc.  Roy.  Soc.  72,  p.  209,  1903 ;  Eve,  Phil.  Mag.  8,  p.  610,  1904. 

When  Rontgen  rays  pass  through  matter  they  produce  secondary  Rontgen  rays  as  well  as  cath- 
odic  rays.  The  former  are  of  two  types :  the  first  is  like  the  original  rays  and  may  be  regarded  as 
scattered  primary  rays ;  the  second  type  varies  with  the  nature  of  the  material  struck  and  is  in- 
dependent of  the  primary  rays.  If  the  atomic  weight  of  the  material  struck  is  less  than  that  of 
Calcium  then  the  first  type  alone  is  present.  The  higher  the  atomic  weight  of  the  material  struck 
the  more  penetrating  is  the  secondary  radiation  given  out.  This  is  shown  in  the  following  table 
where  A  is  the  reciprocal  of  the  distance  (cm.)  in  Al.  through  which  the  rays  must  pass  in  order 
that  their  intensity  is  reduced  to  1/2.7  °f  its  original  intensity. 

TABLE  391.  -  Rontgen  Secondary  Rays. 


Element. 

Cr. 

Fe. 

Co. 

Ni. 

Cu. 

Zn. 

As. 

Se. 

Sr. 

Ag- 

Sn. 

Atomic  weight 

52- 

55-8 

59.0 

58.7 

63.6 

65-4 

7S-o 

79.2 

87.6 

108. 

119. 

A 

367. 

«39- 

193- 

1  60. 

129. 

1  06. 

61. 

§«• 

35-2 

6-75 

4-33 

The  secondary  cathodic  rays  seem  to  be  independent  of  the  material  struck  and  of  the  intensity 
of  the  original  rays.  The  velocity  of  these  secondary  rays  depends  upon  the  hardness  of  the  orig- 
inal rays.  The  following  table  gives  the  thickness  in  cm.  of  the  gas  at  760  mm.,  o°  C.  neces- 
sary to  reduce  the  energy  of  the  cathodic  rays  to  one  half  (t)  as  well  as  A  as  above  defined. 

TABLE  392.  —Rontgen  Secondary  Cathodic  Rays. 


t 

A 

Element. 

Air. 

Hydrogen. 

Air. 

Hydrogen 

Fe 

.0080 

.041 

87.2 

17-0 

Cu 

•o^S 

•073 

Sl-9 

9-5 

Zn 

.0164 

.091 

42.7 

7-7 

As 

Sn 

•0255 
.176 

i-37 

27.4 
3-97 

•51 

SMITHSONIAN  TABLES. 


Beatty,  Phil.  Mag.  20,  p.  320,  1910. 


336 


TABLES  393,394. 
RONTGEN  (X-RAYS)  RAYS. 

TABLE  393.  —  Mean  Absorption  Coefficients,  -.. 


following  coefficients.  The  coefficients  A  have  been  divided  by  the  density  d. 


Radiator. 

Absorber. 

C. 

Mg. 

Al. 

Fe. 

Ni. 

Cu. 

Zn. 

Ag. 

Sn. 

Pt. 

Au. 

Cr. 

15-3 

126. 

I36. 

104- 

I29. 

143- 

170. 

580. 

714. 

(517.) 

(507.) 

Fe. 

JO.I 

80. 

88. 

66. 

84. 

95- 

112. 

38l. 

472. 

340. 

367. 

Co. 

8.0 

64. 

72. 

67- 

67. 

75- 

92. 

392- 

281. 

306. 

Ni. 
Cu. 

6.6 

5-2 

52. 
41. 

59- 

48. 

a 

g 

62. 

53. 

74' 

61. 

262. 

214. 

328. 
272. 

236. 

194. 

2IO. 

Zn. 

As. 

4.3 

2-5 

35- 
19. 

39- 

22. 

221. 
134. 

$ 

50- 
204. 

175- 
105. 

225. 
132. 

162. 

106. 

I78. 

106. 

Se. 

2.0 

id 

19. 

116. 

141. 

150. 

"75- 

88. 

112. 

93- 

100. 

Ag. 

•4 

2.2 

2-5 

17- 

23- 

24. 

27. 

13- 

1  6. 

56- 

61. 

Barkla,  Sadla,  Phil.  Mag.  17,  p.  739,  1909. 


TABLE  394.  —  X  Ray  Spectra  and  Atomic  Numbers. 

Kaye  has  shown  that  an  element  excited  by  sufficiently  rapid  cathode  rays  emits  characteristic 
Rontgen  radiations.  These  have  been  analyzed  and  the  wave-lengths  obtained  by  Moseley  (Phil. 
Mag.  27,  p.  703,  1914)  using  a  crystal  of  potassium  ferrocyanide  as  a  grating.  The  "  K  "  series  of 
elements  shows  2  lines,  a  and  j8,  the  "  L  "  series  several.  The  wave-lengths  of  the  a  and  £  lines  of 
each  series  are  given  in  the  following  table.  QK  =  (V/|  vo)2;  QL  =  (V/^  vo)i  where  v  is  the 
frequency  of  the  o  line  and  v0  the  fundamental  Rydberg  frequency.  The  atomic  number  for  the 
K  series  =  QK~|~I  »  ^or  t^ie  -^  series  =  QL  +  7-4  approximately.  v0  = 


Element. 

a  line 
Axio8cm. 

QK 

Atomic 
Number 

N 

(3  line 

Axio8cm. 

Element. 

a  line 
Axio8cm. 

QL 

Atomic 
Number 
N 

/3  line 
Axio8cm. 

Al 

8.364 

12.0 

13 

7.912 

Zr 

6.091 

32.8 

40 

Si 

7.142 

13.0 

14 

6.729 

Cb 

5-749 

33-8 

41 

5-507 

Cl 

4-750 

16.0 

17 

Mo 

5-423 

34-8 

42 

5-  '87 

K 

3-759 

1  8.0 

19 

3463 

Ru 

4-861 

36.7 

44 

4.660 

Ca 

3-368 

19.0 

2O 

3-°94 

Rh 

4.622 

37-7 

45 

Ti 

2.758 

2I.O 

22 

2.524 

Pd 

4.385 

38.7 

46 

4.168 

V 

2.519 

22.0 

23 

2.297 

Ag 

4.170 

39-6 

47 

Cr 

Mn 

2.301 

2,111 

23.0 
24.0 

24 
25 

2.093 
1.818 

Sn 
Sb 

3.619 

3-458 

42.6 
43-6 

50 
51 

3-245 

Fe 

1.946 

25.0 

26 

1-765 

La 

2.676 

49-5 

57 

2.471 

Co 

1.798 

26.0 

27 

1.629 

Ce 

2.567 

50.6 

58 

2.360 

Ni 

1.662 

27.0 

28 

1.506 

Pr 

(2-47  0 

5i-5 

£9 

2.265 

Cu 

:-549 

28.0 

29 

1.402 

Nd 

2.382 

52-5 

60 

2-175 

Zn 

1-445 

29.O 

30 

1.306 

Sa 

2.208 

54-5 

62 

2.008 

Yt 
Zr 
Cb 

0.838 
0.794 
0.750 

38-1 

39-i 
40.2 

39 
40 

4i 

Eu 
Gd 
Ho 

2.130 
2.057 
1.914 

m 

58.6 

63 
64 
66 

1.925 

.853 
.711 

Mo 

0.721 

41.2 

42 

Er 

1.790 

60.6 

68 

-591 

Ru 
Pd 

Ag 

0.638 
0.584 
0.560 

43-6 

45-6 
46.6 

44 
46 

47 

Ta 
W 
Os 

1.486 
1-397 

65.6 
66.5 

68-5 

73 
74 
76 

•330 

.201 

Ir 

I-354 

69.6 

77 

•J55 

Pt 

1.316 

70.6 

78 

.121 

Au 

1.287 

71.4 

79 

.092 

Moseley's  summary  condensed  is  as  follows:  Every  element  from  Al  to  Au  is  characterized  by 
an  integer  N  which  determines  its  X-ray  spectrum ;  N  is  identified  with  the  number  of  positive 
units  of  electricity  in  its  atomic  nucleus.  The  order  of  these  atomic  numbers  (N)  is  that  of  the 
atomic  weights  except  where  the  latter  disagrees  with  the  order  of  the  chemical  properties.  Known 
elements  correspond  with  all  the  numbers  between  13  and  79  except  3.  There  are  here  3  possible 
elements  still  undiscovered.  The  frequency  of  any  line  in  the  X-ray  spectrum  is  approximately 
proportional  to  A  (N-b)2,  where  A  and  b  are  constants.  AH  X-ray  spectra  of  each  series  are  sim- 
ilar in  structure  differing  only  in  wave-lengths. 
SMITHSONIAN  TABLES. 


TABLES   395-397. -RADIOACTIVITY.  337 

Radioactivity  is  a  property  of  certain  elements  of  high  atomic  weight.  It  is  an  additive 
property  of  the  atom,  dependent  only  on  it  and  not  on  the  chemical  compound  formed  nor 
affected  by  physical  conditions  controlling  ordinary  reactions,  viz  :  temperature,  whether  solid  or 
liquid  or  gaseous,  etc. 

With  the  exception  of  actinium,  radioactive  bodies  emit  a,  /3,  or  y  rays,  a  rays  are  easily  ab- 
sorbed by  thin  metal  foil  or  a  few  cms.  of  air  and  are  positively  charged  atoms  of  helium  emitted 
with  about  1/15  the  velocity  of  light.  They  are  deflected  but  very  slightly  by  intense  electric  or 
magnetic  fields.  The  £  rays  are  on  the  average  more  penetrating,  are  negatively  charged  particles 
projected  with  nearly  the  velocity  of  light,  easily  deflected  by  electric  or  magnetic  fields  and 
identical  in  type  with  the  cathode  rays  of  a  vacuum  tube.  The  y  rays  are  extremely  penetrating 
and  non-deviable,  analogous  in  many  respects  to  the  very  penetrating  Rontgen  rays.  These  rays 
produce  ionization  of  gases,  act  on  the  photographic  plate,  excite  phosphorescence,  produce  certain 
chemical  reactions  such  as  the  formation  of  ozone  or  the  decomposition  of  water.  All  radio- 
active compounds  are  luminous  even  at  the  temperature  of  liquid  air. 

Table  398  is  based  very  greatly  on  Rutherford's  Radioactive  Substances  and  their  radiations 
(Oct.  1912).  To  this  and  to  Landolt-Bornstein  Physikalisch-chemische  Tabellen  the  reader  is  re- 
ferred for  references.  In  the  three  radioactive  series  each  successive  product  (except  Ur.  Y,  and 
Ra.  C2)  results  from  the  transformation  of  the  preceding  product  and  in  turn  produces  the  follow- 
ing. When  the  change  is  accompanied  by  the  ejection  of  an  o  particle  (helium,  atomic  weight  =  4.0) 
the  atomic  weight  decreases  by  4.  The  italicized  atomic  weights  are  thus  computed.  Each  pro- 
duct with  its  radiation  decays  by  an  exponential  law ;  the  product  and  its  radiation  consequently 
depend  on  the  same  law.  I  =  loe-^t  where  IQ  =  radioactivity  when  t  =  O,  I  that  at  the  time  t, 
and  \  the  transformation  constant.  Radioactive  equilibrium  of  a  body  with  its  products  exists 
when  that  body  is  of  such  long  period  that  its  radiation  may  be  considered  constant  and  the 
decay  and  growth  of  its  products  are  balanced. 

International  radium  standard :  As  many  radioactivity  measures  depend  upon  the  purity  of  the 
radium  used,  in  1912  a  committee  appointed  by  the  Congress  of  Radioactivity  and  Electricity, 
Brussels,  1910,  compared  a  standard  of  21.99  mg-  of  Pure  Ra-  chloride  sealed  in  a  thin  glass  tube 
and  prepared  by  Mme.  Curie  with  similar  standards  by  Honigschmid  and  belonging  to  The 
Academy  of  Sciences  of  Vienna.  The  comparison  showed  an  agreement  of  I  in  300.  Mme. 
Curie's  standard  was  accepted  and  is  preserved  in  the  Bureau  international  des  poids  et  mesures 
at  Sevres,  near  Paris.  Arrangements  have  been  made  for  the  preparation  of  duplicate  standards 
for  governments  requiring  them. 

TABLE  395.— Relative  Phosphorescence  Excited  by  Radium. 

(Becquerel,  C.  R.  129,  p.  912,  1899.) 


Without  screen,  Hexagonal  zinc  blende  . 
"        Pt.  cyanide  of  barium    . 

"            DiamnnH 

13-36 
1.99 

05 

•           .            .            .            .OI 

It 

"        Double  sulphate  Ur  and  K   . 

.               I.OO 

«•    «•    .    .    .    :    .o2 

The  screen  of  black  paper  absorbed  most  of  the  a  rays  to  which  the  phosphorescence  was  greatly  due.     For  the  last 
column  the  intensity  without  screen  was  taken  as  unity.     The  y  rays  have  very  little  effect. 

TABLE  396.  — The  Production  of  a  Particles  (Helium). 

(Geiger  and  Rutherford,  Philosophical  Magazine,  20,  p.  691,  1910.) 


Radioactive  substance  (i  gram.) 

a  particles 
per  sec. 

Helium  per  year. 

Uranium    ...... 
Uranium  in  equilibrium  with  products 
Thorium  "          *' 
Radium     
Radium  iti  equilibrium  with  products 

2.37  X  10* 
9.7    X  10* 
2.7    X  10* 
3-4    Xio*> 
13.6    X  io"> 

2.75  X  io—  5  cu.  mm. 
ir.o    X  io—  5  "      " 
3.1    X  to-"  "      " 

,351      ••   "• 

TABLE  397.  — Heating  Effect  of  Radium  and  Its  Emanation. 

(Rutherford  and  Robinson,  Philosophical  Magazine,  25,  p.  312,  1913.) 


Heating  effect  in  gram-calories  per  hour  per  gram  radium. 

a  rays. 

prays. 

yrays. 

Total. 

Radium   .... 
Emanation 
Radium  A       ... 
Radium  B  +  C 

25.1 

28.6 
30.5 
39-4 

4-7 

6.4 

25.1 

28.6 
30.5 
So.S 

Totals      .... 

123.6 

4-7 

6.4 

134-7 

Other  determinations  :  Hess,  Wien.  Ber.  121,  p.  i,  1912,  Radium  (alone)  25.2  cal.  per  hour  per  gram.     Meyer  and 
Hess,  Wien.  Ber.  121,  p.  603,  1912,  Radium  in  equilibrium,  132.3  gram.  cal.  perohour  per  gram.     See  also,  Callendar, 
Phys.  Soc.  Proceed.  23,  p.  i,  1910;  Schweidler  and  Hess,  Ion.  i,  p.  161,  1909;  Angstrom,  Phys.  ZS.  6,  685,  1905,  etc. 
SMITHSONIAN  TABLES. 


338 


TABLE  398. 
RADIOACTIVITY, 


P  =  i /2  period  =  time  when  body  is  one-half  transformed.  A  =  transformation  constant  (see 
previous  page).  The  initial  velocity  of  the  a  particle  is  deduced  from  the  formula  of  Geiger 
V8  =  aR  where  R  =  range  and  assuming  the  velocity  for  RaC  of  range  7.06  cm.  at  20°  is 
2.06  X  io9  cm.  per  sec.,  i.e.  v  =  i.ojjr l/3. 


URANIUM-RADIUM  GROUP. 

a  rays. 

Atomic 
Weights. 

K  Period 
P 

tion 
Constants. 
.6931 

Rays. 

Range. 

760--, 
15°  C. 

Initial 
Velocity. 

Kinetic 
Energy 

Whole  no. 
of  ions 
produced. 

c.m. 

c.m.  per  s. 

Ergs. 

By  an  a 
particle. 

Uranium  i 
Uranium  2 

238.5 
234.5 

SXio«y 
io8  yrs 

i.4Xio-10y 
7X10-7  y 

a 
a 

2.50 
2.90 

1.45X108 
I-53      ' 

.72      " 

1.26X10" 
'•37    " 

Uranium  X 

230.5    • 

24.6  d 

.0282  d 

ft+y 

Ur.  Y 

230.5  ? 

1.5  d 

.46  d 

ft 

Ionium 

230.5 

2X106  yr? 

3.5X10—  °y 

a 

3-00 

1.56      " 

•75      ' 

1.40    " 

Radium 
Ra  Emanation 

226.4 

222 

2000  y 
3-85  d 

.000346  y 
.180  d 

a+ft 
a 

3-30 
4.16 

1.61      ' 
1.73      " 

'.92      " 

1.74    " 

Radium  A 

218 

3.0  m 

.231  m 

a 

4-75 

1.82      " 

I.OI         " 

1.88    " 

Radium  B 

214 

26.8m 

.0258  m 

ft+y 

Radium  C 

214 

19-5  m 

.0355  m 

6.94 

2.06     " 

1.31      " 

2.37    " 

RaC2 

210? 

i.  4m 

•495  m 

ft 

Ra  O,  radio-lead 

2/0 

16.5  y 

.042  y 

slow  ft 

RaE. 
Ra  F.  Polonium 

210 
210 

5-od 
136  d 

.i39d 
.005  io  d 

ft+y 

a 

3-77 

1.68     " 

•87      " 

1.63    " 

ACTINIUM   GROUP. 

Actinium 

A 

? 

none 

Radio-Act. 
Actinium  X 
Act.  Emanation 

A 
A  -4 
A—  8 

19.5  d 
10.2  d 

•0355  d 
.068  d 
.178  s 

a+ft 
a 
a 

4.80 
4.40 
5-70 

i.83Xio9 
1.76     ' 
1.94 

1.02X10—  c 
•94     " 
1.15     " 

1.89X106 
1.79    " 

2.10     " 

Actinium  A 
Actinium  B 

A—  12 

A—ib 

.002  s 
36m 

350  S 

.0193  m 

a 

slow  ft 

6.50 

2.02       ' 

1.25     " 

2.27     " 

Actinium  C 

A—it> 

2.1  m 

•33  m 

a 

5.40 

1.89       " 

X.IO      " 

2.02      " 

Actinium  D 

A—  20 

4.7  m 

.i47m 

0+y 

THORIUM  GROUP. 

Thorium 
Mesothorium  i 

232 

228 

i.3Xio"»y 

5.3X10-" 
.  1  26  yr 

a 

none 

2.72 

i.SoXio9 

.69X10-6 

I.32XI06 

Mesothorium  2 

228 

6.2  hr 

.112  h 

Radiothorium 
Thorium  X 
Th.  Emanation 
Thorium  A 
Thorium  B 

228 
224 

220 
210 
212 

2  yrs 
3.6Sd 
54  sec 
o.i  4  sec 
10.6  h 

•347  T 

.OI28S 

.0654  h 

a+ft 
a 
a 

3.87 
5-7 
5-5 
5-9 

JS  " 

:.£  • 

.89     " 

•15    ' 

.10 

.19    ' 

1.66    " 

2.1         " 
2.0 
2.2 

Thorium  Ct 
Thorium  C2 

212 

212 

60  m 
very  short 

.0118  m 

a+ft 
a 

b 

1.85   " 

2.22       " 

.05     " 
•53      ' 

l'9g      " 

Th.  D 

208 

3.1  m 

.22401 

ft+y 

Potassium 

39.1 

? 

? 

ft 

Rubidium 

? 

? 

SMITHSONIAN  TABLES. 


TABLE  398  (continue*) .-  RADIOACTIVITY.  339 

=  coefficient  of  absorption  for  £  rays  in  terras  of  cms.  of  aluminum,  pi,  of  the  7  rays  in  cms.  of 
lead  so  that  if  J0  is  the  incident  intensity,  J  that  after  passage  through  d  cms.,  J 


URANIUM-RADIUM  GROUP. 

/3  rays. 

y  rays. 

Absorption 
Coefficient  -=n 

Velocity 
Light  =  i 

Absorption 

Remarks. 

c.m.—1 

c.m.-1 

Uri 

— 

— 

— 

i  gram  U  emits  2.37  X  io4  a  particles  per 

sec. 

Ur2 

— 

— 



Not  separable  from  Ur  i. 

UrX 

15,510 

Wide  range 

.72 

/8  rays  show  no  groups  of  definite  veloc- 
ities.    Chemically  allied  to  Th. 

UrY 

— 

— 

— 

Probably  branch  product.    Exists  in  small 

quantity. 

lo 

— 

— 

— 

Chemically  properties  of  and  non-separ- 
able from  Thorium. 

Ra 
Ra  Em 

3I2 

.52,  -65 

~_ 

Chemically  properties  of  Ba.    i  gr.  emits 
per  sec.  in  equilib.  13.6  X  io10  a  particles. 
Inert  gas,  density  in  H,  boils  —  65°  C, 

density  solid  5-6,  condenses  low  pres- 

sure —  150°  C. 

RaA 

— 

— 



Like  solid,  has  +  charge,  volatile  in  H, 

400°,  in  O  about  550°. 

RaB 

I3,  80,  890 

.36  to  .74 

4  to  6 

Volatile  about  400°  C.  in  H.     Separated 

pure  by  recoil  from  Ra  A. 

RaC 

*3»  53 

.80  to  .98 

•50 

Volatile  in  H  about  430°,  in  O  about  1000°. 

RaC2 

13 

— 

Probably  branch  product.     Separated  by 

recoil  from  Ra  C. 

RaD 

•33.  -39 

•33.  -39 

— 

Separated  with  Pb.  not  yet  separable  from 

it.    Volatile  below  1000°. 

RaE 

43 

Wide  range 

Easy  abs. 

RaF 

—~ 

—  — 

Separated  with  Bi.     Probably  changes  to 
Pb.    Volatile  about  1000°. 

ACTINIUM  GROUP. 

Act 

— 

— 

— 

Probably    branch    product    Ur.    series. 
Chemically  allied  to  Lanthanum. 

Rad.  Act 

140 

— 

— 

ActX 
Ac.  Em. 

~~* 

— 

Chemical  properties  analogous  to  Ra. 
Inert  gas,  condenses  between  —  120°  and 

—150°. 

Act  A 

— 

— 

— 

Analogous  to  Ra  A.   Volatile  above  400°. 

Act  B 

Very  soft 

— 

— 

"   Ra  B.         "           "     700°. 

ActC 

— 

— 

— 

"          "  RaC. 

ActD 

28.5 

— 

.217  (Al) 

(Obtained  by  recoil). 

THORIUM  GROUP. 

Th. 





_ 

Volatile  in  electric  arc.    Colorless  salts  not 

spontaneously  phosphorescent. 

Mes.  Th.  i 

— 

.37  to  .66 

— 

Chemical  property  analogous  to  Ra  from 

which  non-separable. 

Mes.Th.2 

20  tO  38.5 



•53 

Rad.  Th. 

— 

Chemically  allied  to  Th.,  non-separable 

from  it. 

Th.  X 

About  330 

47      -51 

— 

Chemically  analogous  to  Ra. 

Th.  Em. 

—  . 

— 

Inert  gas,    condenses    at    low    pressure 

between  —  120°  and  —  150°. 

Th.  A 

_ 



__ 

+charged,  collected  on  —  electrode. 

Th.  B 

no. 

•63      .72 

— 

Chemically  analogous  to  Ra  B.    Volatile 

above  630°  C. 

Th.  Ci 

15.6 

— 

Weak 

Chemically  analogous  to  Ra  C.    Volatile 

above  730°. 

Th.  Ca 
Th.  D 

24.8 

•3»  4,  -93-5 

.46 

Th.C2  and  Th.D  are  probably  respectively 
£  and  a  ray  products  from  Th.Ci. 
Got    by    recoil    from  Th.C.      Probably 

transforms  to  Bi. 

K 

38,  102 

— 

— 

Activity  =  i  /  1000  of  Ur. 

Rb. 

380,  IO2O 

— 

— 

„       =  1/500  of  Ur. 

SMITHSONIAN  TABLES. 


340 


TABLES  399-401. 
RADIOACTIVITY. 

TABLE  399.— Stopping  Powers  of  Various  Substances  for  a  Rays. 


s,  the  stopping  power  of  a  substance  for  the  a  rays  is  approximately  proportional  to  the  square 

root  of  the  atomic  weight,  w. 


Substance 

Hi 

Air 

02 

C2H2 

C2H4 

Al 

N2O 

co? 

CH3Br 

CS2 

Fe 

s       ... 

Vw.     .     . 

2 

I.O 
I.O 

LOS 
1.05 

i.  ii 
1.17 

'•35 
1.44 

MS 
1-37 

1.46 
1.52 

1.47 
i-S1 

2.09 
2-03 

2.18 

i-95 

2.26 
1.97 

Substance 

Cu 

Ni 

Ag 

Sn 

C6H6 

CsHi2 

C2H6I 

CC14 

Pt 

Au 

Pb 

s      ... 

Vw.     .     . 

2.43 

2.10 

2.46 

2.20 

3-17 

2.74 

ffl 

3-37 
3-53 

js 

3-'3 

3-o6 

4.02 
3-59 

4.16 
3.68 

4-45 

3-70 

4.27 
3-78 

Bragg,  Philosophical  Magazine,  ii,  p.  617,  1906. 

TABLE  400.— Absorption  of  /3  Rays  by  Various  Substances. 

the  coefficient  of  absorption  for  )8  rays  is  approximately  proportional  to  the  density,  D.     See 

Table  398  for  p  for  Al. 


Substance   .    . 

B 

C 

Na 

Mg 

Al 

Si 

P 

S 

K 

Ca 

M/D    .     .     .     . 

4.65 

44 

4-95 

5.26 

5-5 

6.1 

6.6 

6.  S3 

6.47 

Atomic  Wt.     . 

ii 

12 

23 

24.4 

27 

28 

31 

32 

39 

40 

Substance    .     . 

Ti 

Cr 

Fe 

Co 

Cu 

Zn 

Ar 

Se 

Sr 

Zr 

Atomic  Wt.     . 

6.2 

48 

6.25 

S2 

6.4 
56 

6.48 
59 

6.8 
63-3 

6-95 
65-5 

8.2 

75 

8.65 
79 

8.5 
87-5 

8-3 

90.7 

Substance   .    . 

Pd 

Ag 

Sn 

Sb 

I 

Ba 

Pt 

Au 

Pb 

U 

Atomic  Wt.     . 

8.0 
106 

a 

9.46 
118 

9.8 

120 

10.8 
126 

8.8 
137 

9.4 
195 

9-5 
197 

10.8 

207 

IO.I 

240 

For  the  above  data  the  /8  rays  from  Uranium  were  used. 
Crowther,  Philosophical  Magazine,  12,  p.  379,  1906. 


TABLE  401.  —Absorption  of  y  Rays  by  Various  Substances. 


Substance. 

Density. 

Radium  rays. 

Uranium  rays. 

Th.  D. 

Meso.  Th2 

Range  of 

thickness 
cm. 

M  (cm)-1 

_*» 

M(cm)-1 

IOOM/D 

Hg    .    . 

13-59 

.642 

4.72 

.832 

6.12 

•3  to    3-5 

Pb     .    . 

11.40 

•495 

4-34 

•725 

6-36 

.462 

.620 

.0"    7.9 

Cu    .      . 

8.8  1 

•351 

3-98 

.416 

4.72 

.294 

•373 

.0  "    7.6 

Brass     . 

8.35 

•325 

3.89 

•392 

470 

.271 

•355 

.0  "    5.86 

Fe     .     . 

7.62 

•3°4 

3-99 

.360 

4-72 

.250 

.316 

.0  "    7.6 

Sn     .     . 
Zn     .    . 

Slate  .    . 

7.24 
7-07 
2.85 

.281 
.228 
.118 

3-88 

3-93 
4.14 

•341 
•329 
•134 

470 
4-65 
4.69 

•236 

3 

•305 
.300 

.0  "    6.0 
.0  "    9.4 

Al      .    . 

2.77 

.in 

4.06 

.130 

4.69 

.092 

.119 

.0   "    II.  2 

Glass      . 

2.52 

.105 

4.16 

.122 

4.84 

.089 

•"3 

.O   "    11.3 

S  .    .    . 
Paraffin  . 

1.79 
.86 

.078 
.042 

4-38 
4.64 

.092 
•043 

5.l6 
5.02 

.066 
.031 

.083 
.050 

.0  "  1  1.6 
.0  "  11.4 

In  determining  the  above  values  the  rays  were  first  passed  through  one  cm.  of  lead. 

Russell  and  Soddy,  Philosophical  Magazine,  21,  p.  130,  1911. 
SMITHSONIAN  TABLES. 


TABLES  402-405.  241 

RADIOACTIVITY. 

TABLE  402.  —Total  Number  of  Ions  produced  by  the  a,  13.  and  7  Rays. 

The  total  number  of  ions  per  second  due  to  the  complete  absorption  in  air  of  the  /3  rays  due  to  i 
gram  of  radium  is  9  Xio14,  to  the  7  rays,  i3Xio14. 

The  total  number  of  ions  due  to  the  a  rays  from  I  gram  of  radium  in  equilibrium  is  2-56XIO16. 
If  it  be  assumed  that  the  ionization  is  proportional  to  the  energy  of  the  radiation,  then  the  total 
energy  emitted  by  radium  in  equilibrium  is  divided  as  follows :  92.1  parts  to  the  a,  3.2  to  the  ft,  47 
to  the  7  rays.  (Rutherford,  Moseley,  Robinson.) 

TABLE  403.  —  Amount  of  Radium  Emanation.    Curie. 


At  the  Radiology  Congress  in  Brussels  in  1910.  it  was  decided  to  call  th 
in  equilibrium  with  i  gram  of  pure  radium  one  Curie.  [More  convenient 
(io~~3Curie)  and  the  microcurie  (io~6Curie)l.  The  rate  of  production  of  this 


the  amount  of  emanation 
units  are  the  millicurie 

(io~~3Curie)andthe  microcurie  (io~6Curie)].  The  rate  of  production  of  this  emanation  is  1.24X10— 9 
cu.  cm.  per  second.  The  volume  in  equilibrium  is  0.59  cu.  mm.  (760  cm.,  O°C.)  assuming  the  emana- 
tion mon-atomic. 

The  Mache  unit  is  the  quantity  of  Radium  emanation  without  disintegration  products  which 
produces  a  saturation  current  of  10— 3  unit  in  a  chamber  of  large  dimensions,  i  curie  =  2.5  Xio9 
Mache  units. 

The  amount  of  the  radium  emanation  in  the  air  varies  from  place  to  place ;  the  amount  per  cubic 
centimeter  of  air  expressed  in  terms  of  the  number  of  grams  of  radium  with  which  it  would  be  in 
equilibrium  varies  from  24Xio~12  to  35oXio~12. 

TABLE  404. —Vapor  Pressure  of  the  Radium  Emanation  in  cms.  of  Mercury. 

(Rutherford  and  Ramsay,  Phil.  Mag.  17,  p.  723,  1909,  Gray  and  Ramsay,  Trans. 
Chem.  Soc.  95,  p.  1073,  I9°9-) 

Temperature  C°.  —127°  — 101°  —65°  —56°  — 10°  +17°  +49°  +73°  +100°  +104°  (crit) 
Vapor  Pressure.  0.9  5  76  100  500  1000  2000  3000  4500  4745 

TABLE  405.  —  References  to  Spectra  of  Radioactive  Substances. 

Radium  spectrum:  Dema^ay,  C.  R.  131,  p.  258,  1900. 

Radium  emanation  spectrum  :     Rutherford  and  Royds,  Phil.  Mag.  16,  p.  313,  1908 ;  Watson,  Proc. 

Roy.  Soc.  A  83,  p.  50,  1909. 
Polonium  spectrum:  Curie  and  Debierne,  Rad.  7,  p.  38,  1910,  C.  R.  150,  p.  386,  1910. 

SMITHSONIAN  TABLES. 


242  TABLE  406. 

MISCELLANEOUS  CONSTANTS  (ATOMIC,  MOLECULAR,  ETC.). 


Elementary  electrical  charge,  charge  on  electron,  1/2  charge 
on  a  particle, 

Mass  of  an  electron, 

Radius  of  an  electron, 

Number  of  molecules  per  gram  molecule, 

Number  of  gas  molecules  per  cc.,  76omm,  o°C, 

Kinetic  energy  of  a  molecule  at  o°C, 

Constant  of  molecular  energy,  Eo/T, 

Constant  of  entropy  equation  (Boltzmann),  =  R/N  |^ 


r  e  =4.774Xio-10  e.  s.  u.  (M) 
=  i.5i9Xio-20  e.  m.  u. 
=  i,59iXio-19  coulombs 
m  =  about  6Xio~s8  grams. 
1    =  about  iXio~13  cm. 
N  =6.o6Xio23  gr-1  (M) 
n  =2.7oXio19  (M) 
Eo=5.62Xio-14  ergs.  (M) 
e   =  2.o6X i o~16  ergs /degrees 

k  = 


Elementary  "  Wirkungsquantum,"  h  =  6.62Xio~27  erg.  sec. 
Mass  of  hydrogen  atom,  =  i. 64X10-2*  gram. 

Radius  of  an  atom,  =  about  10— 8  cm. 

Gas  constant,  R  =  22.412/273.1  for  i  gram  molecule  of  an 

ideal  gas.  Pressure  in  atmospheres,  g  =  980.6,  vol.  in  liters,  R  =  .08207  liter.  Atm  /grm. 


(M) 
(M) 
(M) 


H2 

He 

N3 

02 

Xe 

CO, 

H20 

Sq.    rt.   of   mean    sq.  molec. 

veloc.,  cm.  /sec.  at  o°C.  Xio-4 

18.4 

13.1 

4-93 

4.61 

2.28 

3-92 

7.08 

Mean  free  path  cm.  Xio6 

1  8. 

28. 

94 

9-9 

5.6 

6-4 

7.2 

Molecular  diameter  cm.  Xio8 

2.2 

2.2 

3-3 

3-o 

34 

4.2 

3-8 

(M)  Millikan,  Phys.  Rev.  2,  p.  109,  1913.  The  other  values  are  mostly  means, 
SMITHSONIAN  TABLES. 


TABLE  407. 
PERIODIC  SYSTEM  OF  THE   ELEMENTS. 


343 


0 

I 

II 

III 

IV 

V 

VI 

VII 

- 

R2O 

RO 

R203 

RO2 

R2os 

R03 

R207 

RO4cJBD  Oxides 

- 

- 

- 

- 

RH4 

RH3 

RH2 

RH 

-  «^H  Hydrides 

He 

4 

Li 

7 

Gl 
9 

B 
ii 

C 
12 

N 
14 

C) 
16 

F 
19 

_ 

Ne 

20 

Na 

23 

Mg 
24 

Al 

27 

Si 

28 

P 
31 

S 
32 

Cl 

35 

- 

A 

40 

K 
39 

Ca 

40 

Sc 
44 

Ti 

48 

V 

5i 

Cr 

52 

Mn 

55 

Fe    Ni   Co 
56    59    59 

- 

Cu 

64 

Zn 

65 

Ga 

70 

Ge 

72 

As 
75 

Se 
79 

Br 
80 

- 

Kr 

82 

Rb 

85 

Sr 
88 

Yt 
89 

Zr 
9i 

Cb 

94 

Mo 
96 

- 

Ru   Rh   Pd 

IO2    103    IO7 

- 

Ag 
1  08 

Cd 

112 

In 
"5 

Sn 
119 

Sb 

120 

Te 
128 

I 
127 

- 

X 

128 

Cs 
133 

Ba 

137 

La 
139 

Ce 

140 

- 

1 

1 

- 

- 

- 

- 

Yb 
173 

: 

Ta 
181 

W 
184 

_ 

Os     Ir     Pt 
J9l  193  T95 

- 

Au 
197 

Hg 

201 

Tl 
204 

Pb 

207 

Bi 
208 

- 

- 

- 

- 

"" 

Ra 
226 

1 

Th 
232 

: 

u 

238 

- 

- 

SMITHSONIAN  TABLES. 


APPENDIX. 


DEFINITIONS   OF   UNITS. 

ACTIVITY.     Power  or  rate  of  doing  work;  unit,  the  watt.  - 

AMPERE.  Unit  of  electrical  current.  The  international  ampere,  "which  is  one  tenth  of  the 
unit  of  current  of  the  C.  G.  S.  system  of  electro-magnetic  units,  and  which  is  represented 
sufficiently  well  for  practical  use  by  the  unvarying  current  which,  when  passed  through 
a  solution  of  nitrate  of  silver  in  water,  and  in  accordance  with  accompanying  specifi- 
cations" (see  pages  xxxvi,  261),  "deposits  silver  at  the  rate  of  0.001118  of  a  gram  per 
second." 
The  ampere  =  I  coulomb  per  second  =  I  volt  through  i  ohm  =  io—1  E.  M.  U.  =  3  X 

10  9  E.  S.  U.*  , 

Amperes  =  volts/ohms  =  watts/volts  =  (watts/ohms)  . 
Amperes  X  volts  =  amperes2  X  ohms  =  watts. 
ANGSTROM.     Unit  of  wave-length  =  lo"10  meter. 
ATMOSPHERE.     Unit  of  pressure. 

English  normal  =  14.7  pounds  per  sq.  in=  29.929  in.  =  760.18  mm.  Hg.  32°  F. 
""  French       "         =  760  mm.  of  Hg.  o°  C.  =  29.922  in.  =  14.70  Ibs.  per  sq.  in. 
BOUGIE  DECIMALE.     Photometric  standard;  see  page  178. 

BRITISH  THERMAL  UNIT.     Heat  required  to  raise  one  pound  of  water  at  its  temper- 
ature of  maximum  density,  I  °  F.  =  252  gram-calories. 
CALORY.     Small  calory  =  gram-calory  =  therm  =  quantity  of  heat  required  to  raise  one 

gram  of  water  at  its  maximum  density,  one  degree  Centigrade. 
Large  calory  =  kilogram-calory  =  1000  small  calories  =  one  kilogram  of  water  raised 

one  degree  Centigrade  at  the  temperature  of  maximum  density. 
For  conversion  factors  see  page  237. 
CANDLE.     Photometric  standard,  see  page  178. 
CARAT.     The  diamond  carat  standard  in  U.  S.  =  200  milligrams.    Old  standard  =  205.3 

milligrams  =  3.168  grains. 

The  gold  carat:  pure  gold  is  24  carats;  a  carat  is  1/24  part. 
CARCEL.     Photometric  standard;  see  page  178. 
CIRCULAR  AREA.     The  square  of  the  diameter  =  1.2733  X  true  area. 

True  area  =  0.785398  X  circular  area. 

COULOMB.  Unit  of  quantity.  The  international  coulomb  is  the  quantity  of  electricity 
transferred  by  a  current  of  one  international  ampere  in  one  second.  =  io—1  E.  M.  U. 
=  3  X  10  9  E.  S.  U. 

Coulombs  =  (volts-seconds) /ohms  =  amperes  X  seconds. 
CUBIT  =  18  inches. 
DAY.     Mean  solar  day.  =  1440  minutes  =  86400  seconds  =  1.0027379  sidereal  day. 

Sidereal  day  =  86164.10  mean  solar  seconds. 

DIGIT.     3/4  inch;  1/12  the  apparent  diameter  of  the  sun  or  moon. 
DIOPTER.     Unit  of  "power"  of  a  lens.  The  number  of  diopters  =  the  reciprocal  of  the 

focal  length  in  meters. 

DYNE.  C.  G.  S.  unit  of  force  =  that  force  which  acting  for  one  second  on  one  gram  pro- 
duces a  velocity  of  one  centimeter  per  second. 

=  weight  in  grams  divided  by  the  acceleration  of  gravity  in  cm.  per  sec. 
ELECTROCHEMICAL  EQUIVALENT  is  the  ratio  of  the  mass  in  grams  deposited  in  an 

electrolytic  cell  by  an  electrical  current  to  the  quantity  of  electricity. 
ENERGY.     See  Erg. 
ERG.     C.  G.  S.  unit  of  work  and  energy  =  one  dyne  acting  through  one  centimeter. 

For  conversion  factors  see  page  237. 

FARAD.     Unit  of  electrical  capacity.    The  international  farad  is  the  capacity  of  a  con- 
denser charged  to  a  potential  of  one  international  volt  by  one  international  coulomb 
of  electricity.  =  io~9  E.  M.  U.  =  9  X  io11  E.  S.  U. 
The  one-millionth  part  of  a  farad  (microfarad)  is  more  commonly  used. 
Farads  =  coulombs/volts. 

*  E.  M.U.  =  C.  G.  S.  electromagnetic  units.  E.  S.  U.  =  C.  G.  S.  electrostatic  units. 


346 


APPENDIX. 


FOOT-POUND.    The  work  which  will  raise  one  pound  one  foot  high. 

For  conversion  factors  see  page  237. 
FOOT-POUNDALS.     The  English  unit  of  work  =  foot-pounds/g. 

For  conversion  factors  see  page  237. 
g.     The  acceleration  produced  by  gravity. 

GAUSS.     A  unit  of  intensity  of  magnetic  field  =  I  E.  M.  U.  =  $  X  IQ-10  E.  S.  U. 
GRAM.     See  page  6. 

GRAM-CENTIMETER.     The  gravitation  unit  of  work  =  g.  ergs. 
GRAM-MOLECULE,  =  x  grams  where  x  =  molecular  weight  of  substance. 
GRAVITATION  CONSTANT  =  G  in  formula  G  ^  =  666.07  X  io~10  cm.3/gr.  sec.2 

For  further  conversion  factors  see  page  237. 

HEAT  OF  THE  ELECTRIC  CURRENT  generated  in  a  metallic  circuit  without  self- 
induction  is  proportional  to  the  quantity  of  electricity  which  has  passed  in  coulombs 
multiplied  by  the  fall  of  potential  in  volts,  or  is  equal  to  (coulombs  X  volts)  /  4.181  in 
small  calories. 

The  heat  in  small  or  gram-calories  per  second  =  (amperes2  X  ohms)/4.i8i  =  volts2/ 


(ohms  X  4.181)  =  (volts  X  amperes)/ 4.181  =  watts/4. 181. 
YT.     Absolute  zero  of  heat  =  -273.13°  C,  -459.6°  Fahrei 


HEAT.     Absolute  zero  of  heat  =  -273.13°  C,  -459.6°  Fahrenheit,  -218.5°  Reaumur. 

HEFNER  UNIT.     Photometric  standard;  see  page  178. 

HENRY.  Unit  of  induction.  It  is  "the  induction  in  a  circuit  when  the  electromotive  force 
induced  in  this  circuit  is  one  international  volt,  while  the  inducing  current  varies  at 
the  rate  of  one  ampere  per  second."  =  io9  E.  M.  U.  =  $  X  IQ-11  E.  S.  U. 

HORSE-POWER.  The  practical  unit  of  power  =  33,000  pounds  raised  one  foot  per  min- 
ute. =  55oft.  pds.  per  sec.  =  o.  746  kilowatt  =  746  watts. 

JOULE.     Unit  of  work  =  io7  ergs. 

Joules  =  (volts2  X  seconds)  /  ohms  =  watts  X  seconds  =  amperes2  X  ohms  X  sec. 
For  conversion  factors  see  page  237. 

JOULE'S  EQUIVALENT.     The  mechanical  equivalent  of  heat  =  4.185  X  io7  ergs.   See 

KILODYNE.     1000  dynes.  About  I  gram. 

LITER.     See  page  6. 

LUMEN.     Unit  of  flux  of  light-candles  divided  by  solid  angles. 

MEGABAR.     Unit  of  pressure  =  0.987  atmospheres. 

MEGADYNE.     One  million  dynes.  About  one  kilogram. 

METER.     See  page  6. 

METER  CANDLE.     The  intensity  lumination  due  to  standard  candle  distant  one  meter. 

MHO.     The  unit  of  electrical  conductivity.   It  is  the  reciprocal  of  the  ohm. 

MICRO.     A  prefix  indicating  the  millionth  part. 

MICROFARAD.     One  millionth  of  a  farad,  the  ordinary  measure  of  electrostatic  capacity* 

MICRON.     (/*)  =  one  millionth  of  a  meter. 

MIL.     One  thousandth  of  an  inch. 

MILE.     See  pages  5,  6. 

MILE,  NAUTICAL  or  GEOGRAPHICAL  =  6080.204  feet. 

MILLI-.     A  prefix  denoting  the  thousandth  part. 

MONTH.     The  anomalistic  month  =  time  of  revolution  of  the  moon  from  one  perigee  to 

another  =  27.55460  days. 
The  nodical  month  =  draconitic  month  =  time  of  revolution  from  a  node  to  the  same  node 

again  =  27.21222  days. 

The  sidereal  month  =  the  time  of  revolution  referred  to  the  stars  =  27.32166  days  (mean 
value),  but  varies  by  about  three  hours  on  account  of  the  eccentricity  of  the  orbit  and 
"perturbations." 

The  synodic  month  =  the  revolution  from  one  new  moon  to  another  =  29.5306  days 
(mean  value)  =  the  ordinary  month.  It  varies  by  about  13  hours. 

OHM.     Unit  of  electrical  resistance.   The  international  ohm  is  based  upon  the  ohm  equal 
to  io9  units  of  resistance  of  the  C.  G.  S.  system  of  electromagnetic  units,  and  "is  repre- 
sented by  the  resistance  offered  to  an  unvarying  electric  current  by  a  column  of  mer- 
cury, at  the  temperature  of  melting  ice,  14.4521  grams  in  mass,  of  a  constant  cross 
section  and  of  the  length  of  106.3  centimeters."  =  io9  E.  M.  U.  =  I  X  io~u  E.  S.  U- 
International  ohm  =  1.01367  B.  A.  ohms  =  1.06292  Siemens'  ohms. 
B.  A.  ohm  =  0.98651  international  ohms. 
Siemens'  ohm  =  0.94080  international  ohms.  See  page  272. 

PENTANE  CANDLE.     Photometric  standard.  See  page  178. 

PI  =  Tf  =  ratio  of  the  circumference  of  a  circle  to  the  diameter  =  3.14159265359. 

POUNDAL.  The  British  unit  of  force.  The  force  which  will  in  one  second  impart  a  veloc- 
ity of  one  foot  per  second  to  a  mass  of  one  pound. 

RADIAN  =  i8o°/7r  =  57.295780  =  57°  17'  45"  =  206625". 

SECOHM.    A  unit  of  self-induction  =  I  second  X  I  ohm. 


APPENDIX.  347 

THERM  =  small  calory  =  quantity  of  heat  required  to  warm  one  gram  of  water  at  its 

temperature  of  maximum  density  one  degree  Centigrade. 

THERMAL  UNIT,  BRITISH  =  the  quantity  of  heat  required  to  warm  one  pound  of  water 
at  its  temperature  of  maximum  density  one  degree  Fahrenheit  =  252  gram-calories. 
VOLT.     The  unit  of  electromotive  force  (E.  M.  F.).   The  international  volt  is  "the  elec- 
tromotive force  that,  steadily  applied  to  a  conductor  whose  resistance  is  one  inter- 
national ohm,  will  produce  a  current  of  one  international  ampere,  and  which  is  rep- 
resented sufficiently  well  for  practical  use  by  1000/1434  of  the   electromotive   force 
between  the  poles  or  electrodes  of  the  voltaic  cell  known  as  Clark's  cell,  at  a  temperature 
of  15°  C  and  prepared  in  the  manner  described  in  the  accompanying  specification." 
=  io8  E.  M.  U.  =  1/300  E.  S.  U.     See  pages  xxxiv  and  261. 
VOLT-AMPERE.     Equivalent  to  Watt/ Power  factor. 

WATT.  The  unit  of  electrical  power  =  io7  units  of  power  in  the  C.  G.  S.  system.  It  is  re- 
presented sufficiently  well  for  practical  use  by  the  work  done  at  the  rate  of  one  Joule 
per  second. 

Watts  =  volts  X  amperes  =  amperes2  X  ohms  =  volts2/ ohms  (direct  current  or  alter- 
nating current  with  no  phase  difference). 
For  conversion  factors  see  page  237. 
Watts  X  seconds  =  Joules. 

WEBER.      A  name  formerly  given  to  the  coulomb. 
YEAR.     See  page  109. 

Anomalistic  year  =  365  days,  6  hours,  13  minutes,  48  seconds. 
Sidereal          "     =  365     "      6     "         9      "         9.314  seconds. 
Ordinary        "     =  365     "      5     "       48  46  + 

Tropical         "    same  as  the  ordinary  year. 


INDEX. 


For  the  definition  of  units,  see  Appendix. 


PAGE. 

a  rays,  absorptive  powers  for        340 

definition  and  properties        337 

Aberration  constant 109 

Absorption  coefficient:  air 181, 182 

a-rays        340 

/3-rays        ......  340 

Y-rays       340 

X-rays       ....     335, 336 

Absorptpn  of  gases  by  liquids 144 

Absorption  of  light:  atmospheric       .     .     .     181, 182 

color  screens 201 

Jena  glasses       199 

various  crystals      ....  200 

Acceleration  of  gravity 104-107 

Aerodynamic  data:  soaring  data 125 

wind  pressures 124 

Agonic  line 116 

Air:  density        162 

masses 182 

transmissibility  for,  of  radiation     .     .     181, 182 

viscosity  of 136 

Air  thermometer,  comparisons 245 

Air:  transmissibility  of,  for  radiation      .     .     181,  182 

Alcohol:  density 98-100 

vapor  pressure        149 

viscosity        128 

Alloys:  densities 87 

electrical  conductivity  of       ...     277-280 

resistance  of 273-280 

low  temp.    .     .     .  280 

melting-points 222 

specific  heats        241 

thermal  conductivity 205 

thermoelectric  powers 269 

Alternating  currents,  resistance  of  wires  for    .     .  297 
Altitudes,  determination  of  by  barometer        .     .169 

of  a  few  stations 183 

Aluminum,  resistance 284 

wire  table,  English 292 

metric 293 

Alums:  indices  of  refraction 187 

Antilogarithms 26-28 

Apex,  solar  motion      .     . no 

Aqueous  solutions:  boiling-points 229 

densities 92 

alcohols        98-100 

diffusion  of 138 

electrolytic  conductivities  302-308 

Aqueous  vapor:  pressure i 54-155 

saturated,  weight  of        ....  156 

transparency 182 

Astronomical  data 109,110 

Atmosphere,  aqueous  vapor  in      ....     157, 182 
transmissibility  for  radiation       181, 182 

Atomic  numbers 336 

Atomic  weights 301 

ft  rays,  absorption  coefficients 340 

Barometer:  boiling  temperature  of  water  for  va- 

.     170-171 


rious  heights 

correction  for  capillarity      .     . 
latitude,  inch     . 

metric 

sea  level    .     .     . 
temperature 

heights,  determination  of,  by 
Batteries:  composition,  electromotive  forces 
Baum6  scale:  conversion  to  densities     .     . 
Bismuth,  resistance  of,  in  magnetic  field    . 
"Back-body"  radiation 


123 

121 
122 
120 
119 
169 
262 
81 
333 

251 

Boiling-points:  chemical  elements 218 

inorganic  compounds     .     .     219, 220 
organic  compounds    .     .     .     223-225 


PAGE. 

Boiling-point,  raising  of,  by  salts  in  solution       .  219 
of  water  and  barometric  pressure  .  170 

Brick,  crushing  strength  of 68 

Brightness  of  various  lights 178 

British  weights  and  measures        7-10 

Y  rays,  absorption  coefficients  for 340 

Cadmium  line,  wave-length  of  red 172 

Candle,  energy  from        178 

Candle  power,  standard       178 

Calibration  curves,  for  thermo-elements    .     .       250 

points,  standard,  for  thermometer       247 

Capacity,  specific  inductive:  crystals     ...       314 

gases     ....        309 

liquids       .     .     .        310 

liquid  gases   .     .       312 

solids 313 

Capillarity,  correction  to  barometer  for     ...  123 

liquids 145-146 

liquids  near  solidifying  point  .     .     .  146 

salt  solutions  in  water 145 

thickness  of  soap  films 146 

Carcel  unit 178 

Carrying  capacity  of  wires        279 

Cells,  voltaic:  composition,  E.  M.  F.     .     .     262-263 

double-fluid        263 

secondary 263 

single-fluid 262 

standard 261, 263 

storage 263 

Chemical,  electro-,  equivalents 301 

equivalent  of  silver       .     261,  301 
Chemical  elements:  atomic  weights        ....  301 

boiling-points 218 

compressibility 73 

conductivity,  thermal      .     .  205 

densities 83, 91 

electro-chemical  equivalents,  301 

hardness 73 

melting-points  .  .  .  .  .217 
resistance,  electrical  .  274-276 
specific  heats  .  .  .  238, 240 
thermal  conductivities  .  .  205 
expansion,  linear  .  232 

Circular  functions:  argument  (°') 32 

(radians)      ...    37 

Coals,  heat  of  combustion  of 210 

Cobalt,  magnetic  properties  of 321 

Color  screens 201-202 

Combination,  heat  of 212 

Combustion,  heat  of:  coals       210 

explosives 211 

fuels  (liquid) 210 

peats 210 

Compressibility:  chemical  elements       ....    73 

gases 76-78, 164-168 

liquids       79 

solids 80 

Concretes:  resistance  to  crushing 68 

Conductivity,  electrical:  see  Resistance. 

alloys 277-279 

alternating  currents,  effect  of    .  297 
magnetic  field,  effect  of    ...  333 

electrolytic 302-308 

equivalent    .     .     .     305-308 

ionic  (separate  ions)  .     .  308 

specific  molecular  .    .    .  303 

limiting  values  304 

temp'ture  coef . .  304 

glass    and    porcTn,   temp'ture 

coef 282 

Conductivity,  thermal:  gases 207 

liquids 207 


350 


INDEX. 


Conductivity,  thermal:  salt  solutions     ....  207 

solids         205 

solids,  high  temperature  .  206 

water         207 

Contact  differences  of  potential    ....     264-267 

Convection,  cooling  by 252-253 

Conversion  factors  for  work  units 237 

Baume  to  specific  gravities     .     .     .     81 

Cooling  by  radiation,  perfect  radiator   .     .     .     .251 

and  convection    .     .     252-253 

Copper  wire  tables 284-291 

English  units 286 

metric  units 289 

Cosines,  circular  natural 32, 37 

logarithmic 32, 37 

hyperbolic  natural 41 

logarithmic 41 

Cotangents,  circular  natural 32,37 

logarithmic        ....    32, 37 

hyperbolic  natural 41 

logarithmic 41 

Critical  data  for  gases 231 

Crushing,  resistance  to:  bricks 68 

concretes 68 

stones 68 

timber,  wood    ....     69 

Crystals:  dielectric  constant 314 

elasticity 74~75 

expansion,  cubical  thermal  ....  234 
indices  of  refraction  .  .  .  .'  .  188-190 
transmissibility  for  radiation  .  .  .  200 

Cubical  thermal  expansion:  gases 236 

liquids       .     .     .     .235 

solids 234 

Curie  unit  of  radioactivity        341 

Current,  absolute,  measures 261 

Cutting  tools,  lubricants  for 126 

Cyclic  magnetization,  energy  losses  in   .     .     322-325 

Declination,  secular  change  of  magnetic      .     .     .  in 

Degrees,  length  of,  on  earth 108 

Demagnetizing  factors  for  rods 323 

Densities  in  air,  reduction  to  vacuo 82 

Density:  air:  values  of  A?/ 60 162 

alcohol:  aqueous  ethyl         ....    98-99 

methyl 100 

alloys       87 

aqueous  alcohol 98-99 

cane-sugar 100 

salt,  acid,  basic  solutions    .     .     92 

,          sulphuric  acid 100 

,  chemical  elements    - 83,  91 

earth        108 

gases 91 

inorganic  compounds 219 

liquids 90 

mercury        97 

metals 83 

minerals 88 

organic  compounds  .  .  .  .  .  ,  -  .  223 
water .  94-96 

.  woods .     85 

Dew  points 148 

Dielectric  constant:  (specific  inductive  capacity) 

calibration,  standards  for     .313 

crystals 314 

gases,  atm.  pressure  .  .  .  309 
pressure  coef.  .  .  .310 
temperature  coef.  .  309 

liquids 310-311 

temperature  coef.       .312 

solids 313 

Dielectric  strength:  air:  alternating  potential  294 
steady  potential  .  .  294 
kerosene  ....  296 
large  spark-gaps  .  .  295 
pressure  effect  .  .  295 
various  materials  .  296 
Difference  of  potential: 

..cells:  double  fluid 263 

secondary        263 

single  fluid 262 

standard     261, 263 

storage         263 

contact:  liquids-liquids  in  air  .  .264 
metals  in  salt  solutions  .  267 
salts  with  liquids  .  .  .  264 
solids-solids  in  air  .  .  .  266 

Peltier 271 

thermo-electric 268-270 

platinum    couples  269 


Differential  formulae  ..........    12 

Diffusion:  aqueous  solutions,  water       ....  138 

gases  and  vapors:  coefficients     .     .     .140 
metals  into  metals   .......  140 

vapors    ...........  139 

Diffusion  integral   ...........     60 

Diffusivities,  thermal       .........  208 

Dip,  magnetic    ............  113 

secular  change  .......  113 

Dispersion  of  Kerr  Constant    .......  331 

Dynamical  equivalent  of  thermal  unit        .     .     .237 

e,  value  of     .............  14 

ex,  e-x,  and  their  logarithms    .......  48 

log.  e&,  x,  from  o  to  10     .........  48 

ex2  e-&,  and  their  logarithms  .......  54 

e**,  €~\x,  and  their  logarithms  ......     55 


*' 


Q  — 


their  logarithms 


55 


and  their  logarithms  .......    41 


Earth:  data        108 

densities 108 

distance  from  sun 109 

length  of  degrees 108 

miscellaneous  data 108 

Elasticity:  crystals 74-75 

moduli  of  rigidity 71 

modulus,  Young's 72 

Electric  lights,  efficiency  of 179 

Electrical  conductivity:  alloys     ....     277-279 
alternating  current,  effect  of  297 
magnetic  field,  effect  of   .     .  333 
Electrical  resistance:  see  Conductivity. 

metals  and  alloys,  low  temp.  280 
ohm,  various  determinations  272 
specific:  metallic  wires  .  .273 

metals 274 

temperature  coefficients  .  276 
temperature  effect,  glass  .  282 

Electricity,  specific  heat  of       268 

Electric  units,  dimensional  formulae  ....    xxviii 

Electrochemical  equivalents 301, 261 

silver     .     .     .     301, 261 

Electrolytic  conductivity: 302-308 

dilute  solutions  ....  302 
equivalent  ....  305-308 

ionic 308 

specific  molecular  ....  303 
limiting  values  304 
temp,  coef  .  .  304 

Electromagnetic  system  of  units xxxi 

Electromagnetic  /  electrostatic  units  =  v     ...  260 

Electromotive  force:  cells:  double  fluid       .     .     .  263 

secondary     ....  263 

single  fluid    ....  262 

standard       .     .     261, 263 

storage 263 

contact    264-266 

liquids-liquids  in  air        .     .  264 
metals  in  salt  solutions        .  267 

Peltier 271 

salts  with  liquids        .     .     .  264 

solids-«solids  in  air       ...  266 

thermo-electric      .     .     268-270 

(platinum)     .  269 

Elementary  "Wirkungsquantum"     .     .     .     251,342 

Electrons,  miscellaneous  data 342 

Elements:  atomic  weights 301 

boiling-points 218 

compressibility 73 

conductivity,  thermal        205 

densities 83, 91 

electrochemical  equivalents        .     .     .301 

hardness 73 

melting-points 217 

periodic  system        343 

resistance,  electrical     ....     274-276 

specific  heats       238, 240 

spectra  (prominent  lines)       ....  172 

thermal  conductivities 205 

expansion,  linear      ....  232 
cubical,  gases    .     .  236 

Elliptic  integrals 66 

Emanation,  radium 341 

Emission  of  perfect  radiator 251 


INDEX. 


351 


Energy  from  candle 178 

Equation  of  time no 

Equilibrium,  radioactive 337 

Equivalent,  electro-chemical:  elements       .     .     .  301 

ionic 302 

silver       .     .     261,301 

Equivalent,  mechanical,  of  heat 237 

Energy,  data  relating  to  solar       ....     181-183 

Entropy  equation  constant 342 

Errors,  probable 56-59 

Ethyl  alcohol,  specific  gravity  of  aqueous ...     98 

Ettinghausen  effect 334 

Eutectic  mixtures,  melting-points      .     .     .     222,  226 
Expansion,  thermal:  cubical,  crystals     ....  334 

336 

.8       ....  335 

334 

linear,  elements     .     .     .     .332 
various      ....  333 

gas       164 

Explosives,  composition,  etc 211 

Exponential  functions:  ex,  e—*,  their  logs  ...  48 
log.  e%,  x=o-io  ....  48 
e^'2,  e~ xZ,  their  logs  .  .  54 

X/7T  *^7T 

e~t"x,  e s~x,  their  logs     55 


,  their  logs  . 


diffusion  integral 
gudermanians  . 
hyperbolic  sines 


60 


cotangents 
tangents    . 
logs,  hyperbolic  sines 

cosines 

cotangents       41 

tangents      .     41 

probability  integral     .    56,  57 

Eye,  sensitiveness  of,  to  radiation 180 

Fabry-Buisson,  standard  arc  Fe  wave-lengths     .  172 

Factorials  nl  1-20 47 

gamma  function,  «=i  to  2 62 

logarithms,  i-ioo 40 

Fechner's  law 180 

Field :  earth's  magnetic  field,  components  of     1 1 1-117 
magnetic,  behavior  of  metals  in        .     315-325 

resistance  of  metals  in 333 

rotation  of  plane  of  polarization      326-33 1 

thermo-,  galvanometric  effects  .     .     .  334 

Films,  thin:  thickness,  colors,  tension  of     .     145-146 

Fluorite:  index  of  refraction 186 

Formulae,  conversion:  dynamic  units      ....       2 

electric        ' 3 

fundamental 2 

geometric 2 

heat 3 

magnetic 3 

see  INTRODUCTION. 

Fraunhofer  lines,  wave-lengths  of 177 

Freezing  mixtures        230 

Freezing-points,  lowering  of,  by  salts  in  solution  .  227 
Frequency,  oscillation    constant,    wireless    tele- 
graphy    298 

Friction,  coefficients  of 126 

Fuels,  heats  of  combustion  of        210 

Functions:  circular  arguments  (°') 32 

(radians)     ...    37 

exponential 48-61 

factorials        40,  47,  62 

gamma 62 

hyperbolic 41 

Fundamental  units 2 

Fusion,  latent  heat  of 216 

Fusion  of  wires,  carrying  capacity 279 

Galvanometric  effects  of  magnetic  field      .     .     .  334 

Gamma  function 62 

Gas  constant 342 

Gases:  absorption  of.  by  liquids    ....     142,  144 

atomic  weights 301 

compressibility  of 76-78 

conductivity,  thermal 207 

critical  data  for 231 


Gases:  densities 91 

dielectric  constants        309,310 

diffusion 140 

expansion  of 164-168 

expansion,  thermal 236 

heat,  conductivity  for 207 

indices  of  refraction 193 

magnetic  susceptibility 332 

magneto-optic  rotation 330 

refractive  indices  of 193 

sound,  velocity  of,  in 102 

solubility  of 142,  144 

specific  heats 243 

thermal  conductivity 207 

thermal  expansion 236 

viscosity  of 136 

volume  of  (1+0.003760     ....     164-168 

Gas  thermometry       244-247 

Gages,  wire 283 

Geodetic  data 108 

Geometric  units,  conversion  factors  for      ...       2 

Glass:  indices  of  refraction       184 

silica,  specific  heat 240 

transmissibility  of  Jena 199 

various     .     .     .     201-202 
electric  resistance,  temp,  variation       .     .  282 

Glass  vessels,  volumes  of n 

Gravitation  constant 109 

Gravity,  acceleration  of       104-106 

C9rrection  to  barometer 120 

Gudermanians 41 

Gyration,  radii  of 67 

Hall  effect 334 

Hardness       73 

Harmonics,  zonal 64 

Heat:  combination,  heat  of 212 

combustion:  coals 210 

explosives 211 

fuels  liquid 210 

peats iio 

conductivity  for:  gases        207 

liquids    .     .     .-   .     .     .  207 
salt  solutions  ....  207 

solids 205 

solids,  high  temperature  206 

water 207 

diffusivfcies       208 

latent  heat  of  fusion       216 

vaporization       .     .214,254-259 

mechanical  equivalent  of 237 

specific:  elements        .     .     .     .     ."*    .    238, 240 

gases 243 

liquids 241 

mercury 239 

minerals 242 

rocks 242 

solids        241 

vapors 243 

water        239 

Heating  effect,  radium 337 

"Heat,  specific,"  of  electricity 268 

Hefner  photometric  unit 178 

Heights  determinations  of  by  barometer    .     .     .  169 

Helium,  —  relation  to  radium       .  337 

Horizontal  intensity  of  earth's  field       .     .     .     .115 

secular  change    115 

Humidity,  relative 160 

Humidity  term,  0.378* 161 

Hydrogen  thermometer        244 

Hyperbolic  cosines,  natural 41 

logarithmic 41 

Hyperbolic  cotangents,  natural 41 

logarithmic       ....    41 

Hyperbolic  sines,  natural 4! 

logarithmic        41 

tangents,  natural 41 

logarithmic 41 

Hysteresis:  soft  iron  cable  transformer       .     .     .322 

wire 322 

steel,  transformer        325 

various  substances 324 

Iceland  spar,  refractive  index  of 186 

Ice-point  on  thermodynamic  scale 247 

Inclination  (dip)  of  magnetic  needle       .     .     .     .113 

secuar  change  of        113 

Index  of  refraction -.alums 187 

crystals 185-190 

fluorite 186 

gases  and  vapors    .    .    .    .193 


352 


INDEX. 


Index  of  refraction:  glass 184 

Iceland  spar       186 

liquids 192 

metals 195-196 

monorefringent  solids       .     .188 
nitroso-dimethyl-aniline        .  186 

quartz 187 

rock-salt 185 

salt  solutions 191 

silvine 185 

solids,  isotrppic       .     .     .     .  188 

Inductive  capacity,  specific:  calibration  st'ds  .     .313 

gases,  atm.  pressure    309 

pressure  coef  .  309 

temp.  coef.     .310 

liquids 310 

temp.  coef.    .  312 
solids     .     .     .     313-314 

Inertia,  table  of  moments  of 67 

Inorganic  compounds:  boiling-points     .     .     .     .219 
melting-points    .     .     .     .219 

Insulators,  resistances 282 

temperature  coefficients 282 

Integral,  diffusion       60 

elliptic 56 

gamma  function 62 

probability 54.  57~58 

Integrals,  elementary 12 

Intensity,  horizontal,  of  earth's  field      .     .     .     .114 
secular  variation      1 14 

total,  of  earth's  field 115 

secular  variation    115 
Intrinsic  brightness  of  various  lights      .     .     .     .178 

lonization  of  water 308 

lonization,  a,  /3,  y,  rays 337,  34i 

a 338 

X-rays 335 

Ions:  equivalent  conductivity  of        308 

Iron:  hysteresis  in  soft 322 

magnetic  properties  of,  weak  fields         .       322 
saturated  .       321 

permeabilities 315-320 

standard  arc  lines,  Fabry-Buisson  .  172 
secondary  ^standards  172 
tertiary  standards  .  176 

Joule's  (mechanical)  equivalent  of  heat      .     .     .237 

Kerosene,  dielectric  strength 296 

Kerr's  constant 33i 

Kerr's  constant,  dispersion  of 331 

Kundt's  constant 330 

definition  of 330 

Lamps,  efficiency  of  various  electric       .     .     .     .  179 

Latent  heat  of  fusion 216 

vaporization  .  .  .  .214,254,255 
Latitude  correction  to  barometer  .  .  .  121-122 
Latitudes  of  a  few  stations  117,183 


Least  squares 56-59 

Legal  electrical  units xxxviii 

Leduc  thermomagnetic  effect 334 

Light:  indices  of  refraction 184-196 

reflection  of;  function  of  "»"       .     .     .     .197 

metals       195-198 

sensitiveness  of  eye  to 180 

transmissibility  to,  of  substances     .     199-202 

polarized:  rotation  of  plane  by  solutions  .  203 

rotation,  magneto       .          326-331 

wave-lengths:  cadmium  st'd  line  .        172 

elements,  brighter  lines          172 

Fraunhofer  lines    .          .        177 

st'd  iron  arc,  Fabry        .        172 

solar,  Rowland        .        173 

velocity  of 109 

Lights,     brightness  of  various       178 

efficiency  of  electric 179 

visibility  of  white 178 

Linear  thermal  expansion  coef.  of  elements     .     .232 
various       .     .     .  233 

Liquids:  absorption  of  gases  by 144 

capillarity  of 145-146 

compressibility  of 79-80 

conductivity,  thermal 207 

densities 83,  90,  94-100 

dielectric  constants 310-312 

dielectric  strength 296 

diffusion,  aqueous  solutions      ....  138 

expansion,  thermal 235 

fuels,  heat  of  combustion 210 

magnetic  susceptibility 332 


Liquids:  magneto-optic  rotation 328 

potential  differences  with  liquids  .  .  264 
metals  .  .  .  267 
salts  .  .  .  264 

specific  heats 241 

surface  tensions 145-146 

thermal  conductivity 207 

expansion 235 

vapor  pressures 147-155 

velocity  of  sound 102 

viscosity 129-130 

Logarithms 26 

1000-2000 24 

and- 28 

.9000-1.0000 30 

Longitude  of  a  few  stations 117,  183 

Lowering  of  freezing-points  by  salts       ....  227 

Lubricants  for  cutting  tools 126 

Lunar  parallax 109 

Mache  radioactivity  unit 341 

Maclaurin's  theorem 12 

Magnetic  field :  bismuth,  resistance  in  ....  333 
Ettingshausen  effect  ....  334 
galvanomagnetic  effects  .  .  .  334 

Hall  effect 334 

Leduc  effect 334 

Nernst  effect 334 

nickel,  resistance  in 333 

optical  rotation     ....     326-331 

resistance  of  metals  in  ....  333 

thermo-magnetic  effects     .     .     .  334 

Magnetic  observatories,  magnetic  elements     .     .  H7 

Magnetic  properties:  of  cobalt  at  100°  C    .     .     .321 

iron:  hysteresis      .     322-325 

permeability 

315-317,  320-321 
saturated  .  .  .321 
weak  fields  .  .  .  322 

magnetite 321 

nickel  at  100°  C    .     .     .  321 

Magnetic  susceptibility,  liquids,  gases   ....  332 
Magnetic  units,  conversion  formulae       ....       3 

Magnetism,  terrestrial:  agonic  line 116 

declination m 

dip 113 

horizontal  intensity  .  1 14 
inclination  ...  .113 
intensity,  horizontal  .  114 
total  .  .  .US 
observatories  .  .  .  117 

Magneto-optic  rotation 326-331 

Masses  of  the  earth  and  planets no 

Materials,  strength  of:  bricks 68 

concrete 68 

metals 68 

stones 68 

timber 69-70 

woods        60-70 

Mechanical  equivalent  of  heat 237 

Melting-points:  chemical  elements    .     .     .     .     .217 

eutectics 226 

inorganic  compounds    .     .     .     .219 

minerals 226 

mixtures  (alloys) 222 

(low  melting-points)     .  222 

organic  compounds 223 

pressure  effect 221 

Meniscus,  volume  of  mercury 123 

Mercury:  density  of 97 

electric  resistance  of    ....     273-274 

meniscus,  volume  of 123 

pressure  of  columns  of 118 

specific  heat 239 

vapor  pressure 151 

Metals:  diffusion  of,  into  metals 140 

indices  of  refraction 195-196 

optical  constants 195-196,  198 

potential  differences  with  solids     .     .     .  266 

solutions    .     .  267 

reflection  of  light  by     ....  195-196,198 

refractive  indices '195-196 

resistance,  electrical     ....  273,284-293 

specific 274 

sheet,  weight  of 89 

transparency  of 195 

Metallic  reflection 195-196,198 

Methyl  alcohol,  density  of  aqueous 100 

Metric  weights  and  measures:  British  equiv.   .     7-10 

U.  S.  equivalents    5-6 

Minerals,  densities  of 88 


INDEX. 


353 


Minerals,  specific  heats  of 242 

Mixtures,  freezing 230 

Moduli  of  elasticity:  rigidity 71 

Young's 72 

Molecular  conductivities:  equivalent  .  .  305-308 
specific  .  .  .  301-304 

Molecular  magnitudes 342 

Molecules  per  cu.  cm.  gas 342 

Moments  of  inertia 67 

Monthly  temperature  means 183 

Moon's  light  and  radiation no 

Musical  scales 103 

Nernst  thermo-magnetic  difference  of  potential  .  334 
Neutral  points,  thermo-electric     ....     268-269 

Newton's  rings  and  scale  of  colors 204 

Nickel:  Kerr's  constants  for 331 

magnetic  properties  of,  at  100°  C  .     .     .321 

resistance  in  magnetic  field 333 

Nitroso-dimethyl-aniline,  refractive  index       .     .186 

Numbers  atomic 336 

Nutation 109 

Observatories,  magnetic,  elements 117 

Ohm,  various  determinations  of 272 

legal  value 272 

Oils,  viscosity  of 128 

Organic  compounds,  boiling-points  .     .     .     223-224 

densities 223-224 

melting-points  .     .     .     223-224 
Oscillation  constant,  wireless  telegraphy    .     .     .  298 

Parallax:  solar;  lunar 109 

Parallax:  stellar no 

Peltier  effect 268,  271 

Pendulum,  length  of  seconds 107 

Periodic  system  of  the  elements 343 

Permeabilities,  magnetic      .     .     .    315-317, 320-321 
Phosphorescence  from  radio-active  bodies       .     .337 

Photometric  standards 178 

Pi,  IT,  value  of 12 

Planck's  radiation  formula 251 

Plane,  data  for  the  soaring  of  a 125 

Planetary  data no 

Planets,  miscellaneous  data no 

Platinum  resistance  thermometer      .....  247 

Poisson's  ratio 73 

Polarized  light:  by  reflection 197 

by  metallic  reflection    ....  195 

rotation  by  magnetic  field      326-331 

solutions     ....  203 

Potential  difference:  cells:  double  fluid  .  .  .263 
secondary  ....  263 
single  fluid  ....  262 
standard  .  .  .  261, 263 

storage 263 

contact:  liquid-liquid      .     .  264 

liquid-salt     .     .     .  264 

metal-liquid       .     .  267 

solid-solid     .     .     .266 

sparking:  air     ...     294-295 

kerosene     .     .     .  296 

various  ....  296 

thermoelectric  .     .     .     268-271 

Precession 109 

Pressure:  barometric  measures      .     .     .     .     119-123 
barometric  and  boiling  water      .     170-171 

heights 169 

mercury  columns,  due  to 118 

water  columns,  " 118 

wind 124 

Pressure  effect  on  melting-points 221 

solubility 143 

Pressure,  vapor:  alcohol,  ethyl  and  methyl     .     .  149 

aqueous     154-155 

in  atmosphere    .     .     .  T57 

mercury 151 

salt  solutions 152 

various 147-155 

Probable  errors 56-59 

Probability  tables        56-59 

Purkinje's  phenomenon 180 

Quartz  fibers,  strength  of 68 

refractive  index  of    . 187 

specific  heat 240 

Radiation:  black-body 251 

constants  of 251 

cooling  by,  and  convection  .     .     252-253 
eye,  sensitiveness  of,  to 180 


Radiation:  Planck's  formula 251 

resistance,  wireless  telegraphy        .     .  300 
sensitiveness  of  the  eye  to    .     .     .     .180 

"  solar  constant "  of 181 

solar,  monthly  change 183 

Stefan's  formula 251 

transmissibility  of  atmosphere  to  181,  182 

Radii  of  gyration 67 

Radio-activity 337-341 

Radium 337~34i 

Radium  emanation 337-341 

Radio-active  equilibrium 337 

Reflection  of  light:  by  metals  .  .  .  195,  196,  198 
terms  of  "«"  and  "»"  .197 
various  substances  .  .198 

Refraction,  indices  of:  alums 187 

crystals      ....     185-190 
fluorite 186 


glass 

Iceland  spar 186 

liquids 192 

metals 195-196 

monorefringent  solids       .  188 
nitroso-dimethyl-aniline  .  186 

quartz 187 

rock-salt 185 

salt  solutions       .     .     .     .191 

silvine 185 

solids,  isotropic  .     .     .     .188 

Relative  humidity 160 

Resistance:  see  also  Conductivity. 

alloys,  low  temperature       ....  280 
alternating  current,  effect  of    ...  297 

aluminum 284 

copper 284 

electrolytic,  see  Conductivity. 

glass  and  porcelain 282 

legal  unit  of 272 

magnetic  field,  of  bismuth  in  .  333 

metals  in      .  333 

nickel  in       .  333 

metals  at  low  temperatures      .  280 

ohm,  various  determinations  of  272 

platinum,  thermometer 247 

radiation,  wireless  telegraphy       .     .  300 

specific:  metals 274-276 

wires 273,286-293 

temperature  variation  276,  280,  282,  285 

Rigidity,  modulus  of 71 

temperature  variation    .     .71 

Ring  correction  (magnetization) 317 

Rock-salt,  indices  of  refraction 185 

Rods,  demagnetizing  factors  for 323 

Rdntgen  rays 335-336 

ray  spectra 336 

Rotation  of  polarized  light:  by  solutions    .     .     .  203 

Rotation,  magneto-optic:  formulae 326 

gases 330 

Kerr's  constant       .     .331 

liquids 328 

solids 327 

solutions 329 

Verdet's  constant    326-330 
Rowland's  standard  wave-lengths 173 

Salts,  lowering  of  freezing-point  by 227 

raising      "  boiling-  " 229 

Saturation,  magnetic,  for  steel 321 

Scales,  musical 103 

Screens,  color 201-202 

Seconds  pendulum 107 

Secondary  batteries 263 

Sections  of  wires 283 

Shearing  tests  of  timber 69-70 

Sheet  metal,  weights  of 89 

Silica  glass  specific  heats 240 

Silver,  electro-chemical  equivalent    .     .     .     261, 301 

Silvine,  indices  of  refraction 185 

Sines,  natural  and  logarithmic,  circular      .     .   32-40 

hyperbolic .    .   41-47 

Sky-light,  comparison  with  sunlight       ....  182 

Soaring  of  planes,  data  for  .  • 125 

Solar  constant  of  radiation       181 

distance  from  earth 109 

energy,  data  of 181-183 

motion no 

parallax 109 

radiation  monthly  change 183 

spectrum 181,  183 

temperature 181 


354 


INDEX. 


Solar  wave-lengths,  Rowland's 173 

Solids:  compressibility 73,  80 

densities 83-87 

dielectric  constant 313 

electrical  resistance 272-29? 

hardness 73 

indices  of  refraction 185-190 

magneto-optic  rotation  by 327 

thermal  conductivity 205-206 

expansion .     232-234 

Solubility  gases 142 

pressure  effect 143 

salts 141 

Solutions:  boiling-point,  raising  by  salts  in     .     .  229 
boiling-points  of  aqueous       .     .     .     .229 

conductivity,  thermal ......  207 

electrolytic       .     .     302-308 
densities  of  aqueous      .     .     92-93,  98-100 

diffusion  of  aqueous 138 

freezing-points,  lowering  by  salt     .     .227 
of  aqueous    ....  227 

indices  of  refraction 191 

magneto-optic  rotation  of      ....  329 
potential  (contact)  differences    .     264-267 

specific  heats 241-242 

surface  tensions 145 

viscosities 131-135 

Sound,  velocity  of,  in  solids 101 

liquids  and  gases     .     .     .102 

Sparking  potentials 294-296 

Specific  gravity,  see  Density. 

heat  of  air 243  * 

elements 238, 240 

gases 243 

liquids 241 

mercury 239 

minerals  and  rocks 242 

platinum 240 

quartz 240 

silica  glass 240 

solids 241 

vapors 243 

water 239  ' 

"  Specific  heat  of  electricity  " 268 

Specific  inductive  capacity:  gases      .     .     .     300-310 
liquids    .     .     .     310-312 

solids 313 

molecular  conductivities  ....     303-304 

resistance       273-276 

viscosity:  gases  and  vapors  .     .     .     136-137 
liquids  and  oils      .     .     .     128-130 

solutions I3I-I35 

Spectra:  elements,  brighter  lines 172 

iron,  Fabry-Buisson 172 

Rontgen  ray 336 

solar,  Fraunhofer  lines 177 

Rowland's  measures 173 

Squares,  least,  tables       47~49 

Standard  calibration  temperature 247 

Standard  cells 261-263 

wave-lengths:  Fabry-Buisson      .     .     .172 

primary 172 

Rowland 173 

secondary 172 

tertiary 176 

Standards,  photometric 178 

Stars,  distance  of no 

Stars,  parallax no 

Stars,  velocities  of no 

Steam  tables:  metric  units 254 

common  " 255 

Steel:  magnetic  properties:  hysteresis     .  319,  322-325 

permeabilities       315-322 

Stefan-Boltzmann  radiation  formula      .     .     .     .251 

Stellar  velocities no 

Stone:  strength  of 68 

thermal  conductivity 205 

Storage  batteries 263 

Strength  of  materials:  bricks 68 

concrete 68 

metals 68 

stones 68 

timber,  woods     .     .     .    60-70 

Sugar,  densities  aqueous  solutions 100 

Sulphuric  acid,  densities  aqueous  solutions     .     .  100 

Sun:  constant  of  radiation 181 

disk;  distribution  of  intensity 181 

distance  from  earth 109 

light;  ratio  to  sky-light 182 

magnitude no 

motion       no 


Sun:  parallax 109 

radiation 181 

spectrum 173,  181 

temperature 181 

Surface  tension 145-146 

Sylvine,  refractive  indices 185 

Tangents  circular,  natural 32,  37 

logarithmic 32,  37 

hyperbolic  natural 41 

logarithmic 41 

Taylor's  series 13 

Telegraphy,  wireless 298,  300 

Temperature,  critical,  for  gases 231 

resistances  for  low       280 

resistance  coefficients  .     .     .     276-285 

sun's 181 

thermodynamic 247 

Temperatures,  mean  monthly       183 

Tensile  strengths 68-70 

Tension,  surface 145-146 

vapor,  see  Vapor  pressure. 

Terrestrial  magnetism:  agonic  line 116 

declination,  secular  change    in 

dip 113 

secular  change      .     .     .113 

horizontal  intensity   .     .     .114 

secular  change    114 

inclination 113 

secular  change    113 

observatories 117 

total  intensity       .     .     .     .115 
secular  change    115 

Thermal  conductivities:  gases       207 

liquids 207 

salt  solutions    ....  207 

solids 205 

solids,  high  temperature  206 

water 207 

Thermal  diffusiyities 208 

Thermal  expansion:  cubical:  crystals     ....  234 

gases 236 

liquids       ....  235 

solids 234 

linear:  elements      .     .     .     .232 

various 233 

Thermal  unit,  dynamical  equivalent      ....  227 

Thermodynamic  ice-point 247 

Thermodynamic  scale  of  temperature    ....  247 

Thermo-electricity 268-271 

Peltier  effect      .     .     .         268,  271 
Thermo-elements,  calibration  curves      .          .     .  250 

Thermo-magnetic  effects .     .  334 

Thermometer:  air-i6,  o°  to  300°  C  .       .          .        245 

59,  100°  to  200°  C     .          .        245 

high-temperature-59  .        246 

hydrogen-i6,  o°  to  100°  C        .        244 

16,  59,  -5°  to  -35°  C        244 

59,  p°  to  100°  C  .     .        244 

various 246 

platinum  resistance 247 

standard  calibration  points      .     .  247 
Thermometer  stem  correction       ....     248-249 

Thomson  thermo-electric  effect 268 

Timber,  strength  of 69-70 

Time  equation  of no 

Time,  sidereal,  solar 109 

Tools,  lubricants  for  cutting 126 

Transformation  points,  minerals 226 

Transformer-iron,  permeability  of     .     .315-316,320 

steels,  energy  losses  in       .     .     322-325 

Transmissibility  to  radiation:  atmospheric    .  181,  182 

crystals   ....  200 

glass 199 

water       ....  202 

Trigonometric  functions:  arguments  (°0     .     .     .    32 

(radians)     .    37 

United  States  weights  and  measures,  conversion 

to  metric  units 5-6 

Units  of  measurement:  definitions,  see  APPENDIX. 

conversion  factors       ....  2-3 
discussion,  see    INTRODUCTION. 

photometric 178 

ratio  of  electro-magnetic  to  static     .     .     .  260 

V,  ratio  of  electro-magnetic  to  -static  units    .     .  260 

Vacuo,  reduction  of  densities 82 

weighings 82 

Vapor,  aqueous:  vapor  pressure    ....     i54-i55 
pressure  of,  in  atmosphere    .     .  157 


INDEX. 


355 


Vapor,  aqueous:  relative  humidity 160 

(saturated)  weight  of  .     .     .     .156 

Vaporization,  latent  heat  of .     .214 

for  steam    .     .     254, 255 

Vapors:  densities 91 

diffusion  of 139,  140 

indices  of  refraction 193 

pressures:  alcohol,  ethyl,  methyl   .     .     .  149 

aqueous       I54-I55 

mercury 151 

salt  solutions 152 

various 147-155 

specific  heats 243 

viscosity 136-137 

Velocity  of  light 109 

sound;  in  gases  and  liquids       .     .     .102 

solids 101 

stars no 

sun       no 

Verdet's  constants:  Verdet  and  Kundt's     .     .     .  330 

gases 330 

liquids 328 

solids 327 

solutions,  aqueous  .     .     .     .329 

Viscosity:  alcohol  in  water 128 

pses 136-137 

liquids 128-129 

vapors    138-137 

water:  temperature  variation     .     .     .127 

specific:  gases 136-137 

oUs 128 

solutions 131-135 

vapors    136-137 

water:  temp,  var 127 

Visibility  of  white  lights 178 

Voltaic  cells:  composition,  E.  M.  F.       .     .     262-263 

double-fluid 263 

secondary 263 

single-fluid 262 

standard 261,  263 

storage 263 

Volts,  legal  (international)        ....      xxxvi,  261 

Volume  of  mercury  meniscus 123 

Volumes:  critical,  for  gases 231 

gases 164 

glass  vessels,  determinations  of   .     .     .     n 
Water:  boiling-points  for  various  pressures: 

common  measures  .     .170 

metric  measures       .     .171 

densities,  temperature  variation      .     .    95,  96 


Water:  ionization  of 309 

solutions  in:  boiling-points 228 

densities    ....      92, 98-100 

diffusion 138 

electrolytic  conduction    302-308 
solutions  of  alcohol,  densities      .     .     .  98-100 

thermal  conductivity 207 

transparency  of 202 

vapor  pressure 154-155 

vapor,  pressure  of,  in  atmosphere   .     .     .157 
(saturated)  weights  of     .     .     .     .156 

transparency  of 181 

viscosity:  absolute,  temp,  var 127 

specific,  temp,  var 127 

Wave-lengths:  cadmium  red  line 172 

elements,  brighter  lines  .     .     .     .172 
Fabry-Buisson  iron  arc  lines    .     .172 

Fraunhofer  lines 177 

iron  lines,  Fabry-Buisson    .     .     .172 

primary  standards 172 

Rowland's  solar  lines      .     .     .     .173 

secondary  standards 172 

solar  lines  (Rowland) '    .     .     .     .173 

tertiary  standards 176 

wireless  telegraphy     .     .     .     298-300 

Weighings-reduction  to  vacuo 82 

Weights  and  measures:  British  to  metric  .  .  o-io 
metric  to  British  .  .  .  7-8 
metric  to  U.  S.  ...  6 
U.  S.  to  metric  ...  5 

Weights  of  bodies \     .     .    67 

Weights  of  sheet  metal 89 

Wind  pressures 124 

Wire  gages 283 

Wire  tables,  aluminum  English 292 

metric 293 

copper        English 286 

metric 289 

Wires,  carrying  capacity  of 279 

Wireless  telegraphy 298-300 

Woods:  densities  of 85 

strength  of 69-70 

X-rays 33S-336 

Yearly  temperature  means 183 

Young's  modulus  of  elasticity 72 

Zero,  thermodynamic  ice-point 247 

Zonal  harmonics 164 


Htoerstoe 


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